ConnectPP---0.7.2.THM-Prf.s

%------------------------------------------------------------------------------
% File     : ConnectPP---0.7.2
% Problem  : SWW473+7 : TPTP v9.3.1. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p

% Computer : n026.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Sep 24 09:08:01 AM UTC 2026

% Result   : Theorem 273.54s 273.86s
% Output   : Proof 273.74s
% 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_Ofold__image_res,axiom,
    ! [X_b,X_c] : ti(fun(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b)))),finite_fold_image(X_b,X_c)) = finite_fold_image(X_b,X_c),
    file('theBenchmark.p',tsy_c_Finite__Set_Ofold__image_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__image__simple__idem_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)))),finite908156982e_idem(X_b,X_c)) = finite908156982e_idem(X_b,X_c),
    file('theBenchmark.p',tsy_c_Finite__Set_Ofolding__image__simple__idem_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_Oabs__class_Oabs_res,axiom,
    ! [X_a] :
      ( ordere142940540dd_abs(X_a)
     => ti(fun(X_a,X_a),abs_abs(X_a)) = abs_abs(X_a) ),
    file('theBenchmark.p',tsy_c_Groups_Oabs__class_Oabs_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_b] :
      ( cancel_semigroup_add(X_b)
     => ti(fun(X_b,fun(X_b,X_b)),plus_plus(X_b)) = plus_plus(X_b) ),
    file('theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_1_res) ).

fof(tsy_c_Groups_Oplus__class_Oplus_2_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_2_res) ).

fof(tsy_c_Groups_Otimes__class_Otimes_0_res,axiom,
    ! [X_a] :
      ( ab_semigroup_mult(X_a)
     => ti(fun(X_a,fun(X_a,X_a)),times_times(X_a)) = times_times(X_a) ),
    file('theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_0_res) ).

fof(tsy_c_Groups_Otimes__class_Otimes_1_res,axiom,
    ! [X_a] :
      ( monoid_mult(X_a)
     => ti(fun(X_a,fun(X_a,X_a)),times_times(X_a)) = times_times(X_a) ),
    file('theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_1_res) ).

fof(tsy_c_Groups_Otimes__class_Otimes_2_res,axiom,
    ! [X_a] :
      ( semiring(X_a)
     => ti(fun(X_a,fun(X_a,X_a)),times_times(X_a)) = times_times(X_a) ),
    file('theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_2_res) ).

fof(tsy_c_Groups_Otimes__class_Otimes_3_res,axiom,
    ! [X_a] :
      ( no_zero_divisors(X_a)
     => ti(fun(X_a,fun(X_a,X_a)),times_times(X_a)) = times_times(X_a) ),
    file('theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_3_res) ).

fof(tsy_c_Groups_Otimes__class_Otimes_4_res,axiom,
    ! [X_a] :
      ( mult_zero(X_a)
     => ti(fun(X_a,fun(X_a,X_a)),times_times(X_a)) = times_times(X_a) ),
    file('theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_4_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_If_res,axiom,
    ! [X_a] : ti(fun(bool,fun(X_a,fun(X_a,X_a))),if(X_a)) = if(X_a),
    file('theBenchmark.p',tsy_c_If_res) ).

fof(tsy_c_Int_OBit1_res,axiom,
    ti(fun(int,int),bit1) = bit1,
    file('theBenchmark.p',tsy_c_Int_OBit1_res) ).

fof(tsy_c_Int_OPls_res,axiom,
    ti(int,pls) = pls,
    file('theBenchmark.p',tsy_c_Int_OPls_res) ).

fof(tsy_c_Int_Onumber__class_Onumber__of_res,axiom,
    ! [X_b] :
      ( number(X_b)
     => ti(fun(int,X_b),number_number_of(X_b)) = number_number_of(X_b) ),
    file('theBenchmark.p',tsy_c_Int_Onumber__class_Onumber__of_res) ).

fof(tsy_c_Int_Oring__1__class_OInts_res,axiom,
    ! [X_b] :
      ( ring_1(X_b)
     => ti(fun(X_b,bool),ring_1_Ints(X_b)) = ring_1_Ints(X_b) ),
    file('theBenchmark.p',tsy_c_Int_Oring__1__class_OInts_res) ).

fof(tsy_c_Int_Osucc_res,axiom,
    ti(fun(int,int),succ) = succ,
    file('theBenchmark.p',tsy_c_Int_Osucc_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_Nat_Osemiring__1__class_Oof__nat_res,axiom,
    ! [X_a] :
      ( semiring_1(X_a)
     => ti(fun(nat,X_a),semiring_1_of_nat(X_a)) = semiring_1_of_nat(X_a) ),
    file('theBenchmark.p',tsy_c_Nat_Osemiring__1__class_Oof__nat_res) ).

fof(tsy_c_Nat_Osemiring__1__class_Oof__nat__aux_res,axiom,
    ! [X_b] :
      ( semiring_1(X_b)
     => ti(fun(fun(X_b,X_b),fun(nat,fun(X_b,X_b))),semiri532925092at_aux(X_b)) = semiri532925092at_aux(X_b) ),
    file('theBenchmark.p',tsy_c_Nat_Osemiring__1__class_Oof__nat__aux_res) ).

fof(tsy_c_Nat__Numeral_Oneg_res,axiom,
    ti(fun(int,bool),nat_neg) = nat_neg,
    file('theBenchmark.p',tsy_c_Nat__Numeral_Oneg_res) ).

fof(tsy_c_Nat__Transfer_Otsub_res,axiom,
    ti(fun(int,fun(int,int)),nat_tsub) = nat_tsub,
    file('theBenchmark.p',tsy_c_Nat__Transfer_Otsub_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_b] :
      ( bot(X_b)
     => ti(X_b,bot_bot(X_b)) = bot_bot(X_b) ),
    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_a] :
      ( ord(X_a)
     => ti(fun(X_a,fun(X_a,bool)),ord_less_eq(X_a)) = ord_less_eq(X_a) ),
    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_1] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),F_1))
     => 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_1))) ),
    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_1] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_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),B_1))
       => 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_1))) ) ),
    file('theBenchmark.p',fact_5_card__mono) ).

fof(fact_6_card__seteq,axiom,
    ! [X_b,A_3,B_1] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_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),B_1))
       => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_1)),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_1) ) ) ),
    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_3,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_3)))
        | 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_3)))) ),
    file('theBenchmark.p',fact_10_finite__Collect__conjI) ).

fof(fact_11_Suc__diff__le,axiom,
    ! [N,M_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M_1))
     => hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M_1)),N) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N)) ),
    file('theBenchmark.p',fact_11_Suc__diff__le) ).

fof(fact_12_finite__Collect__le__nat,axiom,
    ! [K] : 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)))),
    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_3,Nat_4] :
      ( hAPP(nat,nat,suc,Nat_3) = hAPP(nat,nat,suc,Nat_4)
    <=> Nat_3 = Nat_4 ),
    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_1,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M_1))
       => M_1 = N ) ),
    file('theBenchmark.p',fact_20_le__antisym) ).

fof(fact_21_le__trans,axiom,
    ! [K_1,I_2,J] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),J))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J),K_1))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),K_1)) ) ),
    file('theBenchmark.p',fact_21_le__trans) ).

fof(fact_22_eq__imp__le,axiom,
    ! [M_1,N] :
      ( M_1 = N
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)) ),
    file('theBenchmark.p',fact_22_eq__imp__le) ).

fof(fact_23_nat__le__linear,axiom,
    ! [M_1,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M_1))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),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_2,J,K_1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_2),J)),K_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_2),K_1)),J),
    file('theBenchmark.p',fact_25_diff__commute) ).

fof(fact_26_finite__Collect__disjI,axiom,
    ! [X_b,Pa,Q_3] :
      ( 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_3))))
    <=> ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Q_3)))
        & 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_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),B_1))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_1))
       => 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_1] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_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),B_1))
       => 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_1,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M_1)),N))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)) ),
    file('theBenchmark.p',fact_30_Suc__leD) ).

fof(fact_31_le__SucE,axiom,
    ! [M_1,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),hAPP(nat,nat,suc,N)))
     => ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N))
       => M_1 = hAPP(nat,nat,suc,N) ) ),
    file('theBenchmark.p',fact_31_le__SucE) ).

fof(fact_32_le__SucI,axiom,
    ! [M_1,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),hAPP(nat,nat,suc,N))) ),
    file('theBenchmark.p',fact_32_le__SucI) ).

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

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

fof(fact_35_not__less__eq__eq,axiom,
    ! [M,Na] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Na)),M)) ),
    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_1,N,K_1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M_1)),N)),hAPP(nat,nat,suc,K_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N)),K_1),
    file('theBenchmark.p',fact_37_Suc__diff__diff) ).

fof(fact_38_diff__Suc__Suc,axiom,
    ! [M_1,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M_1)),hAPP(nat,nat,suc,N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N),
    file('theBenchmark.p',fact_38_diff__Suc__Suc) ).

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

fof(fact_40_Nat_Odiff__diff__eq,axiom,
    ! [N,K_1,M_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),M_1))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N))
       => hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),K_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N) ) ),
    file('theBenchmark.p',fact_40_Nat_Odiff__diff__eq) ).

fof(fact_41_eq__diff__iff,axiom,
    ! [Na,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),Na))
       => ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Na),K)
        <=> M = Na ) ) ),
    file('theBenchmark.p',fact_41_eq__diff__iff) ).

fof(fact_42_diff__diff__cancel,axiom,
    ! [I_2,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),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_2)) = I_2 ),
    file('theBenchmark.p',fact_42_diff__diff__cancel) ).

fof(fact_43_diff__le__mono,axiom,
    ! [L_1,M_1,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),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_1),L_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),L_1))) ),
    file('theBenchmark.p',fact_43_diff__le__mono) ).

fof(fact_44_diff__le__mono2,axiom,
    ! [L_1,M_1,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),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_1),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L_1),M_1))) ),
    file('theBenchmark.p',fact_44_diff__le__mono2) ).

fof(fact_45_diff__le__self,axiom,
    ! [M_1,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_1),N)),M_1)),
    file('theBenchmark.p',fact_45_diff__le__self) ).

fof(fact_46_finite__surj,axiom,
    ! [X_c,X_b,B_1,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_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_c,bool),bool,finite_finite(X_c),B_1)) ) ),
    file('theBenchmark.p',fact_46_finite__surj) ).

fof(fact_47_finite__subset__image,axiom,
    ! [X_c,X_b,F,A_3,B_1] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_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)),B_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)))
       => ? [C_3] :
            ( ti(fun(X_b,bool),B_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),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_1] : hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(nat,X_b,F,N_1)),hAPP(nat,X_b,F,hAPP(nat,nat,suc,N_1))))
         => ( 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_3,F,X_1] :
      ( ti(X_b,B_3) = 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_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))) ) ),
    file('theBenchmark.p',fact_50_image__eqI) ).

fof(fact_51_equalityI,axiom,
    ! [X_b,A_3,B_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),B_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)),B_1),A_3))
       => ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_1) ) ),
    file('theBenchmark.p',fact_51_equalityI) ).

fof(fact_52_subsetD,axiom,
    ! [X_b,C_1,A_3,B_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),B_1))
     => ( 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_1)) ) ),
    file('theBenchmark.p',fact_52_subsetD) ).

fof(fact_53_insertCI,axiom,
    ! [X_b,B_3,A_2,B_1] :
      ( ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),B_1))
       => ti(X_b,A_2) = ti(X_b,B_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_3),B_1))) ),
    file('theBenchmark.p',fact_53_insertCI) ).

fof(fact_54_insertE,axiom,
    ! [X_b,A_2,B_3,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_3),A_3)))
     => ( ti(X_b,A_2) != ti(X_b,B_3)
       => 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] :
      ( hBOOL(hAPP(nat,bool,Pa,K))
     => ( ! [N_1] :
            ( hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,N_1)))
           => hBOOL(hAPP(nat,bool,Pa,N_1)) )
       => hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),K),I_1))) ) ),
    file('theBenchmark.p',fact_55_zero__induct__lemma) ).

fof(fact_56_Suc__le__D,axiom,
    ! [N,M_4] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N)),M_4))
     => ? [M_2] : M_4 = hAPP(nat,nat,suc,M_2) ),
    file('theBenchmark.p',fact_56_Suc__le__D) ).

fof(fact_57_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_57_order__refl) ).

fof(fact_58_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_58_linorder__linear) ).

fof(fact_59_order__eq__iff,axiom,
    ! [X_b] :
      ( order(X_b)
     => ! [X_1,Y_2] :
          ( ti(X_b,X_1) = ti(X_b,Y_2)
        <=> ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_2),X_1))
            & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2)) ) ) ),
    file('theBenchmark.p',fact_59_order__eq__iff) ).

fof(fact_60_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_60_order__eq__refl) ).

fof(fact_61_order__antisym__conv,axiom,
    ! [X_b] :
      ( order(X_b)
     => ! [Y_2,X_1] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_2),X_1))
         => ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2))
          <=> ti(X_b,X_1) = ti(X_b,Y_2) ) ) ),
    file('theBenchmark.p',fact_61_order__antisym__conv) ).

fof(fact_62_ord__eq__le__trans,axiom,
    ! [X_a] :
      ( ord(X_a)
     => ! [C,A_1,B] :
          ( A_1 = B
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),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_62_ord__eq__le__trans) ).

fof(fact_63_xt1_I3_J,axiom,
    ! [X_a] :
      ( order(X_a)
     => ! [C,A_1,B] :
          ( ti(X_a,A_1) = ti(X_a,B)
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),B))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),A_1)) ) ) ),
    file('theBenchmark.p',fact_63_xt1_I3_J) ).

fof(fact_64_ord__le__eq__trans,axiom,
    ! [X_a] :
      ( ord(X_a)
     => ! [C,A_1,B] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B))
         => ( B = 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_64_ord__le__eq__trans) ).

fof(fact_65_xt1_I4_J,axiom,
    ! [X_a] :
      ( order(X_a)
     => ! [C,B,A_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1))
         => ( ti(X_a,B) = 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_65_xt1_I4_J) ).

fof(fact_66_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_66_order__antisym) ).

fof(fact_67_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_67_order__trans) ).

fof(fact_68_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_68_xt1_I5_J) ).

fof(fact_69_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_69_xt1_I6_J) ).

fof(fact_70_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_70_linorder__le__cases) ).

fof(fact_71_insertI1,axiom,
    ! [X_b,A_2,B_1] : 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_1))),
    file('theBenchmark.p',fact_71_insertI1) ).

fof(fact_72_insert__compr,axiom,
    ! [X_b,A_2,B_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),B_1) = 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_1))),
    file('theBenchmark.p',fact_72_insert__compr) ).

fof(fact_73_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_73_insert__Collect) ).

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_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_77_insert__absorb2) ).

fof(fact_78_insert__commute,axiom,
    ! [X_b,X_1,Y_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),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_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),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_1),A_3)),
    file('theBenchmark.p',fact_78_insert__commute) ).

fof(fact_79_insert__iff,axiom,
    ! [X_b,A_2,B_3,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_3),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_3) ) ),
    file('theBenchmark.p',fact_79_insert__iff) ).

fof(fact_80_insert__code,axiom,
    ! [X_b,Y_2,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_2),A_3),X_1))
    <=> ( hBOOL(hAPP(X_b,bool,A_3,X_1))
        | ti(X_b,Y_2) = ti(X_b,X_1) ) ),
    file('theBenchmark.p',fact_80_insert__code) ).

fof(fact_81_insert__ident,axiom,
    ! [X_b,B_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))
     => ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_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),B_1)
        <=> ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_1) ) ) ),
    file('theBenchmark.p',fact_81_insert__ident) ).

fof(fact_82_insertI2,axiom,
    ! [X_b,B_3,A_2,B_1] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),B_1))
     => 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_3),B_1))) ),
    file('theBenchmark.p',fact_82_insertI2) ).

fof(fact_83_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_83_insert__absorb) ).

fof(fact_84_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_84_subset__refl) ).

fof(fact_85_set__eq__subset,axiom,
    ! [X_b,A_3,B_1] :
      ( ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_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)),B_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_1)) ) ),
    file('theBenchmark.p',fact_85_set__eq__subset) ).

fof(fact_86_equalityD1,axiom,
    ! [X_b,A_3,B_1] :
      ( ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_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),B_1)) ),
    file('theBenchmark.p',fact_86_equalityD1) ).

fof(fact_87_equalityD2,axiom,
    ! [X_b,A_3,B_1] :
      ( ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_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)),B_1),A_3)) ),
    file('theBenchmark.p',fact_87_equalityD2) ).

fof(fact_88_in__mono,axiom,
    ! [X_b,X_1,A_3,B_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),B_1))
     => ( 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_1)) ) ),
    file('theBenchmark.p',fact_88_in__mono) ).

fof(fact_89_set__rev__mp,axiom,
    ! [X_b,B_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))
     => ( 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_1))
       => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_1)) ) ),
    file('theBenchmark.p',fact_89_set__rev__mp) ).

fof(fact_90_set__mp,axiom,
    ! [X_b,X_1,A_3,B_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),B_1))
     => ( 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_1)) ) ),
    file('theBenchmark.p',fact_90_set__mp) ).

fof(fact_91_subset__trans,axiom,
    ! [X_b,C_2,A_3,B_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),B_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)),B_1),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_91_subset__trans) ).

fof(fact_92_equalityE,axiom,
    ! [X_b,A_3,B_1] :
      ( ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_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),B_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)),B_1),A_3)) ) ),
    file('theBenchmark.p',fact_92_equalityE) ).

fof(fact_93_image__iff,axiom,
    ! [X_b,X_c,Z_2,F,A_3] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Z_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)))
    <=> ? [X_2] :
          ( ti(X_b,Z_2) = 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_93_image__iff) ).

fof(fact_94_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_94_imageI) ).

fof(fact_95_rev__image__eqI,axiom,
    ! [X_c,X_b,B_3,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_3) = 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_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_95_rev__image__eqI) ).

fof(fact_96_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_96_insert__compr__raw) ).

fof(fact_97_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_97_image__image) ).

fof(fact_98_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_98_image__ident) ).

fof(fact_99_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_99_le__fun__def) ).

fof(fact_100_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_100_le__funD) ).

fof(fact_101_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_101_le__funE) ).

fof(fact_102_subset__insertI,axiom,
    ! [X_b,B_1,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_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),B_1))),
    file('theBenchmark.p',fact_102_subset__insertI) ).

fof(fact_103_insert__subset,axiom,
    ! [X_b,X_1,A_3,B_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)),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_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),B_1))
        & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_1)) ) ),
    file('theBenchmark.p',fact_103_insert__subset) ).

fof(fact_104_subset__insert,axiom,
    ! [X_b,B_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))
     => ( 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_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),B_1)) ) ),
    file('theBenchmark.p',fact_104_subset__insert) ).

fof(fact_105_subset__insertI2,axiom,
    ! [X_b,B_3,A_3,B_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),B_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),B_3),B_1))) ),
    file('theBenchmark.p',fact_105_subset__insertI2) ).

fof(fact_106_insert__mono,axiom,
    ! [X_b,A_2,C_2,D_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)),C_2),D_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(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_3))) ),
    file('theBenchmark.p',fact_106_insert__mono) ).

fof(fact_107_image__insert,axiom,
    ! [X_c,X_b,F,A_2,B_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),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_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),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_1)),
    file('theBenchmark.p',fact_107_image__insert) ).

fof(fact_108_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_108_insert__image) ).

fof(fact_109_subset__image__iff,axiom,
    ! [X_b,X_c,B_1,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_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)))
    <=> ? [AA] :
          ( ti(fun(X_b,bool),B_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),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_109_subset__image__iff) ).

fof(fact_110_image__mono,axiom,
    ! [X_c,X_b,F,A_3,B_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),B_1))
     => 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_1))) ),
    file('theBenchmark.p',fact_110_image__mono) ).

fof(fact_111_imageE,axiom,
    ! [X_b,X_c,B_3,F,A_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_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_3) = 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_111_imageE) ).

fof(fact_112_subsetI,axiom,
    ! [X_b,B_1,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_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),B_1)) ),
    file('theBenchmark.p',fact_112_subsetI) ).

fof(fact_113_image__subsetI,axiom,
    ! [X_c,X_b,F,B_1,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_1)) )
     => 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_1)) ),
    file('theBenchmark.p',fact_113_image__subsetI) ).

fof(fact_114_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_114_le__funI) ).

fof(fact_115_finite__nat__set__iff__bounded__le,axiom,
    ! [N_2] :
      ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),N_2))
    <=> ? [M_2] :
        ! [X_2] :
          ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),N_2))
         => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X_2),M_2)) ) ),
    file('theBenchmark.p',fact_115_finite__nat__set__iff__bounded__le) ).

fof(fact_116_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_116_assms_I3_J) ).

fof(fact_117_diff__eq__diff__less__eq,axiom,
    ! [X_b] :
      ( ordered_ab_group_add(X_b)
     => ! [A_2,B_3,C_1,D_1] :
          ( hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3) = 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_3))
          <=> 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_117_diff__eq__diff__less__eq) ).

fof(fact_118_less__eq__nat_Osimps_I2_J,axiom,
    ! [M,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M)),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)),Na)) ),
    file('theBenchmark.p',fact_118_less__eq__nat_Osimps_I2_J) ).

fof(fact_119_folding__image__simple__idem_Osubset__idem,axiom,
    ! [X_c,X_b,B_1,A_3,F,Z_2,G,F_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))),finite908156982e_idem(X_b,X_c),F),Z_2),G),F_1))
     => ( hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),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_1),A_3))
         => hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(fun(X_c,bool),X_b,F_1,B_1)),hAPP(fun(X_c,bool),X_b,F_1,A_3)) = hAPP(fun(X_c,bool),X_b,F_1,A_3) ) ) ),
    file('theBenchmark.p',fact_119_folding__image__simple__idem_Osubset__idem) ).

fof(fact_120_folding__image__simple__idem_Oinsert__idem,axiom,
    ! [X_c,X_b,X_1,A_3,F,Z_2,G,F_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))),finite908156982e_idem(X_b,X_c),F),Z_2),G),F_1))
     => ( hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),A_3))
       => hAPP(fun(X_c,bool),X_b,F_1,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_1,A_3)) ) ),
    file('theBenchmark.p',fact_120_folding__image__simple__idem_Oinsert__idem) ).

fof(fact_121_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_121_emptyE) ).

fof(fact_122_finite__Diff,axiom,
    ! [X_b,B_1,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_1))) ),
    file('theBenchmark.p',fact_122_finite__Diff) ).

fof(fact_123_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_123_finite_OemptyI) ).

fof(fact_124_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_124_empty__subsetI) ).

fof(fact_125_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_125_equals0D) ).

fof(fact_126_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_126_Collect__empty__eq) ).

fof(fact_127_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_127_Diff__cancel) ).

fof(fact_128_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_128_Diff__empty) ).

fof(fact_129_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_129_empty__iff) ).

fof(fact_130_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_130_empty__Collect__eq) ).

fof(fact_131_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_131_empty__Diff) ).

fof(fact_132_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_132_ex__in__conv) ).

fof(fact_133_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_133_all__not__in__conv) ).

fof(fact_134_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_134_bot__apply) ).

fof(fact_135_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_135_empty__def) ).

fof(fact_136_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_136_bot__fun__def) ).

fof(fact_137_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_137_insert__Diff) ).

fof(fact_138_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_138_Diff__insert__absorb) ).

fof(fact_139_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_139_insert__Diff__single) ).

fof(fact_140_Diff__insert2,axiom,
    ! [X_b,A_3,A_2,B_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),A_2),B_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)),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_1),
    file('theBenchmark.p',fact_140_Diff__insert2) ).

fof(fact_141_Diff__insert,axiom,
    ! [X_b,A_3,A_2,B_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),A_2),B_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)),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_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),bot_bot(fun(X_b,bool)))),
    file('theBenchmark.p',fact_141_Diff__insert) ).

fof(fact_142_folding__image__simple__idem_Oidem,axiom,
    ! [X_c,X_b,X_1,F,Z_2,G,F_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))),finite908156982e_idem(X_b,X_c),F),Z_2),G),F_1))
     => 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_142_folding__image__simple__idem_Oidem) ).

fof(fact_143_diff__single__insert,axiom,
    ! [X_b,A_3,X_1,B_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)),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_1))
     => ( 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_1))) ) ),
    file('theBenchmark.p',fact_143_diff__single__insert) ).

fof(fact_144_subset__insert__iff,axiom,
    ! [X_b,A_3,X_1,B_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),B_1)))
    <=> ( ( ~ 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_1)) )
        & ( 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_1)) ) ) ),
    file('theBenchmark.p',fact_144_subset__insert__iff) ).

fof(fact_145_finite__Diff2,axiom,
    ! [X_b,A_3,B_1] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_1))
     => ( 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_1)))
      <=> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) ) ),
    file('theBenchmark.p',fact_145_finite__Diff2) ).

fof(fact_146_insert__Diff1,axiom,
    ! [X_b,A_3,X_1,B_1] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_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)),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_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_1) ),
    file('theBenchmark.p',fact_146_insert__Diff1) ).

fof(fact_147_insert__Diff__if,axiom,
    ! [X_b,A_3,X_1,B_1] :
      ( ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_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)),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_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),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_1)) )
      & ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_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)),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_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_1) ) ),
    file('theBenchmark.p',fact_147_insert__Diff__if) ).

fof(fact_148_double__diff,axiom,
    ! [X_b,C_2,A_3,B_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),B_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)),B_1),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_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)),C_2),A_3)) = ti(fun(X_b,bool),A_3) ) ),
    file('theBenchmark.p',fact_148_double__diff) ).

fof(fact_149_Diff__mono,axiom,
    ! [X_b,D_3,B_1,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_3),B_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)),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_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)),C_2),D_3))) ) ),
    file('theBenchmark.p',fact_149_Diff__mono) ).

fof(fact_150_Diff__subset,axiom,
    ! [X_b,A_3,B_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)),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_1)),A_3)),
    file('theBenchmark.p',fact_150_Diff__subset) ).

fof(fact_151_singleton__inject,axiom,
    ! [X_b,A_2,B_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),B_3),bot_bot(fun(X_b,bool)))
     => ti(X_b,A_2) = ti(X_b,B_3) ),
    file('theBenchmark.p',fact_151_singleton__inject) ).

fof(fact_152_singletonE,axiom,
    ! [X_b,B_3,A_2] :
      ( 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(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_3) = ti(X_b,A_2) ),
    file('theBenchmark.p',fact_152_singletonE) ).

fof(fact_153_doubleton__eq__iff,axiom,
    ! [X_b,A_2,B_3,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_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),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_3) = ti(X_b,C_1)
          & ti(X_b,A_2) = ti(X_b,D_1) )
        | ( ti(X_b,B_3) = ti(X_b,D_1)
          & ti(X_b,A_2) = ti(X_b,C_1) ) ) ),
    file('theBenchmark.p',fact_153_doubleton__eq__iff) ).

fof(fact_154_singleton__iff,axiom,
    ! [X_b,B_3,A_2] :
      ( 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(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_3) = ti(X_b,A_2) ),
    file('theBenchmark.p',fact_154_singleton__iff) ).

fof(fact_155_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_155_insert__not__empty) ).

fof(fact_156_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_156_empty__not__insert) ).

fof(fact_157_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_157_subset__empty) ).

fof(fact_158_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_158_image__is__empty) ).

fof(fact_159_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_159_image__empty) ).

fof(fact_160_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_160_empty__is__image) ).

fof(fact_161_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_161_le__bot) ).

fof(fact_162_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_162_bot__unique) ).

fof(fact_163_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_163_bot__least) ).

fof(fact_164_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_164_Collect__conv__if) ).

fof(fact_165_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_165_Collect__conv__if2) ).

fof(fact_166_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_166_singleton__conv) ).

fof(fact_167_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_167_singleton__conv2) ).

fof(fact_168_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_168_card__Suc__Diff1) ).

fof(fact_169_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_169_card__insert) ).

fof(fact_170_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_170_card__Diff1__le) ).

fof(fact_171_finite__Diff__insert,axiom,
    ! [X_b,A_3,A_2,B_1] :
      ( 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_1))))
    <=> 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_1))) ),
    file('theBenchmark.p',fact_171_finite__Diff__insert) ).

fof(fact_172_image__diff__subset,axiom,
    ! [X_b,X_c,F,A_3,B_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)),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_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),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_1)))),
    file('theBenchmark.p',fact_172_image__diff__subset) ).

fof(fact_173_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_173_subset__singletonD) ).

fof(fact_174_nat__case__Suc,axiom,
    ! [X_b,F1,F2,Nat_3] : 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_3)) = hAPP(nat,X_b,F2,Nat_3),
    file('theBenchmark.p',fact_174_nat__case__Suc) ).

fof(fact_175_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_175_image__constant) ).

fof(fact_176_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_176_image__constant__conv) ).

fof(fact_177_folding__image__simple__idem_Oin__idem,axiom,
    ! [X_c,X_b,X_1,A_3,F,Z_2,G,F_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))),finite908156982e_idem(X_b,X_c),F),Z_2),G),F_1))
     => ( 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(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_1,A_3)) = hAPP(fun(X_c,bool),X_b,F_1,A_3) ) ) ),
    file('theBenchmark.p',fact_177_folding__image__simple__idem_Oin__idem) ).

fof(fact_178_diff__eq__diff__eq,axiom,
    ! [X_b] :
      ( ab_group_add(X_b)
     => ! [A_2,B_3,C_1,D_1] :
          ( hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3) = 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_3)
          <=> ti(X_b,C_1) = ti(X_b,D_1) ) ) ),
    file('theBenchmark.p',fact_178_diff__eq__diff__eq) ).

fof(fact_179_card__Diff__subset,axiom,
    ! [X_b,A_3,B_1] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_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)),B_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),B_1)) = 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_1)) ) ),
    file('theBenchmark.p',fact_179_card__Diff__subset) ).

fof(fact_180_diff__card__le__card__Diff,axiom,
    ! [X_b,A_3,B_1] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_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),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_1))),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_1)))) ),
    file('theBenchmark.p',fact_180_diff__card__le__card__Diff) ).

fof(fact_181_finite__subset__induct,axiom,
    ! [X_b,Pa,A_3,F_1] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),F_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)),F_1),A_3))
       => ( hBOOL(hAPP(fun(X_b,bool),bool,Pa,bot_bot(fun(X_b,bool))))
         => ( ! [A_4,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_4),A_3))
                 => ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_4),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_4),F_3))) ) ) ) )
           => hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_1)) ) ) ) ),
    file('theBenchmark.p',fact_181_finite__subset__induct) ).

fof(fact_182_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_182_assms_I2_J) ).

fof(fact_183_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_4,A_5] :
              ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_5))
             => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_4),A_5))
               => ( hBOOL(hAPP(fun(X_b,bool),bool,Pa,A_5))
                 => 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_5),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_4),bot_bot(fun(X_b,bool)))))) ) ) )
         => hBOOL(hAPP(fun(X_b,bool),bool,Pa,bot_bot(fun(X_b,bool)))) ) ) ),
    file('theBenchmark.p',fact_183_finite__empty__induct) ).

fof(fact_184_finite__induct,axiom,
    ! [X_b,Pa,F_1] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),F_1))
     => ( 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_1)) ) ) ),
    file('theBenchmark.p',fact_184_finite__induct) ).

fof(fact_185_finite_Osimps,axiom,
    ! [X_b,A_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_2))
    <=> ( ? [A_5,A_4] :
            ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_5))
            & 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_4),A_5) )
        | ti(fun(X_b,bool),A_2) = bot_bot(fun(X_b,bool)) ) ),
    file('theBenchmark.p',fact_185_finite_Osimps) ).

fof(fact_186_finite__less__ub,axiom,
    ! [U,F] :
      ( ! [N_1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),hAPP(nat,nat,F,N_1)))
     => 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_186_finite__less__ub) ).

fof(fact_187_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_187_the__elem__eq) ).

fof(fact_188_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_188_nonempty__iff) ).

fof(fact_189_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_189_assms_I4_J) ).

fof(fact_190_DiffE,axiom,
    ! [X_b,C_1,A_3,B_1] :
      ( 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_1)))
     => ~ ( 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_1)) ) ),
    file('theBenchmark.p',fact_190_DiffE) ).

fof(fact_191_DiffI,axiom,
    ! [X_b,B_1,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_1))
       => 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_1))) ) ),
    file('theBenchmark.p',fact_191_DiffI) ).

fof(fact_192_DiffD2,axiom,
    ! [X_b,C_1,A_3,B_1] :
      ( 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_1)))
     => ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_1)) ),
    file('theBenchmark.p',fact_192_DiffD2) ).

fof(fact_193_DiffD1,axiom,
    ! [X_b,C_1,A_3,B_1] :
      ( 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_1)))
     => 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_193_DiffD1) ).

fof(fact_194_Diff__idemp,axiom,
    ! [X_b,A_3,B_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)),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_1)),B_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_1),
    file('theBenchmark.p',fact_194_Diff__idemp) ).

fof(fact_195_Diff__iff,axiom,
    ! [X_b,C_1,A_3,B_1] :
      ( 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_1)))
    <=> ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_1))
        & 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_195_Diff__iff) ).

fof(fact_196_set__diff__eq,axiom,
    ! [X_b,A_3,B_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_1) = 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_1)))),
    file('theBenchmark.p',fact_196_set__diff__eq) ).

fof(fact_197_folding__one_Oinsert__remove,axiom,
    ! [X_b,X_1,A_3,F,F_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_1))
     => ( 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_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(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),hAPP(fun(X_b,bool),X_b,F_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)))))) )
          & ( 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_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)) = ti(X_b,X_1) ) ) ) ),
    file('theBenchmark.p',fact_197_folding__one_Oinsert__remove) ).

fof(fact_198_folding__one_Oremove,axiom,
    ! [X_b,X_1,A_3,F,F_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_1))
     => ( 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_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_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)))))) )
            & ( 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_1,A_3) = ti(X_b,X_1) ) ) ) ) ),
    file('theBenchmark.p',fact_198_folding__one_Oremove) ).

fof(fact_199_folding__image__simple_Oinsert__remove,axiom,
    ! [X_c,X_b,X_1,A_3,F,Z_2,G,F_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_2),G),F_1))
     => ( hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),A_3))
       => hAPP(fun(X_c,bool),X_b,F_1,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_1,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_199_folding__image__simple_Oinsert__remove) ).

fof(fact_200_folding__image__simple_Oremove,axiom,
    ! [X_c,X_b,X_1,A_3,F,Z_2,G,F_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_2),G),F_1))
     => ( 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_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_1,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_200_folding__image__simple_Oremove) ).

fof(fact_201_fun__diff__def,axiom,
    ! [X_b,X_c] :
      ( minus(X_c)
     => ! [A_3,B_1,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_1),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_1,X_2)) ),
    file('theBenchmark.p',fact_201_fun__diff__def) ).

fof(fact_202_minus__apply,axiom,
    ! [X_c,X_b] :
      ( minus(X_b)
     => ! [A_3,B_1,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_1),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_1,X_1)) ),
    file('theBenchmark.p',fact_202_minus__apply) ).

fof(fact_203_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_203_card__Diff__singleton__if) ).

fof(fact_204_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_204_card__Diff__singleton) ).

fof(fact_205_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_205_one__reorient) ).

fof(fact_206_folding__image__simple_Oempty,axiom,
    ! [X_c,X_b,F,Z_2,G,F_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_2),G),F_1))
     => hAPP(fun(X_c,bool),X_b,F_1,bot_bot(fun(X_c,bool))) = ti(X_b,Z_2) ),
    file('theBenchmark.p',fact_206_folding__image__simple_Oempty) ).

fof(fact_207_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_207_diff__Suc__1) ).

fof(fact_208_diff__Suc__eq__diff__pred,axiom,
    ! [M_1,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),hAPP(nat,nat,suc,N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),one_one(nat))),N),
    file('theBenchmark.p',fact_208_diff__Suc__eq__diff__pred) ).

fof(fact_209_folding__one_Osingleton,axiom,
    ! [X_b,X_1,F,F_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_1))
     => hAPP(fun(X_b,bool),X_b,F_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),bot_bot(fun(X_b,bool)))) = ti(X_b,X_1) ),
    file('theBenchmark.p',fact_209_folding__one_Osingleton) ).

fof(fact_210_folding__image__simple_Oinsert,axiom,
    ! [X_c,X_b,X_1,A_3,F,Z_2,G,F_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_2),G),F_1))
     => ( 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_1,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_1,A_3)) ) ) ),
    file('theBenchmark.p',fact_210_folding__image__simple_Oinsert) ).

fof(fact_211_card__Diff__insert,axiom,
    ! [X_b,B_1,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_1))
         => 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_1))) = 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_1))),one_one(nat)) ) ) ),
    file('theBenchmark.p',fact_211_card__Diff__insert) ).

fof(fact_212_folding__one_Oinsert,axiom,
    ! [X_b,X_1,A_3,F,F_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_1))
     => ( 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_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(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),hAPP(fun(X_b,bool),X_b,F_1,A_3)) ) ) ) ),
    file('theBenchmark.p',fact_212_folding__one_Oinsert) ).

fof(fact_213_folding__one_Oclosed,axiom,
    ! [X_b,A_3,F,F_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_1))
     => ( 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_1] : 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_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_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_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),hAPP(fun(X_b,bool),X_b,F_1,A_3)),A_3)) ) ) ) ),
    file('theBenchmark.p',fact_213_folding__one_Oclosed) ).

fof(fact_214_folding__image__simple_Oneutral,axiom,
    ! [X_c,X_b,A_3,F,Z_2,G,F_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_2),G),F_1))
     => ( 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_2) )
         => hAPP(fun(X_c,bool),X_b,F_1,A_3) = ti(X_b,Z_2) ) ) ),
    file('theBenchmark.p',fact_214_folding__image__simple_Oneutral) ).

fof(fact_215_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_215_card_Oremove) ).

fof(fact_216_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_216_card_Oinsert__remove) ).

fof(fact_217_folding__one__idem_Osubset__idem,axiom,
    ! [X_b,B_1,A_3,F,F_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_1))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))
       => ( ti(fun(X_b,bool),B_1) != 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_1),A_3))
           => hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(fun(X_b,bool),X_b,F_1,B_1)),hAPP(fun(X_b,bool),X_b,F_1,A_3)) = hAPP(fun(X_b,bool),X_b,F_1,A_3) ) ) ) ),
    file('theBenchmark.p',fact_217_folding__one__idem_Osubset__idem) ).

fof(fact_218_folding__one__idem_Oinsert__idem,axiom,
    ! [X_b,X_1,A_3,F,F_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_1))
     => ( 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_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(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),hAPP(fun(X_b,bool),X_b,F_1,A_3)) ) ) ),
    file('theBenchmark.p',fact_218_folding__one__idem_Oinsert__idem) ).

fof(fact_219_finite__ne__induct,axiom,
    ! [X_b,Pa,F_1] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),F_1))
     => ( ti(fun(X_b,bool),F_1) != 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_1)) ) ) ) ),
    file('theBenchmark.p',fact_219_finite__ne__induct) ).

fof(fact_220_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_220_the__elem__def) ).

fof(fact_221_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
    ! [X_a] :
      ( ab_semigroup_add(X_a)
     => ! [A_1,B,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)),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),C)) ),
    file('theBenchmark.p',fact_221_ab__semigroup__add__class_Oadd__ac_I1_J) ).

fof(fact_222_add__left__cancel,axiom,
    ! [X_b] :
      ( cancel_semigroup_add(X_b)
     => ! [A_2,B_3,C_1] :
          ( hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),B_3) = 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_3) = ti(X_b,C_1) ) ),
    file('theBenchmark.p',fact_222_add__left__cancel) ).

fof(fact_223_add__right__cancel,axiom,
    ! [X_b] :
      ( cancel_semigroup_add(X_b)
     => ! [B_3,A_2,C_1] :
          ( hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),B_3),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_3) = ti(X_b,C_1) ) ),
    file('theBenchmark.p',fact_223_add__right__cancel) ).

fof(fact_224_add__left__imp__eq,axiom,
    ! [X_a] :
      ( cancel_semigroup_add(X_a)
     => ! [A_1,B,C] :
          ( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)
         => ti(X_a,B) = ti(X_a,C) ) ),
    file('theBenchmark.p',fact_224_add__left__imp__eq) ).

fof(fact_225_add__imp__eq,axiom,
    ! [X_a] :
      ( cancel146912293up_add(X_a)
     => ! [A_1,B,C] :
          ( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)
         => ti(X_a,B) = ti(X_a,C) ) ),
    file('theBenchmark.p',fact_225_add__imp__eq) ).

fof(fact_226_add__right__imp__eq,axiom,
    ! [X_a] :
      ( cancel_semigroup_add(X_a)
     => ! [B,A_1,C] :
          ( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),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) = ti(X_a,C) ) ),
    file('theBenchmark.p',fact_226_add__right__imp__eq) ).

fof(fact_227_folding__one__idem_Oidem,axiom,
    ! [X_b,X_1,F,F_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_1))
     => 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_227_folding__one__idem_Oidem) ).

fof(fact_228_nat__add__commute,axiom,
    ! [M_1,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M_1),
    file('theBenchmark.p',fact_228_nat__add__commute) ).

fof(fact_229_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_229_nat__add__left__commute) ).

fof(fact_230_nat__add__assoc,axiom,
    ! [M_1,N,K_1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N)),K_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),K_1)),
    file('theBenchmark.p',fact_230_nat__add__assoc) ).

fof(fact_231_nat__add__left__cancel,axiom,
    ! [K,M,Na] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),M) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),Na)
    <=> M = Na ),
    file('theBenchmark.p',fact_231_nat__add__left__cancel) ).

fof(fact_232_nat__add__right__cancel,axiom,
    ! [M,K,Na] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Na),K)
    <=> M = Na ),
    file('theBenchmark.p',fact_232_nat__add__right__cancel) ).

fof(fact_233_add__le__cancel__right,axiom,
    ! [X_b] :
      ( ordere236663937imp_le(X_b)
     => ! [A_2,C_1,B_3] :
          ( 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_3),C_1)))
        <=> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),B_3)) ) ),
    file('theBenchmark.p',fact_233_add__le__cancel__right) ).

fof(fact_234_add__le__cancel__left,axiom,
    ! [X_b] :
      ( ordere236663937imp_le(X_b)
     => ! [C_1,A_2,B_3] :
          ( 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_3)))
        <=> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),B_3)) ) ),
    file('theBenchmark.p',fact_234_add__le__cancel__left) ).

fof(fact_235_add__right__mono,axiom,
    ! [X_a] :
      ( ordere779506340up_add(X_a)
     => ! [C,A_1,B] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B))
         => 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),C))) ) ),
    file('theBenchmark.p',fact_235_add__right__mono) ).

fof(fact_236_add__left__mono,axiom,
    ! [X_a] :
      ( ordere779506340up_add(X_a)
     => ! [C,A_1,B] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B))
         => 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))) ) ),
    file('theBenchmark.p',fact_236_add__left__mono) ).

fof(fact_237_add__mono,axiom,
    ! [X_a] :
      ( ordere779506340up_add(X_a)
     => ! [C,D,A_1,B] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B))
         => ( 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),D))) ) ) ),
    file('theBenchmark.p',fact_237_add__mono) ).

fof(fact_238_add__le__imp__le__right,axiom,
    ! [X_a] :
      ( ordere236663937imp_le(X_a)
     => ! [A_1,C,B] :
          ( 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),C)))
         => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) ) ),
    file('theBenchmark.p',fact_238_add__le__imp__le__right) ).

fof(fact_239_add__le__imp__le__left,axiom,
    ! [X_a] :
      ( ordere236663937imp_le(X_a)
     => ! [C,A_1,B] :
          ( 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)))
         => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) ) ),
    file('theBenchmark.p',fact_239_add__le__imp__le__left) ).

fof(fact_240_diff__add__cancel,axiom,
    ! [X_a] :
      ( group_add(X_a)
     => ! [A_1,B] : 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)),B) = ti(X_a,A_1) ),
    file('theBenchmark.p',fact_240_diff__add__cancel) ).

fof(fact_241_add__diff__cancel,axiom,
    ! [X_a] :
      ( group_add(X_a)
     => ! [A_1,B] : 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)),B) = ti(X_a,A_1) ),
    file('theBenchmark.p',fact_241_add__diff__cancel) ).

fof(fact_242_add__Suc__right,axiom,
    ! [M_1,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),hAPP(nat,nat,suc,N)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N)),
    file('theBenchmark.p',fact_242_add__Suc__right) ).

fof(fact_243_add__Suc,axiom,
    ! [M_1,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M_1)),N) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N)),
    file('theBenchmark.p',fact_243_add__Suc) ).

fof(fact_244_add__Suc__shift,axiom,
    ! [M_1,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M_1)),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),hAPP(nat,nat,suc,N)),
    file('theBenchmark.p',fact_244_add__Suc__shift) ).

fof(fact_245_le__add2,axiom,
    ! [N,M_1] : 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_1),N))),
    file('theBenchmark.p',fact_245_le__add2) ).

fof(fact_246_le__add1,axiom,
    ! [N,M_1] : 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_1))),
    file('theBenchmark.p',fact_246_le__add1) ).

fof(fact_247_le__iff__add,axiom,
    ! [M,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na))
    <=> ? [K_2] : Na = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_2) ),
    file('theBenchmark.p',fact_247_le__iff__add) ).

fof(fact_248_nat__add__left__cancel__le,axiom,
    ! [K,M,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),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),Na)))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)) ),
    file('theBenchmark.p',fact_248_nat__add__left__cancel__le) ).

fof(fact_249_trans__le__add1,axiom,
    ! [M_1,I_2,J] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),J))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),M_1))) ),
    file('theBenchmark.p',fact_249_trans__le__add1) ).

fof(fact_250_trans__le__add2,axiom,
    ! [M_1,I_2,J] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),J))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),J))) ),
    file('theBenchmark.p',fact_250_trans__le__add2) ).

fof(fact_251_add__le__mono1,axiom,
    ! [K_1,I_2,J] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),J))
     => 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_2),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),K_1))) ),
    file('theBenchmark.p',fact_251_add__le__mono1) ).

fof(fact_252_add__le__mono,axiom,
    ! [K_1,L_1,I_2,J] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),J))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),L_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_2),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),L_1))) ) ),
    file('theBenchmark.p',fact_252_add__le__mono) ).

fof(fact_253_add__leD2,axiom,
    ! [M_1,K_1,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_1),K_1)),N))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N)) ),
    file('theBenchmark.p',fact_253_add__leD2) ).

fof(fact_254_add__leD1,axiom,
    ! [M_1,K_1,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_1),K_1)),N))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)) ),
    file('theBenchmark.p',fact_254_add__leD1) ).

fof(fact_255_add__leE,axiom,
    ! [M_1,K_1,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_1),K_1)),N))
     => ~ ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N))
         => ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N)) ) ),
    file('theBenchmark.p',fact_255_add__leE) ).

fof(fact_256_diff__add__inverse2,axiom,
    ! [M_1,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N)),N) = M_1,
    file('theBenchmark.p',fact_256_diff__add__inverse2) ).

fof(fact_257_diff__add__inverse,axiom,
    ! [N,M_1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M_1)),N) = M_1,
    file('theBenchmark.p',fact_257_diff__add__inverse) ).

fof(fact_258_diff__diff__left,axiom,
    ! [I_2,J,K_1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_2),J)),K_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),K_1)),
    file('theBenchmark.p',fact_258_diff__diff__left) ).

fof(fact_259_diff__cancel,axiom,
    ! [K_1,M_1,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N),
    file('theBenchmark.p',fact_259_diff__cancel) ).

fof(fact_260_diff__cancel2,axiom,
    ! [M_1,K_1,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),K_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N),
    file('theBenchmark.p',fact_260_diff__cancel2) ).

fof(fact_261_diff__diff__right,axiom,
    ! [I_2,K_1,J] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),J))
     => hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),K_1)),J) ),
    file('theBenchmark.p',fact_261_diff__diff__right) ).

fof(fact_262_le__diff__conv,axiom,
    ! [J_1,K,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)),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))) ),
    file('theBenchmark.p',fact_262_le__diff__conv) ).

fof(fact_263_le__add__diff,axiom,
    ! [M_1,K_1,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M_1)),K_1))) ),
    file('theBenchmark.p',fact_263_le__add__diff) ).

fof(fact_264_le__add__diff__inverse,axiom,
    ! [N,M_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M_1))
     => hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N)) = M_1 ),
    file('theBenchmark.p',fact_264_le__add__diff__inverse) ).

fof(fact_265_add__diff__assoc,axiom,
    ! [I_2,K_1,J] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),J))
     => hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),J)),K_1) ),
    file('theBenchmark.p',fact_265_add__diff__assoc) ).

fof(fact_266_le__diff__conv2,axiom,
    ! [I_1,K,J_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),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)))
      <=> 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)),J_1)) ) ),
    file('theBenchmark.p',fact_266_le__diff__conv2) ).

fof(fact_267_le__add__diff__inverse2,axiom,
    ! [N,M_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M_1))
     => hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N)),N) = M_1 ),
    file('theBenchmark.p',fact_267_le__add__diff__inverse2) ).

fof(fact_268_le__imp__diff__is__add,axiom,
    ! [K,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
      <=> J_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),I_1) ) ),
    file('theBenchmark.p',fact_268_le__imp__diff__is__add) ).

fof(fact_269_diff__add__assoc,axiom,
    ! [I_2,K_1,J] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),J))
     => hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),J)),K_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K_1)) ),
    file('theBenchmark.p',fact_269_diff__add__assoc) ).

fof(fact_270_add__diff__assoc2,axiom,
    ! [I_2,K_1,J] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),J))
     => hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K_1)),I_2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),I_2)),K_1) ),
    file('theBenchmark.p',fact_270_add__diff__assoc2) ).

fof(fact_271_diff__add__assoc2,axiom,
    ! [I_2,K_1,J] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),J))
     => hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),I_2)),K_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K_1)),I_2) ),
    file('theBenchmark.p',fact_271_diff__add__assoc2) ).

fof(fact_272_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_272_Suc__eq__plus1__left) ).

fof(fact_273_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_273_Suc__eq__plus1) ).

fof(fact_274_folding__one__idem_Oin__idem,axiom,
    ! [X_b,X_1,A_3,F,F_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_1))
     => ( 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_1,A_3)) = hAPP(fun(X_b,bool),X_b,F_1,A_3) ) ) ),
    file('theBenchmark.p',fact_274_folding__one__idem_Oin__idem) ).

fof(fact_275_diff__Suc__diff__eq1,axiom,
    ! [M_1,K_1,J] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),J))
     => hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K_1))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_1)),hAPP(nat,nat,suc,J)) ),
    file('theBenchmark.p',fact_275_diff__Suc__diff__eq1) ).

fof(fact_276_diff__Suc__diff__eq2,axiom,
    ! [M_1,K_1,J] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),J))
     => hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K_1))),M_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,J)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),M_1)) ),
    file('theBenchmark.p',fact_276_diff__Suc__diff__eq2) ).

fof(fact_277_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_277_card_Oinsert) ).

fof(fact_278_folding__one__idem_Ohom__commute,axiom,
    ! [X_b,N_2,H,F,F_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_1))
     => ( ! [X_2,Y_1] : hAPP(X_b,X_b,H,hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_2),Y_1)) = 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_1))
       => ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),N_2))
         => ( ti(fun(X_b,bool),N_2) != bot_bot(fun(X_b,bool))
           => hAPP(X_b,X_b,H,hAPP(fun(X_b,bool),X_b,F_1,N_2)) = hAPP(fun(X_b,bool),X_b,F_1,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_2)) ) ) ) ),
    file('theBenchmark.p',fact_278_folding__one__idem_Ohom__commute) ).

fof(fact_279_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_279_termination__basic__simps_I4_J) ).

fof(fact_280_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_280_termination__basic__simps_I3_J) ).

fof(fact_281_flat__lub__def,axiom,
    ! [X_b,A_3,B_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),B_3),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_3),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_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),B_3),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_3),A_3) = ti(X_b,B_3) ) ),
    file('theBenchmark.p',fact_281_flat__lub__def) ).

fof(fact_282_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_282_comp__fun__idem__remove) ).

fof(fact_283_If__def,axiom,
    ! [X_b,X_1,Y_2,Pa] :
      ( ( ~ hBOOL(Pa)
       => ti(X_b,Y_2) = 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_2)))) )
      & ( 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_2)))) ) ),
    file('theBenchmark.p',fact_283_If__def) ).

fof(fact_284_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_284_the__eq__trivial) ).

fof(fact_285_comp__fun__idem_Ofun__left__idem,axiom,
    ! [X_b,X_c,X_1,Z_2,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_2)) = hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),Z_2) ),
    file('theBenchmark.p',fact_285_comp__fun__idem_Ofun__left__idem) ).

fof(fact_286_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_286_comp__fun__idem__insert) ).

fof(fact_287_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_287_the__sym__eq__trivial) ).

fof(fact_288_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_288_the__equality) ).

fof(fact_289_theI_H,axiom,
    ! [X_b,Pa] :
      ( ? [X_2] :
          ( ! [Y_1] :
              ( hBOOL(hAPP(X_b,bool,Pa,Y_1))
             => ti(X_b,Y_1) = 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_289_theI_H) ).

fof(fact_290_the1__equality,axiom,
    ! [X_b,A_2,Pa] :
      ( ? [X_2] :
          ( ! [Y_1] :
              ( hBOOL(hAPP(X_b,bool,Pa,Y_1))
             => ti(X_b,Y_1) = 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_290_the1__equality) ).

fof(fact_291_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_291_theI) ).

fof(fact_292_card__Diff2__less,axiom,
    ! [X_b,Y_2,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_2),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_2),bot_bot(fun(X_b,bool)))))),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))) ) ) ),
    file('theBenchmark.p',fact_292_card__Diff2__less) ).

fof(fact_293_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_293_card__Diff1__less) ).

fof(fact_294_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_294_lessI) ).

fof(fact_295_Suc__mono,axiom,
    ! [M_1,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_1)),hAPP(nat,nat,suc,N))) ),
    file('theBenchmark.p',fact_295_Suc__mono) ).

fof(fact_296_finite__Collect__less__nat,axiom,
    ! [K] : 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)))),
    file('theBenchmark.p',fact_296_finite__Collect__less__nat) ).

fof(fact_297_less__not__refl,axiom,
    ! [N] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N)),
    file('theBenchmark.p',fact_297_less__not__refl) ).

fof(fact_298_nat__neq__iff,axiom,
    ! [M,Na] :
      ( M != Na
    <=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)) ) ),
    file('theBenchmark.p',fact_298_nat__neq__iff) ).

fof(fact_299_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_299_linorder__neqE__nat) ).

fof(fact_300_less__irrefl__nat,axiom,
    ! [N] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N)),
    file('theBenchmark.p',fact_300_less__irrefl__nat) ).

fof(fact_301_less__not__refl2,axiom,
    ! [N,M_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M_1))
     => M_1 != N ),
    file('theBenchmark.p',fact_301_less__not__refl2) ).

fof(fact_302_less__not__refl3,axiom,
    ! [S_1,T_4] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),S_1),T_4))
     => S_1 != T_4 ),
    file('theBenchmark.p',fact_302_less__not__refl3) ).

fof(fact_303_nat__less__cases,axiom,
    ! [Pa,M,Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,Na),M)) )
     => ( ( M = Na
         => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,Na),M)) )
       => ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M))
           => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,Na),M)) )
         => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,Na),M)) ) ) ),
    file('theBenchmark.p',fact_303_nat__less__cases) ).

fof(fact_304_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_304_order__less__irrefl) ).

fof(fact_305_linorder__neq__iff,axiom,
    ! [X_b] :
      ( linorder(X_b)
     => ! [X_1,Y_2] :
          ( ti(X_b,X_1) != ti(X_b,Y_2)
        <=> ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_1))
            | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2)) ) ) ),
    file('theBenchmark.p',fact_305_linorder__neq__iff) ).

fof(fact_306_not__less__iff__gr__or__eq,axiom,
    ! [X_b] :
      ( linorder(X_b)
     => ! [X_1,Y_2] :
          ( ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2))
        <=> ( ti(X_b,X_1) = ti(X_b,Y_2)
            | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_1)) ) ) ),
    file('theBenchmark.p',fact_306_not__less__iff__gr__or__eq) ).

fof(fact_307_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_307_linorder__less__linear) ).

fof(fact_308_linorder__antisym__conv3,axiom,
    ! [X_b] :
      ( linorder(X_b)
     => ! [Y_2,X_1] :
          ( ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_1))
         => ( ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2))
          <=> ti(X_b,X_1) = ti(X_b,Y_2) ) ) ),
    file('theBenchmark.p',fact_308_linorder__antisym__conv3) ).

fof(fact_309_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_309_linorder__neqE) ).

fof(fact_310_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_310_less__imp__neq) ).

fof(fact_311_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_311_order__less__not__sym) ).

fof(fact_312_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_312_order__less__imp__not__less) ).

fof(fact_313_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_313_order__less__imp__not__eq) ).

fof(fact_314_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_314_order__less__imp__not__eq2) ).

fof(fact_315_order__less__imp__triv,axiom,
    ! [X_b] :
      ( preorder(X_b)
     => ! [Pa,X_1,Y_2] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2))
         => ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_1))
           => hBOOL(Pa) ) ) ),
    file('theBenchmark.p',fact_315_order__less__imp__triv) ).

fof(fact_316_order__less__asym_H,axiom,
    ! [X_a] :
      ( preorder(X_a)
     => ! [A_1,B] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))
         => ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)) ) ),
    file('theBenchmark.p',fact_316_order__less__asym_H) ).

fof(fact_317_xt1_I9_J,axiom,
    ! [X_a] :
      ( order(X_a)
     => ! [B,A_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1))
         => ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) ) ),
    file('theBenchmark.p',fact_317_xt1_I9_J) ).

fof(fact_318_ord__eq__less__trans,axiom,
    ! [X_a] :
      ( ord(X_a)
     => ! [C,A_1,B] :
          ( A_1 = B
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),C))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),C)) ) ) ),
    file('theBenchmark.p',fact_318_ord__eq__less__trans) ).

fof(fact_319_xt1_I1_J,axiom,
    ! [X_a] :
      ( order(X_a)
     => ! [C,A_1,B] :
          ( ti(X_a,A_1) = ti(X_a,B)
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),B))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),A_1)) ) ) ),
    file('theBenchmark.p',fact_319_xt1_I1_J) ).

fof(fact_320_ord__less__eq__trans,axiom,
    ! [X_a] :
      ( ord(X_a)
     => ! [C,A_1,B] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))
         => ( B = C
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),C)) ) ) ),
    file('theBenchmark.p',fact_320_ord__less__eq__trans) ).

fof(fact_321_xt1_I2_J,axiom,
    ! [X_a] :
      ( order(X_a)
     => ! [C,B,A_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1))
         => ( ti(X_a,B) = 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_321_xt1_I2_J) ).

fof(fact_322_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_322_order__less__trans) ).

fof(fact_323_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_323_xt1_I10_J) ).

fof(fact_324_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_324_order__less__asym) ).

fof(fact_325_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_325_linorder__cases) ).

fof(fact_326_linorder__not__less,axiom,
    ! [X_b] :
      ( linorder(X_b)
     => ! [X_1,Y_2] :
          ( ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2))
        <=> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_2),X_1)) ) ),
    file('theBenchmark.p',fact_326_linorder__not__less) ).

fof(fact_327_linorder__not__le,axiom,
    ! [X_b] :
      ( linorder(X_b)
     => ! [X_1,Y_2] :
          ( ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2))
        <=> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_1)) ) ),
    file('theBenchmark.p',fact_327_linorder__not__le) ).

fof(fact_328_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_328_linorder__le__less__linear) ).

fof(fact_329_order__less__le,axiom,
    ! [X_b] :
      ( order(X_b)
     => ! [X_1,Y_2] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2))
        <=> ( ti(X_b,X_1) != ti(X_b,Y_2)
            & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2)) ) ) ),
    file('theBenchmark.p',fact_329_order__less__le) ).

fof(fact_330_less__le__not__le,axiom,
    ! [X_b] :
      ( preorder(X_b)
     => ! [X_1,Y_2] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2))
        <=> ( ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_2),X_1))
            & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2)) ) ) ),
    file('theBenchmark.p',fact_330_less__le__not__le) ).

fof(fact_331_order__le__less,axiom,
    ! [X_b] :
      ( order(X_b)
     => ! [X_1,Y_2] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2))
        <=> ( ti(X_b,X_1) = ti(X_b,Y_2)
            | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2)) ) ) ),
    file('theBenchmark.p',fact_331_order__le__less) ).

fof(fact_332_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_332_leI) ).

fof(fact_333_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_333_not__leE) ).

fof(fact_334_linorder__antisym__conv1,axiom,
    ! [X_b] :
      ( linorder(X_b)
     => ! [X_1,Y_2] :
          ( ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2))
         => ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2))
          <=> ti(X_b,X_1) = ti(X_b,Y_2) ) ) ),
    file('theBenchmark.p',fact_334_linorder__antisym__conv1) ).

fof(fact_335_order__neq__le__trans,axiom,
    ! [X_a] :
      ( order(X_a)
     => ! [A_1,B] :
          ( ti(X_a,A_1) != ti(X_a,B)
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) ) ) ),
    file('theBenchmark.p',fact_335_order__neq__le__trans) ).

fof(fact_336_xt1_I12_J,axiom,
    ! [X_a] :
      ( order(X_a)
     => ! [A_1,B] :
          ( ti(X_a,A_1) != ti(X_a,B)
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)) ) ) ),
    file('theBenchmark.p',fact_336_xt1_I12_J) ).

fof(fact_337_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_337_leD) ).

fof(fact_338_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_338_order__less__imp__le) ).

fof(fact_339_linorder__antisym__conv2,axiom,
    ! [X_b] :
      ( linorder(X_b)
     => ! [X_1,Y_2] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2))
         => ( ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2))
          <=> ti(X_b,X_1) = ti(X_b,Y_2) ) ) ),
    file('theBenchmark.p',fact_339_linorder__antisym__conv2) ).

fof(fact_340_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_340_order__le__imp__less__or__eq) ).

fof(fact_341_order__le__neq__trans,axiom,
    ! [X_a] :
      ( order(X_a)
     => ! [A_1,B] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B))
         => ( ti(X_a,A_1) != ti(X_a,B)
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) ) ) ),
    file('theBenchmark.p',fact_341_order__le__neq__trans) ).

fof(fact_342_xt1_I11_J,axiom,
    ! [X_a] :
      ( order(X_a)
     => ! [B,A_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1))
         => ( ti(X_a,A_1) != ti(X_a,B)
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)) ) ) ),
    file('theBenchmark.p',fact_342_xt1_I11_J) ).

fof(fact_343_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_343_order__less__le__trans) ).

fof(fact_344_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_344_xt1_I7_J) ).

fof(fact_345_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_345_order__le__less__trans) ).

fof(fact_346_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_346_xt1_I8_J) ).

fof(fact_347_add__less__cancel__right,axiom,
    ! [X_b] :
      ( ordere236663937imp_le(X_b)
     => ! [A_2,C_1,B_3] :
          ( 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_3),C_1)))
        <=> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_3)) ) ),
    file('theBenchmark.p',fact_347_add__less__cancel__right) ).

fof(fact_348_add__less__cancel__left,axiom,
    ! [X_b] :
      ( ordere236663937imp_le(X_b)
     => ! [C_1,A_2,B_3] :
          ( 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_3)))
        <=> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_3)) ) ),
    file('theBenchmark.p',fact_348_add__less__cancel__left) ).

fof(fact_349_add__strict__right__mono,axiom,
    ! [X_a] :
      ( ordere223160158up_add(X_a)
     => ! [C,A_1,B] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))
         => 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),C))) ) ),
    file('theBenchmark.p',fact_349_add__strict__right__mono) ).

fof(fact_350_add__strict__left__mono,axiom,
    ! [X_a] :
      ( ordere223160158up_add(X_a)
     => ! [C,A_1,B] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))
         => 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))) ) ),
    file('theBenchmark.p',fact_350_add__strict__left__mono) ).

fof(fact_351_add__strict__mono,axiom,
    ! [X_a] :
      ( ordere223160158up_add(X_a)
     => ! [C,D,A_1,B] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))
         => ( 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),D))) ) ) ),
    file('theBenchmark.p',fact_351_add__strict__mono) ).

fof(fact_352_add__less__imp__less__right,axiom,
    ! [X_a] :
      ( ordere236663937imp_le(X_a)
     => ! [A_1,C,B] :
          ( 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),C)))
         => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) ) ),
    file('theBenchmark.p',fact_352_add__less__imp__less__right) ).

fof(fact_353_add__less__imp__less__left,axiom,
    ! [X_a] :
      ( ordere236663937imp_le(X_a)
     => ! [C,A_1,B] :
          ( 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)))
         => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) ) ),
    file('theBenchmark.p',fact_353_add__less__imp__less__left) ).

fof(fact_354_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_354_not__less__bot) ).

fof(fact_355_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_355_bot__less) ).

fof(fact_356_diff__eq__diff__less,axiom,
    ! [X_b] :
      ( ordered_ab_group_add(X_b)
     => ! [A_2,B_3,C_1,D_1] :
          ( hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3) = 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_3))
          <=> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),D_1)) ) ) ),
    file('theBenchmark.p',fact_356_diff__eq__diff__less) ).

fof(fact_357_not__less__eq,axiom,
    ! [M,Na] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,M))) ),
    file('theBenchmark.p',fact_357_not__less__eq) ).

fof(fact_358_less__Suc__eq,axiom,
    ! [M,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,Na)))
    <=> ( M = Na
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)) ) ),
    file('theBenchmark.p',fact_358_less__Suc__eq) ).

fof(fact_359_Suc__less__eq,axiom,
    ! [M,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,Na)))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)) ),
    file('theBenchmark.p',fact_359_Suc__less__eq) ).

fof(fact_360_not__less__less__Suc__eq,axiom,
    ! [Na,M] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,M)))
      <=> Na = M ) ),
    file('theBenchmark.p',fact_360_not__less__less__Suc__eq) ).

fof(fact_361_less__antisym,axiom,
    ! [N,M_1] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M_1))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,suc,M_1)))
       => M_1 = N ) ),
    file('theBenchmark.p',fact_361_less__antisym) ).

fof(fact_362_less__SucI,axiom,
    ! [M_1,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N))) ),
    file('theBenchmark.p',fact_362_less__SucI) ).

fof(fact_363_Suc__lessI,axiom,
    ! [M_1,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N))
     => ( hAPP(nat,nat,suc,M_1) != N
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_1)),N)) ) ),
    file('theBenchmark.p',fact_363_Suc__lessI) ).

fof(fact_364_less__trans__Suc,axiom,
    ! [K_1,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),J),K_1))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,I_2)),K_1)) ) ),
    file('theBenchmark.p',fact_364_less__trans__Suc) ).

fof(fact_365_less__SucE,axiom,
    ! [M_1,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N)))
     => ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N))
       => M_1 = N ) ),
    file('theBenchmark.p',fact_365_less__SucE) ).

fof(fact_366_Suc__lessD,axiom,
    ! [M_1,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_1)),N))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)) ),
    file('theBenchmark.p',fact_366_Suc__lessD) ).

fof(fact_367_Suc__less__SucD,axiom,
    ! [M_1,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_1)),hAPP(nat,nat,suc,N)))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)) ),
    file('theBenchmark.p',fact_367_Suc__less__SucD) ).

fof(fact_368_not__add__less1,axiom,
    ! [I_2,J] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),J)),I_2)),
    file('theBenchmark.p',fact_368_not__add__less1) ).

fof(fact_369_not__add__less2,axiom,
    ! [J,I_2] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),I_2)),I_2)),
    file('theBenchmark.p',fact_369_not__add__less2) ).

fof(fact_370_nat__add__left__cancel__less,axiom,
    ! [K,M,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),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),Na)))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)) ),
    file('theBenchmark.p',fact_370_nat__add__left__cancel__less) ).

fof(fact_371_trans__less__add1,axiom,
    ! [M_1,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),I_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),M_1))) ),
    file('theBenchmark.p',fact_371_trans__less__add1) ).

fof(fact_372_trans__less__add2,axiom,
    ! [M_1,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),I_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),J))) ),
    file('theBenchmark.p',fact_372_trans__less__add2) ).

fof(fact_373_add__less__mono1,axiom,
    ! [K_1,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,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),K_1))) ),
    file('theBenchmark.p',fact_373_add__less__mono1) ).

fof(fact_374_add__less__mono,axiom,
    ! [K_1,L_1,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),K_1),L_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_2),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),L_1))) ) ),
    file('theBenchmark.p',fact_374_add__less__mono) ).

fof(fact_375_less__add__eq__less,axiom,
    ! [M_1,N,K_1,L_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_1),L_1))
     => ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),L_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N)
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)) ) ),
    file('theBenchmark.p',fact_375_less__add__eq__less) ).

fof(fact_376_add__lessD1,axiom,
    ! [I_2,J,K_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_2),J)),K_1))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),K_1)) ),
    file('theBenchmark.p',fact_376_add__lessD1) ).

fof(fact_377_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_377_termination__basic__simps_I1_J) ).

fof(fact_378_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_378_termination__basic__simps_I2_J) ).

fof(fact_379_nat__less__le,axiom,
    ! [M,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))
    <=> ( M != Na
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)) ) ),
    file('theBenchmark.p',fact_379_nat__less__le) ).

fof(fact_380_le__eq__less__or__eq,axiom,
    ! [M,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na))
    <=> ( M = Na
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)) ) ),
    file('theBenchmark.p',fact_380_le__eq__less__or__eq) ).

fof(fact_381_less__imp__le__nat,axiom,
    ! [M_1,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)) ),
    file('theBenchmark.p',fact_381_less__imp__le__nat) ).

fof(fact_382_le__neq__implies__less,axiom,
    ! [M_1,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N))
     => ( M_1 != N
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)) ) ),
    file('theBenchmark.p',fact_382_le__neq__implies__less) ).

fof(fact_383_less__or__eq__imp__le,axiom,
    ! [M_1,N] :
      ( ( M_1 = N
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)) )
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)) ),
    file('theBenchmark.p',fact_383_less__or__eq__imp__le) ).

fof(fact_384_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_384_termination__basic__simps_I5_J) ).

fof(fact_385_less__imp__diff__less,axiom,
    ! [N,J,K_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J),K_1))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),N)),K_1)) ),
    file('theBenchmark.p',fact_385_less__imp__diff__less) ).

fof(fact_386_diff__less__mono2,axiom,
    ! [L_1,M_1,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),L_1))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L_1),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L_1),M_1))) ) ),
    file('theBenchmark.p',fact_386_diff__less__mono2) ).

fof(fact_387_finite__nat__set__iff__bounded,axiom,
    ! [N_2] :
      ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),N_2))
    <=> ? [M_2] :
        ! [X_2] :
          ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),N_2))
         => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_2),M_2)) ) ),
    file('theBenchmark.p',fact_387_finite__nat__set__iff__bounded) ).

fof(fact_388_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_388_nat__seg__image__imp__finite) ).

fof(fact_389_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_389_card__Collect__less__nat) ).

fof(fact_390_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_390_finite__M__bounded__by__nat) ).

fof(fact_391_add__less__le__mono,axiom,
    ! [X_a] :
      ( ordere223160158up_add(X_a)
     => ! [C,D,A_1,B] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))
         => ( 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),D))) ) ) ),
    file('theBenchmark.p',fact_391_add__less__le__mono) ).

fof(fact_392_add__le__less__mono,axiom,
    ! [X_a] :
      ( ordere223160158up_add(X_a)
     => ! [C,D,A_1,B] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B))
         => ( 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),D))) ) ) ),
    file('theBenchmark.p',fact_392_add__le__less__mono) ).

fof(fact_393_less__add__Suc1,axiom,
    ! [I_2,M_1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),M_1)))),
    file('theBenchmark.p',fact_393_less__add__Suc1) ).

fof(fact_394_less__add__Suc2,axiom,
    ! [I_2,M_1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),I_2)))),
    file('theBenchmark.p',fact_394_less__add__Suc2) ).

fof(fact_395_less__iff__Suc__add,axiom,
    ! [M,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))
    <=> ? [K_2] : Na = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_2)) ),
    file('theBenchmark.p',fact_395_less__iff__Suc__add) ).

fof(fact_396_less__eq__Suc__le,axiom,
    ! [Na,M] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Na)),M)) ),
    file('theBenchmark.p',fact_396_less__eq__Suc__le) ).

fof(fact_397_less__Suc__eq__le,axiom,
    ! [M,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,Na)))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)) ),
    file('theBenchmark.p',fact_397_less__Suc__eq__le) ).

fof(fact_398_Suc__le__eq,axiom,
    ! [M,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M)),Na))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)) ),
    file('theBenchmark.p',fact_398_Suc__le__eq) ).

fof(fact_399_le__imp__less__Suc,axiom,
    ! [M_1,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N))) ),
    file('theBenchmark.p',fact_399_le__imp__less__Suc) ).

fof(fact_400_Suc__leI,axiom,
    ! [M_1,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M_1)),N)) ),
    file('theBenchmark.p',fact_400_Suc__leI) ).

fof(fact_401_le__less__Suc__eq,axiom,
    ! [M,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,M)))
      <=> Na = M ) ),
    file('theBenchmark.p',fact_401_le__less__Suc__eq) ).

fof(fact_402_Suc__le__lessD,axiom,
    ! [M_1,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M_1)),N))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)) ),
    file('theBenchmark.p',fact_402_Suc__le__lessD) ).

fof(fact_403_diff__less__Suc,axiom,
    ! [M_1,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_1),N)),hAPP(nat,nat,suc,M_1))),
    file('theBenchmark.p',fact_403_diff__less__Suc) ).

fof(fact_404_less__diff__conv,axiom,
    ! [I_1,J_1,K] :
      ( 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)))
    <=> 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)),J_1)) ),
    file('theBenchmark.p',fact_404_less__diff__conv) ).

fof(fact_405_add__diff__inverse,axiom,
    ! [M_1,N] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N))
     => hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N)) = M_1 ),
    file('theBenchmark.p',fact_405_add__diff__inverse) ).

fof(fact_406_diff__less__mono,axiom,
    ! [C,A_1,B] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_1),B))
     => ( 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),C))) ) ),
    file('theBenchmark.p',fact_406_diff__less__mono) ).

fof(fact_407_less__diff__iff,axiom,
    ! [Na,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),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),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Na),K)))
        <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)) ) ) ),
    file('theBenchmark.p',fact_407_less__diff__iff) ).

fof(fact_408_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_408_less__eq__Suc__le__raw) ).

fof(fact_409_mono__nat__linear__lb,axiom,
    ! [M,K,F] :
      ( ! [M_2,N_1] :
          ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_1))
         => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,F,M_2)),hAPP(nat,nat,F,N_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),hAPP(nat,nat,F,M)),K)),hAPP(nat,nat,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)))) ),
    file('theBenchmark.p',fact_409_mono__nat__linear__lb) ).

fof(fact_410_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] :
              ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_1))
             => ( hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,I)))
               => hBOOL(hAPP(nat,bool,Pa,I)) ) )
         => hBOOL(hAPP(nat,bool,Pa,I_1)) ) ) ),
    file('theBenchmark.p',fact_410_inc__induct) ).

fof(fact_411_less__imp__Suc__add,axiom,
    ! [M_1,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N))
     => ? [K_2] : N = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_2)) ),
    file('theBenchmark.p',fact_411_less__imp__Suc__add) ).

fof(fact_412_lift__Suc__mono__less__iff,axiom,
    ! [X_b] :
      ( order(X_b)
     => ! [Na,M,F] :
          ( ! [N_1] : hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(nat,X_b,F,N_1)),hAPP(nat,X_b,F,hAPP(nat,nat,suc,N_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)))
          <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M)) ) ) ),
    file('theBenchmark.p',fact_412_lift__Suc__mono__less__iff) ).

fof(fact_413_lift__Suc__mono__less,axiom,
    ! [X_b] :
      ( order(X_b)
     => ! [Na,N_3,F] :
          ( ! [N_1] : hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(nat,X_b,F,N_1)),hAPP(nat,X_b,F,hAPP(nat,nat,suc,N_1))))
         => ( 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_413_lift__Suc__mono__less) ).

fof(fact_414_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_414_less__add__one) ).

fof(fact_415_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_415_less__fun__def) ).

fof(fact_416_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_416_not__psubset__empty) ).

fof(fact_417_subset__psubset__trans,axiom,
    ! [X_b,C_2,A_3,B_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),B_1))
     => ( 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_1),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_417_subset__psubset__trans) ).

fof(fact_418_psubset__subset__trans,axiom,
    ! [X_b,C_2,A_3,B_1] :
      ( 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_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)),B_1),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_418_psubset__subset__trans) ).

fof(fact_419_psubset__imp__subset,axiom,
    ! [X_b,A_3,B_1] :
      ( 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_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),B_1)) ),
    file('theBenchmark.p',fact_419_psubset__imp__subset) ).

fof(fact_420_subset__iff__psubset__eq,axiom,
    ! [X_b,A_3,B_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),B_1))
    <=> ( ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_1)
        | 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_1)) ) ),
    file('theBenchmark.p',fact_420_subset__iff__psubset__eq) ).

fof(fact_421_psubset__eq,axiom,
    ! [X_b,A_3,B_1] :
      ( 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_1))
    <=> ( ti(fun(X_b,bool),A_3) != ti(fun(X_b,bool),B_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),B_1)) ) ),
    file('theBenchmark.p',fact_421_psubset__eq) ).

fof(fact_422_psubset__card__mono,axiom,
    ! [X_b,A_3,B_1] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_1))
     => ( 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_1))
       => 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_1))) ) ),
    file('theBenchmark.p',fact_422_psubset__card__mono) ).

fof(fact_423_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_423_linorder__neqE__linordered__idom) ).

fof(fact_424_psubset__insert__iff,axiom,
    ! [X_b,A_3,X_1,B_1] :
      ( 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_1)))
    <=> ( ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_1))
         => ( ( ~ 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_1)) )
            & ( 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_1)) ) ) )
        & ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_1))
         => 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_1)) ) ) ),
    file('theBenchmark.p',fact_424_psubset__insert__iff) ).

fof(fact_425_card__psubset,axiom,
    ! [X_b,A_3,B_1] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_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),B_1))
       => ( 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_1)))
         => 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_1)) ) ) ),
    file('theBenchmark.p',fact_425_card__psubset) ).

fof(fact_426_finite__conv__nat__seg__image,axiom,
    ! [X_b,A_3] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))
    <=> ? [N_1,F_2] : 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_2),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_1))) ),
    file('theBenchmark.p',fact_426_finite__conv__nat__seg__image) ).

fof(fact_427_bounded__nat__set__is__finite,axiom,
    ! [Na,N_2] :
      ( ! [X_2] :
          ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),N_2))
         => 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_2)) ),
    file('theBenchmark.p',fact_427_bounded__nat__set__is__finite) ).

fof(fact_428_less__mono__imp__le__mono,axiom,
    ! [I_1,J_1,F] :
      ( ! [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,F,I)),hAPP(nat,nat,F,J_2))) )
     => ( 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_428_less__mono__imp__le__mono) ).

fof(fact_429_lessE,axiom,
    ! [I_2,K_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),K_1))
     => ( K_1 != hAPP(nat,nat,suc,I_2)
       => ~ ! [J_2] :
              ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_2))
             => K_1 != hAPP(nat,nat,suc,J_2) ) ) ),
    file('theBenchmark.p',fact_429_lessE) ).

fof(fact_430_Suc__lessE,axiom,
    ! [I_2,K_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,I_2)),K_1))
     => ~ ! [J_2] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_2))
           => K_1 != hAPP(nat,nat,suc,J_2) ) ),
    file('theBenchmark.p',fact_430_Suc__lessE) ).

fof(fact_431_psubsetD,axiom,
    ! [X_b,C_1,A_3,B_1] :
      ( 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_1))
     => ( 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_1)) ) ),
    file('theBenchmark.p',fact_431_psubsetD) ).

fof(fact_432_psubset__trans,axiom,
    ! [X_b,C_2,A_3,B_1] :
      ( 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_1))
     => ( 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_1),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_432_psubset__trans) ).

fof(fact_433_psubset__imp__ex__mem,axiom,
    ! [X_b,A_3,B_1] :
      ( 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_1))
     => ? [B_5] : hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_5),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_1),A_3))) ),
    file('theBenchmark.p',fact_433_psubset__imp__ex__mem) ).

fof(fact_434_xt6,axiom,
    ! [X_c,X_b] :
      ( ( ord(X_c)
        & order(X_b) )
     => ! [C_1,F,B_3,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_3)),A_2))
         => ( hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),C_1),B_3))
           => ( ! [X_2,Y_1] :
                  ( hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),Y_1),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_1)),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_434_xt6) ).

fof(fact_435_xt4,axiom,
    ! [X_c,X_b] :
      ( ( order(X_c)
        & order(X_b) )
     => ! [C_1,F,B_3,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_3)),A_2))
         => ( hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),C_1),B_3))
           => ( ! [X_2,Y_1] :
                  ( hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),Y_1),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_1)),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_435_xt4) ).

fof(fact_436_order__le__less__subst1,axiom,
    ! [X_b,X_c] :
      ( ( order(X_b)
        & order(X_c) )
     => ! [C_1,A_2,F,B_3] :
          ( 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_3)))
         => ( hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),B_3),C_1))
           => ( ! [X_2,Y_1] :
                  ( hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),X_2),Y_1))
                 => 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_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,C_1))) ) ) ) ),
    file('theBenchmark.p',fact_436_order__le__less__subst1) ).

fof(fact_437_order__less__le__subst1,axiom,
    ! [X_b,X_c] :
      ( ( order(X_b)
        & order(X_c) )
     => ! [C_1,A_2,F,B_3] :
          ( 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_3)))
         => ( hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),B_3),C_1))
           => ( ! [X_2,Y_1] :
                  ( hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),X_2),Y_1))
                 => 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_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,C_1))) ) ) ) ),
    file('theBenchmark.p',fact_437_order__less__le__subst1) ).

fof(fact_438_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_438_dense__le) ).

fof(fact_439_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_3] :
                ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),W_3))
               => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),W_3),Y))
                 => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),W_3),Z)) ) )
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z)) ) ) ),
    file('theBenchmark.p',fact_439_dense__le__bounded) ).

fof(fact_440_xt5,axiom,
    ! [X_c,X_b] :
      ( ( order(X_c)
        & order(X_b) )
     => ! [C_1,F,B_3,A_2] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),B_3),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_3)))
           => ( ! [X_2,Y_1] :
                  ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_1),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_1)),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_440_xt5) ).

fof(fact_441_xt7,axiom,
    ! [X_c,X_b] :
      ( ( order(X_c)
        & order(X_b) )
     => ! [C_1,F,B_3,A_2] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),B_3),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_3)))
           => ( ! [X_2,Y_1] :
                  ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_1),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_1)),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_441_xt7) ).

fof(fact_442_order__le__less__subst2,axiom,
    ! [X_b,X_c] :
      ( ( order(X_b)
        & order(X_c) )
     => ! [F,C_1,A_2,B_3] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),B_3))
         => ( hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),hAPP(X_b,X_c,F,B_3)),C_1))
           => ( ! [X_2,Y_1] :
                  ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_2),Y_1))
                 => 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_1))) )
             => 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_442_order__le__less__subst2) ).

fof(fact_443_order__less__le__subst2,axiom,
    ! [X_b,X_c] :
      ( ( order(X_b)
        & order(X_c) )
     => ! [F,C_1,A_2,B_3] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_3))
         => ( hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,B_3)),C_1))
           => ( ! [X_2,Y_1] :
                  ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_2),Y_1))
                 => 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_1))) )
             => 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_443_order__less__le__subst2) ).

fof(fact_444_card__Plus,axiom,
    ! [X_c,X_b,B_1,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_1))
       => 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_1)) = 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_1)) ) ),
    file('theBenchmark.p',fact_444_card__Plus) ).

fof(fact_445_image__cong,axiom,
    ! [X_c,X_b,F,G,M_3,N_2] :
      ( ti(fun(X_b,bool),M_3) = ti(fun(X_b,bool),N_2)
     => ( ! [X_2] :
            ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),N_2))
           => hAPP(X_b,X_c,F,X_2) = hAPP(X_b,X_c,G,X_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),M_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),G),N_2) ) ),
    file('theBenchmark.p',fact_445_image__cong) ).

fof(fact_446_finite__PlusD_I2_J,axiom,
    ! [X_b,X_c,A_3,B_1] :
      ( 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_1)))
     => hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),B_1)) ),
    file('theBenchmark.p',fact_446_finite__PlusD_I2_J) ).

fof(fact_447_finite__PlusD_I1_J,axiom,
    ! [X_b,X_c,A_3,B_1] :
      ( 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_1)))
     => hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) ),
    file('theBenchmark.p',fact_447_finite__PlusD_I1_J) ).

fof(fact_448_finite__Plus,axiom,
    ! [X_c,X_b,B_1,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_1))
       => 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_1))) ) ),
    file('theBenchmark.p',fact_448_finite__Plus) ).

fof(fact_449_finite__Plus__iff,axiom,
    ! [X_b,X_c,A_3,B_1] :
      ( 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_1)))
    <=> ( hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),B_1))
        & hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) ) ),
    file('theBenchmark.p',fact_449_finite__Plus__iff) ).

fof(fact_450_Plus__eq__empty__conv,axiom,
    ! [X_c,X_b,A_3,B_1] :
      ( 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_1) = bot_bot(fun(sum_sum(X_b,X_c),bool))
    <=> ( ti(fun(X_c,bool),B_1) = bot_bot(fun(X_c,bool))
        & ti(fun(X_b,bool),A_3) = bot_bot(fun(X_b,bool)) ) ),
    file('theBenchmark.p',fact_450_Plus__eq__empty__conv) ).

fof(fact_451_card__Plus__conv__if,axiom,
    ! [X_c,X_b,B_1,A_3] :
      ( ( ~ ( hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),B_1))
            & 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_1)) = zero_zero(nat) )
      & ( ( hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),B_1))
          & 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_1)) = 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_1)) ) ),
    file('theBenchmark.p',fact_451_card__Plus__conv__if) ).

fof(fact_452_pred__subset__eq,axiom,
    ! [X_b,R_1,S] :
      ( 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,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)),R_1)),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)),S)))
    <=> 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)),R_1),S)) ),
    file('theBenchmark.p',fact_452_pred__subset__eq) ).

fof(fact_453_Collect__mono,axiom,
    ! [X_b,Q_3,Pa] :
      ( ! [X_2] :
          ( hBOOL(hAPP(X_b,bool,Pa,X_2))
         => hBOOL(hAPP(X_b,bool,Q_3,X_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),collect(X_b),Pa)),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Q_3))) ),
    file('theBenchmark.p',fact_453_Collect__mono) ).

fof(fact_454_less__zeroE,axiom,
    ! [N] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat))),
    file('theBenchmark.p',fact_454_less__zeroE) ).

fof(fact_455_le0,axiom,
    ! [N] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),N)),
    file('theBenchmark.p',fact_455_le0) ).

fof(fact_456_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_456_zero__less__Suc) ).

fof(fact_457_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_457_le__0__eq) ).

fof(fact_458_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_458_less__eq__nat_Osimps_I1_J) ).

fof(fact_459_diffs0__imp__equal,axiom,
    ! [M_1,N] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N) = zero_zero(nat)
     => ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),M_1) = zero_zero(nat)
       => M_1 = N ) ),
    file('theBenchmark.p',fact_459_diffs0__imp__equal) ).

fof(fact_460_diff__self__eq__0,axiom,
    ! [M_1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),M_1) = zero_zero(nat),
    file('theBenchmark.p',fact_460_diff__self__eq__0) ).

fof(fact_461_minus__nat_Odiff__0,axiom,
    ! [M_1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),zero_zero(nat)) = M_1,
    file('theBenchmark.p',fact_461_minus__nat_Odiff__0) ).

fof(fact_462_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_462_diff__0__eq__0) ).

fof(fact_463_one__neq__zero,axiom,
    ! [X_a] :
      ( zero_neq_one(X_a)
     => one_one(X_a) != zero_zero(X_a) ),
    file('theBenchmark.p',fact_463_one__neq__zero) ).

fof(fact_464_zero__neq__one,axiom,
    ! [X_a] :
      ( zero_neq_one(X_a)
     => zero_zero(X_a) != one_one(X_a) ),
    file('theBenchmark.p',fact_464_zero__neq__one) ).

fof(fact_465_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_465_add_Ocomm__neutral) ).

fof(fact_466_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_466_add__0__right) ).

fof(fact_467_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_467_double__zero__sym) ).

fof(fact_468_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_468_add__0) ).

fof(fact_469_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_469_add__0__left) ).

fof(fact_470_right__minus__eq,axiom,
    ! [X_b] :
      ( group_add(X_b)
     => ! [A_2,B_3] :
          ( hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3) = zero_zero(X_b)
        <=> ti(X_b,A_2) = ti(X_b,B_3) ) ),
    file('theBenchmark.p',fact_470_right__minus__eq) ).

fof(fact_471_eq__iff__diff__eq__0,axiom,
    ! [X_b] :
      ( ab_group_add(X_b)
     => ! [A_2,B_3] :
          ( ti(X_b,A_2) = ti(X_b,B_3)
        <=> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3) = zero_zero(X_b) ) ),
    file('theBenchmark.p',fact_471_eq__iff__diff__eq__0) ).

fof(fact_472_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_472_diff__self) ).

fof(fact_473_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_473_diff__0__right) ).

fof(fact_474_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_474_zero__reorient) ).

fof(fact_475_bot__nat__def,axiom,
    bot_bot(nat) = zero_zero(nat),
    file('theBenchmark.p',fact_475_bot__nat__def) ).

fof(fact_476_add__eq__self__zero,axiom,
    ! [M_1,N] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N) = M_1
     => N = zero_zero(nat) ),
    file('theBenchmark.p',fact_476_add__eq__self__zero) ).

fof(fact_477_add__is__0,axiom,
    ! [M,Na] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),Na) = zero_zero(nat)
    <=> ( Na = zero_zero(nat)
        & M = zero_zero(nat) ) ),
    file('theBenchmark.p',fact_477_add__is__0) ).

fof(fact_478_Nat_Oadd__0__right,axiom,
    ! [M_1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),zero_zero(nat)) = M_1,
    file('theBenchmark.p',fact_478_Nat_Oadd__0__right) ).

fof(fact_479_plus__nat_Oadd__0,axiom,
    ! [N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),N) = N,
    file('theBenchmark.p',fact_479_plus__nat_Oadd__0) ).

fof(fact_480_gr0I,axiom,
    ! [N] :
      ( N != zero_zero(nat)
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) ),
    file('theBenchmark.p',fact_480_gr0I) ).

fof(fact_481_gr__implies__not0,axiom,
    ! [M_1,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N))
     => N != zero_zero(nat) ),
    file('theBenchmark.p',fact_481_gr__implies__not0) ).

fof(fact_482_less__nat__zero__code,axiom,
    ! [N] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat))),
    file('theBenchmark.p',fact_482_less__nat__zero__code) ).

fof(fact_483_neq0__conv,axiom,
    ! [Na] :
      ( Na != zero_zero(nat)
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)) ),
    file('theBenchmark.p',fact_483_neq0__conv) ).

fof(fact_484_not__less0,axiom,
    ! [N] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat))),
    file('theBenchmark.p',fact_484_not__less0) ).

fof(fact_485_Suc__neq__Zero,axiom,
    ! [M_1] : hAPP(nat,nat,suc,M_1) != zero_zero(nat),
    file('theBenchmark.p',fact_485_Suc__neq__Zero) ).

fof(fact_486_Zero__neq__Suc,axiom,
    ! [M_1] : zero_zero(nat) != hAPP(nat,nat,suc,M_1),
    file('theBenchmark.p',fact_486_Zero__neq__Suc) ).

fof(fact_487_nat_Osimps_I3_J,axiom,
    ! [Nat_2] : hAPP(nat,nat,suc,Nat_2) != zero_zero(nat),
    file('theBenchmark.p',fact_487_nat_Osimps_I3_J) ).

fof(fact_488_Suc__not__Zero,axiom,
    ! [M_1] : hAPP(nat,nat,suc,M_1) != zero_zero(nat),
    file('theBenchmark.p',fact_488_Suc__not__Zero) ).

fof(fact_489_nat_Osimps_I2_J,axiom,
    ! [Nat_1] : zero_zero(nat) != hAPP(nat,nat,suc,Nat_1),
    file('theBenchmark.p',fact_489_nat_Osimps_I2_J) ).

fof(fact_490_Zero__not__Suc,axiom,
    ! [M_1] : zero_zero(nat) != hAPP(nat,nat,suc,M_1),
    file('theBenchmark.p',fact_490_Zero__not__Suc) ).

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_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_492_zero__le__double__add__iff__zero__le__single__add) ).

fof(fact_493_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_493_double__add__le__zero__iff__single__add__le__zero) ).

fof(fact_494_add__nonneg__nonneg,axiom,
    ! [X_a] :
      ( ordere216010020id_add(X_a)
     => ! [B,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))
           => 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))) ) ) ),
    file('theBenchmark.p',fact_494_add__nonneg__nonneg) ).

fof(fact_495_add__nonneg__eq__0__iff,axiom,
    ! [X_b] :
      ( ordere216010020id_add(X_b)
     => ! [Y_2,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_2))
           => ( hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),X_1),Y_2) = zero_zero(X_b)
            <=> ( ti(X_b,Y_2) = zero_zero(X_b)
                & ti(X_b,X_1) = zero_zero(X_b) ) ) ) ) ),
    file('theBenchmark.p',fact_495_add__nonneg__eq__0__iff) ).

fof(fact_496_add__increasing,axiom,
    ! [X_a] :
      ( ordere216010020id_add(X_a)
     => ! [B,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),C))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C))) ) ) ),
    file('theBenchmark.p',fact_496_add__increasing) ).

fof(fact_497_add__increasing2,axiom,
    ! [X_a] :
      ( ordere216010020id_add(X_a)
     => ! [B,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),A_1))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C))) ) ) ),
    file('theBenchmark.p',fact_497_add__increasing2) ).

fof(fact_498_add__nonpos__nonpos,axiom,
    ! [X_a] :
      ( ordere216010020id_add(X_a)
     => ! [B,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),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)),zero_zero(X_a))) ) ) ),
    file('theBenchmark.p',fact_498_add__nonpos__nonpos) ).

fof(fact_499_zero__less__double__add__iff__zero__less__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(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(X_b),zero_zero(X_b)),A_2)) ) ),
    file('theBenchmark.p',fact_499_zero__less__double__add__iff__zero__less__single__add) ).

fof(fact_500_double__add__less__zero__iff__single__add__less__zero,axiom,
    ! [X_b] :
      ( linord219039673up_add(X_b)
     => ! [A_2] :
          ( 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),A_2)),zero_zero(X_b)))
        <=> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),zero_zero(X_b))) ) ),
    file('theBenchmark.p',fact_500_double__add__less__zero__iff__single__add__less__zero) ).

fof(fact_501_add__pos__pos,axiom,
    ! [X_a] :
      ( ordere216010020id_add(X_a)
     => ! [B,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),zero_zero(X_a)),B))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(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))) ) ) ),
    file('theBenchmark.p',fact_501_add__pos__pos) ).

fof(fact_502_add__neg__neg,axiom,
    ! [X_a] :
      ( ordere216010020id_add(X_a)
     => ! [B,A_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a)))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a)))
           => 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),B)),zero_zero(X_a))) ) ) ),
    file('theBenchmark.p',fact_502_add__neg__neg) ).

fof(fact_503_pos__add__strict,axiom,
    ! [X_a] :
      ( linordered_semidom(X_a)
     => ! [B,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),C))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C))) ) ) ),
    file('theBenchmark.p',fact_503_pos__add__strict) ).

fof(fact_504_le__iff__diff__le__0,axiom,
    ! [X_b] :
      ( ordered_ab_group_add(X_b)
     => ! [A_2,B_3] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),B_3))
        <=> 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_3)),zero_zero(X_b))) ) ),
    file('theBenchmark.p',fact_504_le__iff__diff__le__0) ).

fof(fact_505_less__iff__diff__less__0,axiom,
    ! [X_b] :
      ( ordered_ab_group_add(X_b)
     => ! [A_2,B_3] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_3))
        <=> 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),minus_minus(X_b),A_2),B_3)),zero_zero(X_b))) ) ),
    file('theBenchmark.p',fact_505_less__iff__diff__less__0) ).

fof(fact_506_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_506_not__one__le__zero) ).

fof(fact_507_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_507_zero__le__one) ).

fof(fact_508_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_508_zero__less__one) ).

fof(fact_509_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_509_not__one__less__zero) ).

fof(fact_510_gr0__conv__Suc,axiom,
    ! [Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na))
    <=> ? [M_2] : Na = hAPP(nat,nat,suc,M_2) ),
    file('theBenchmark.p',fact_510_gr0__conv__Suc) ).

fof(fact_511_less__Suc0,axiom,
    ! [Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,zero_zero(nat))))
    <=> Na = zero_zero(nat) ),
    file('theBenchmark.p',fact_511_less__Suc0) ).

fof(fact_512_less__Suc__eq__0__disj,axiom,
    ! [M,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,Na)))
    <=> ( ? [J_2] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_2),Na))
            & M = hAPP(nat,nat,suc,J_2) )
        | M = zero_zero(nat) ) ),
    file('theBenchmark.p',fact_512_less__Suc__eq__0__disj) ).

fof(fact_513_one__is__add,axiom,
    ! [M,Na] :
      ( hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),Na)
    <=> ( ( Na = hAPP(nat,nat,suc,zero_zero(nat))
          & M = zero_zero(nat) )
        | ( Na = zero_zero(nat)
          & M = hAPP(nat,nat,suc,zero_zero(nat)) ) ) ),
    file('theBenchmark.p',fact_513_one__is__add) ).

fof(fact_514_add__is__1,axiom,
    ! [M,Na] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),Na) = hAPP(nat,nat,suc,zero_zero(nat))
    <=> ( ( Na = hAPP(nat,nat,suc,zero_zero(nat))
          & M = zero_zero(nat) )
        | ( Na = zero_zero(nat)
          & M = hAPP(nat,nat,suc,zero_zero(nat)) ) ) ),
    file('theBenchmark.p',fact_514_add__is__1) ).

fof(fact_515_add__gr__0,axiom,
    ! [M,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),Na)))
    <=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M)) ) ),
    file('theBenchmark.p',fact_515_add__gr__0) ).

fof(fact_516_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_516_card_Oempty) ).

fof(fact_517_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_517_card__infinite) ).

fof(fact_518_zero__less__diff,axiom,
    ! [Na,M] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Na),M)))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)) ),
    file('theBenchmark.p',fact_518_zero__less__diff) ).

fof(fact_519_diff__less,axiom,
    ! [M_1,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),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),N)),M_1)) ) ),
    file('theBenchmark.p',fact_519_diff__less) ).

fof(fact_520_diff__add__0,axiom,
    ! [N,M_1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M_1)) = zero_zero(nat),
    file('theBenchmark.p',fact_520_diff__add__0) ).

fof(fact_521_diff__is__0__eq,axiom,
    ! [M,Na] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),Na) = zero_zero(nat)
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)) ),
    file('theBenchmark.p',fact_521_diff__is__0__eq) ).

fof(fact_522_diff__is__0__eq_H,axiom,
    ! [M_1,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N))
     => hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N) = zero_zero(nat) ),
    file('theBenchmark.p',fact_522_diff__is__0__eq_H) ).

fof(fact_523_One__nat__def,axiom,
    one_one(nat) = hAPP(nat,nat,suc,zero_zero(nat)),
    file('theBenchmark.p',fact_523_One__nat__def) ).

fof(fact_524_diff__Suc,axiom,
    ! [M,Na] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,suc,Na)) = hAPP(nat,nat,hAPP(fun(nat,nat),fun(nat,nat),hAPP(nat,fun(fun(nat,nat),fun(nat,nat)),nat_case(nat),zero_zero(nat)),combi(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),Na)),
    file('theBenchmark.p',fact_524_diff__Suc) ).

fof(fact_525_add__pos__nonneg,axiom,
    ! [X_a] :
      ( ordere216010020id_add(X_a)
     => ! [B,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_eq(X_a),zero_zero(X_a)),B))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(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))) ) ) ),
    file('theBenchmark.p',fact_525_add__pos__nonneg) ).

fof(fact_526_add__nonneg__pos,axiom,
    ! [X_a] :
      ( ordere216010020id_add(X_a)
     => ! [B,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(X_a),zero_zero(X_a)),B))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(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))) ) ) ),
    file('theBenchmark.p',fact_526_add__nonneg__pos) ).

fof(fact_527_add__strict__increasing,axiom,
    ! [X_a] :
      ( ordere216010020id_add(X_a)
     => ! [B,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_eq(X_a),B),C))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C))) ) ) ),
    file('theBenchmark.p',fact_527_add__strict__increasing) ).

fof(fact_528_add__strict__increasing2,axiom,
    ! [X_a] :
      ( ordere216010020id_add(X_a)
     => ! [B,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(X_a),B),C))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C))) ) ) ),
    file('theBenchmark.p',fact_528_add__strict__increasing2) ).

fof(fact_529_add__neg__nonpos,axiom,
    ! [X_a] :
      ( ordere216010020id_add(X_a)
     => ! [B,A_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(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),zero_zero(X_a)))
           => 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),B)),zero_zero(X_a))) ) ) ),
    file('theBenchmark.p',fact_529_add__neg__nonpos) ).

fof(fact_530_add__nonpos__neg,axiom,
    ! [X_a] :
      ( ordere216010020id_add(X_a)
     => ! [B,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(X_a),B),zero_zero(X_a)))
           => 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),B)),zero_zero(X_a))) ) ) ),
    file('theBenchmark.p',fact_530_add__nonpos__neg) ).

fof(fact_531_zero__less__two,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)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),one_one(X_a)))) ),
    file('theBenchmark.p',fact_531_zero__less__two) ).

fof(fact_532_bot__empty__eq,axiom,
    ! [X_b,X_2] :
      ( hBOOL(hAPP(X_b,bool,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),bot_bot(fun(X_b,bool)))) ),
    file('theBenchmark.p',fact_532_bot__empty__eq) ).

fof(fact_533_card__eq__0__iff,axiom,
    ! [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))
        | ti(fun(X_b,bool),A_3) = bot_bot(fun(X_b,bool)) ) ),
    file('theBenchmark.p',fact_533_card__eq__0__iff) ).

fof(fact_534_card__ge__0__finite,axiom,
    ! [X_b,A_3] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),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)) ),
    file('theBenchmark.p',fact_534_card__ge__0__finite) ).

fof(fact_535_Suc__pred,axiom,
    ! [N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))
     => hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,suc,zero_zero(nat)))) = N ),
    file('theBenchmark.p',fact_535_Suc__pred) ).

fof(fact_536_diff__Suc__less,axiom,
    ! [I_2,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,suc,I_2))),N)) ),
    file('theBenchmark.p',fact_536_diff__Suc__less) ).

fof(fact_537_rev__predicate1D,axiom,
    ! [X_b,Q_3,Pa,X_1] :
      ( hBOOL(hAPP(X_b,bool,Pa,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)),Pa),Q_3))
       => hBOOL(hAPP(X_b,bool,Q_3,X_1)) ) ),
    file('theBenchmark.p',fact_537_rev__predicate1D) ).

fof(fact_538_predicate1D,axiom,
    ! [X_b,X_1,Pa,Q_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)),Pa),Q_3))
     => ( hBOOL(hAPP(X_b,bool,Pa,X_1))
       => hBOOL(hAPP(X_b,bool,Q_3,X_1)) ) ),
    file('theBenchmark.p',fact_538_predicate1D) ).

fof(fact_539_nat__diff__split,axiom,
    ! [Pa,A_2,B_3] :
      ( hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A_2),B_3)))
    <=> ( ! [D_2] :
            ( A_2 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B_3),D_2)
           => hBOOL(hAPP(nat,bool,Pa,D_2)) )
        & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_2),B_3))
         => hBOOL(hAPP(nat,bool,Pa,zero_zero(nat))) ) ) ),
    file('theBenchmark.p',fact_539_nat__diff__split) ).

fof(fact_540_nat__diff__split__asm,axiom,
    ! [Pa,A_2,B_3] :
      ( hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A_2),B_3)))
    <=> ~ ( ? [D_2] :
              ( ~ hBOOL(hAPP(nat,bool,Pa,D_2))
              & A_2 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B_3),D_2) )
          | ( ~ hBOOL(hAPP(nat,bool,Pa,zero_zero(nat)))
            & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_2),B_3)) ) ) ),
    file('theBenchmark.p',fact_540_nat__diff__split__asm) ).

fof(fact_541_card__less__Suc,axiom,
    ! [I_1,M_3] :
      ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),M_3))
     => hAPP(nat,nat,suc,hAPP(fun(nat,bool),nat,finite_card(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),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),M_3))),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))))) = hAPP(fun(nat,bool),nat,finite_card(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),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),M_3))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,I_1))))) ),
    file('theBenchmark.p',fact_541_card__less__Suc) ).

fof(fact_542_card__less,axiom,
    ! [I_1,M_3] :
      ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),M_3))
     => hAPP(fun(nat,bool),nat,finite_card(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),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),M_3))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,I_1))))) != zero_zero(nat) ),
    file('theBenchmark.p',fact_542_card__less) ).

fof(fact_543_card__less__Suc2,axiom,
    ! [I_1,M_3] :
      ( ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),M_3))
     => hAPP(fun(nat,bool),nat,finite_card(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),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),M_3))),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)))) = hAPP(fun(nat,bool),nat,finite_card(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),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),M_3))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,I_1))))) ),
    file('theBenchmark.p',fact_543_card__less__Suc2) ).

fof(fact_544_card__gt__0__iff,axiom,
    ! [X_b,A_3] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),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))
        & ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) ) ),
    file('theBenchmark.p',fact_544_card__gt__0__iff) ).

fof(fact_545_Suc__diff__1,axiom,
    ! [N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))
     => hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat))) = N ),
    file('theBenchmark.p',fact_545_Suc__diff__1) ).

fof(fact_546_Suc__pred_H,axiom,
    ! [N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))
     => N = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat))) ),
    file('theBenchmark.p',fact_546_Suc__pred_H) ).

fof(fact_547_add__eq__if,axiom,
    ! [N,M_1] :
      ( ( M_1 != zero_zero(nat)
       => hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),one_one(nat))),N)) )
      & ( M_1 = zero_zero(nat)
       => hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N) = N ) ),
    file('theBenchmark.p',fact_547_add__eq__if) ).

fof(fact_548_ex__least__nat__less,axiom,
    ! [Na,Pa] :
      ( ~ hBOOL(hAPP(nat,bool,Pa,zero_zero(nat)))
     => ( hBOOL(hAPP(nat,bool,Pa,Na))
       => ? [K_2] :
            ( hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_2),one_one(nat))))
            & ! [I] :
                ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),K_2))
               => ~ hBOOL(hAPP(nat,bool,Pa,I)) )
            & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_2),Na)) ) ) ),
    file('theBenchmark.p',fact_548_ex__least__nat__less) ).

fof(fact_549_card__Suc__eq,axiom,
    ! [X_b,A_3,K] :
      ( hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3) = hAPP(nat,nat,suc,K)
    <=> ? [B_5,B_4] :
          ( ( K = zero_zero(nat)
           => ti(fun(X_b,bool),B_4) = bot_bot(fun(X_b,bool)) )
          & hAPP(fun(X_b,bool),nat,finite_card(X_b),B_4) = K
          & ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_5),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),B_5),B_4) ) ),
    file('theBenchmark.p',fact_549_card__Suc__eq) ).

fof(fact_550_card_Oneutral,axiom,
    ! [X_b,A_3] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(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))
         => one_one(nat) = zero_zero(nat) )
       => hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3) = zero_zero(nat) ) ),
    file('theBenchmark.p',fact_550_card_Oneutral) ).

fof(fact_551_ex__least__nat__le,axiom,
    ! [Na,Pa] :
      ( ~ hBOOL(hAPP(nat,bool,Pa,zero_zero(nat)))
     => ( hBOOL(hAPP(nat,bool,Pa,Na))
       => ? [K_2] :
            ( hBOOL(hAPP(nat,bool,Pa,K_2))
            & ! [I] :
                ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),K_2))
               => ~ hBOOL(hAPP(nat,bool,Pa,I)) )
            & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_2),Na)) ) ) ),
    file('theBenchmark.p',fact_551_ex__least__nat__le) ).

fof(fact_552_less__imp__add__positive,axiom,
    ! [I_2,J] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J))
     => ? [K_2] :
          ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),K_2) = J
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_2)) ) ),
    file('theBenchmark.p',fact_552_less__imp__add__positive) ).

fof(fact_553_gr0__implies__Suc,axiom,
    ! [N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))
     => ? [M_2] : N = hAPP(nat,nat,suc,M_2) ),
    file('theBenchmark.p',fact_553_gr0__implies__Suc) ).

fof(fact_554_even__less__0__iff,axiom,
    ! [X_b] :
      ( linordered_idom(X_b)
     => ! [A_2] :
          ( 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),A_2)),zero_zero(X_b)))
        <=> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),zero_zero(X_b))) ) ),
    file('theBenchmark.p',fact_554_even__less__0__iff) ).

fof(fact_555_double__eq__0__iff,axiom,
    ! [X_b] :
      ( linord219039673up_add(X_b)
     => ! [A_2] :
          ( 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)
        <=> ti(X_b,A_2) = zero_zero(X_b) ) ),
    file('theBenchmark.p',fact_555_double__eq__0__iff) ).

fof(fact_556_card__eq__SucD,axiom,
    ! [X_b,A_3,K] :
      ( hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3) = hAPP(nat,nat,suc,K)
     => ? [B_5,B_4] :
          ( ( K = zero_zero(nat)
           => ti(fun(X_b,bool),B_4) = bot_bot(fun(X_b,bool)) )
          & hAPP(fun(X_b,bool),nat,finite_card(X_b),B_4) = K
          & ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_5),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),B_5),B_4) ) ),
    file('theBenchmark.p',fact_556_card__eq__SucD) ).

fof(fact_557_nat_Oexhaust,axiom,
    ! [Y] :
      ( Y != zero_zero(nat)
     => ~ ! [Nat] : Y != hAPP(nat,nat,suc,Nat) ),
    file('theBenchmark.p',fact_557_nat_Oexhaust) ).

fof(fact_558_zero__induct,axiom,
    ! [Pa,K] :
      ( hBOOL(hAPP(nat,bool,Pa,K))
     => ( ! [N_1] :
            ( hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,N_1)))
           => hBOOL(hAPP(nat,bool,Pa,N_1)) )
       => hBOOL(hAPP(nat,bool,Pa,zero_zero(nat))) ) ),
    file('theBenchmark.p',fact_558_zero__induct) ).

fof(fact_559_not0__implies__Suc,axiom,
    ! [N] :
      ( N != zero_zero(nat)
     => ? [M_2] : N = hAPP(nat,nat,suc,M_2) ),
    file('theBenchmark.p',fact_559_not0__implies__Suc) ).

fof(fact_560_nat__induct,axiom,
    ! [Na,Pa] :
      ( hBOOL(hAPP(nat,bool,Pa,zero_zero(nat)))
     => ( ! [N_1] :
            ( hBOOL(hAPP(nat,bool,Pa,N_1))
           => hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,N_1))) )
       => hBOOL(hAPP(nat,bool,Pa,Na)) ) ),
    file('theBenchmark.p',fact_560_nat__induct) ).

fof(fact_561_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
    ! [X_a] :
      ( comm_semiring_1(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_561_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).

fof(fact_562_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
    ! [X_a] :
      ( comm_semiring_1(X_a)
     => ! [A_1,B,C,D] : 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)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),D)) = 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),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D)) ),
    file('theBenchmark.p',fact_562_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).

fof(fact_563_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
    ! [X_a] :
      ( comm_semiring_1(X_a)
     => ! [A_1,B,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)),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),C)),B) ),
    file('theBenchmark.p',fact_563_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).

fof(fact_564_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
    ! [X_a] :
      ( comm_semiring_1(X_a)
     => ! [A_1,B,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)),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),C)) ),
    file('theBenchmark.p',fact_564_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).

fof(fact_565_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
    ! [X_a] :
      ( comm_semiring_1(X_a)
     => ! [A_1,C,D] : 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),C),D)) = 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),C)),D) ),
    file('theBenchmark.p',fact_565_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).

fof(fact_566_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
    ! [X_a] :
      ( comm_semiring_1(X_a)
     => ! [A_1,C,D] : 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),C),D)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),D)) ),
    file('theBenchmark.p',fact_566_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).

fof(fact_567_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
    ! [X_a] :
      ( comm_semiring_1(X_a)
     => ! [A_1,C] : 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),C),A_1) ),
    file('theBenchmark.p',fact_567_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).

fof(fact_568_add__0__iff,axiom,
    ! [X_b] :
      ( semiri456707255roduct(X_b)
     => ! [B_3,A_2] :
          ( ti(X_b,B_3) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),B_3),A_2)
        <=> ti(X_b,A_2) = zero_zero(X_b) ) ),
    file('theBenchmark.p',fact_568_add__0__iff) ).

fof(fact_569_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
    ! [X_a] :
      ( comm_semiring_1(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_569_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).

fof(fact_570_field__le__epsilon,axiom,
    ! [X_a] :
      ( linordered_field(X_a)
     => ! [X,Y] :
          ( ! [E_2] :
              ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),E_2))
             => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Y),E_2))) )
         => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) ) ),
    file('theBenchmark.p',fact_570_field__le__epsilon) ).

fof(fact_571_card_Oeq__fold__g,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) = hAPP(fun(X_b,bool),nat,hAPP(nat,fun(fun(X_b,bool),nat),hAPP(fun(X_b,nat),fun(nat,fun(fun(X_b,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(X_b,nat),fun(nat,fun(fun(X_b,bool),nat))),finite_fold_image(nat,X_b),plus_plus(nat)),hAPP(nat,fun(X_b,nat),combk(nat,X_b),one_one(nat))),zero_zero(nat)),A_3) ),
    file('theBenchmark.p',fact_571_card_Oeq__fold__g) ).

fof(fact_572_card__def,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) )
      & ( 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) = hAPP(fun(X_b,bool),nat,hAPP(nat,fun(fun(X_b,bool),nat),hAPP(fun(X_b,nat),fun(nat,fun(fun(X_b,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(X_b,nat),fun(nat,fun(fun(X_b,bool),nat))),finite_fold_image(nat,X_b),plus_plus(nat)),hAPP(nat,fun(X_b,nat),combk(nat,X_b),one_one(nat))),zero_zero(nat)),A_3) ) ),
    file('theBenchmark.p',fact_572_card__def) ).

fof(fact_573_fold__image__empty,axiom,
    ! [X_c,X_b,F,G,Z_2] : hAPP(fun(X_c,bool),X_b,hAPP(X_b,fun(fun(X_c,bool),X_b),hAPP(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b))),finite_fold_image(X_b,X_c),F),G),Z_2),bot_bot(fun(X_c,bool))) = ti(X_b,Z_2),
    file('theBenchmark.p',fact_573_fold__image__empty) ).

fof(fact_574_folding__image__simple_Oeq__fold__g,axiom,
    ! [X_c,X_b,A_3,F,Z_2,G,F_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_2),G),F_1))
     => ( hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),A_3))
       => hAPP(fun(X_c,bool),X_b,F_1,A_3) = hAPP(fun(X_c,bool),X_b,hAPP(X_b,fun(fun(X_c,bool),X_b),hAPP(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b))),finite_fold_image(X_b,X_c),F),G),Z_2),A_3) ) ),
    file('theBenchmark.p',fact_574_folding__image__simple_Oeq__fold__g) ).

fof(fact_575_Ints__odd__less__0,axiom,
    ! [X_b] :
      ( linordered_idom(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),ring_1_Ints(X_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),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),one_one(X_b)),A_2)),A_2)),zero_zero(X_b)))
          <=> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),zero_zero(X_b))) ) ) ),
    file('theBenchmark.p',fact_575_Ints__odd__less__0) ).

fof(fact_576_expand__Suc,axiom,
    ! [V] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),V)))
     => hAPP(int,nat,number_number_of(nat),V) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,number_number_of(nat),V)),one_one(nat))) ),
    file('theBenchmark.p',fact_576_expand__Suc) ).

fof(fact_577_convex__bound__lt,axiom,
    ! [X_a] :
      ( linord626643107strict(X_a)
     => ! [V,U_1,Y,X,A_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),A_1))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),A_1))
           => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),U_1))
             => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),V))
               => ( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),U_1),V) = one_one(X_a)
                 => 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),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),U_1),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),V),Y))),A_1)) ) ) ) ) ) ),
    file('theBenchmark.p',fact_577_convex__bound__lt) ).

fof(fact_578_Ints__diff,axiom,
    ! [X_b] :
      ( ring_1(X_b)
     => ! [B_3,A_2] :
          ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),ring_1_Ints(X_b)))
         => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_3),ring_1_Ints(X_b)))
           => 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),minus_minus(X_b),A_2),B_3)),ring_1_Ints(X_b))) ) ) ),
    file('theBenchmark.p',fact_578_Ints__diff) ).

fof(fact_579_mult__zero__left,axiom,
    ! [X_a] :
      ( mult_zero(X_a)
     => ! [A_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),zero_zero(X_a)),A_1) = zero_zero(X_a) ),
    file('theBenchmark.p',fact_579_mult__zero__left) ).

fof(fact_580_mult__zero__right,axiom,
    ! [X_a] :
      ( mult_zero(X_a)
     => ! [A_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),zero_zero(X_a)) = zero_zero(X_a) ),
    file('theBenchmark.p',fact_580_mult__zero__right) ).

fof(fact_581_mult__eq__0__iff,axiom,
    ! [X_b] :
      ( ring_n68954251visors(X_b)
     => ! [A_2,B_3] :
          ( hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),B_3) = zero_zero(X_b)
        <=> ( ti(X_b,B_3) = zero_zero(X_b)
            | ti(X_b,A_2) = zero_zero(X_b) ) ) ),
    file('theBenchmark.p',fact_581_mult__eq__0__iff) ).

fof(fact_582_no__zero__divisors,axiom,
    ! [X_a] :
      ( no_zero_divisors(X_a)
     => ! [B,A_1] :
          ( ti(X_a,A_1) != zero_zero(X_a)
         => ( ti(X_a,B) != zero_zero(X_a)
           => hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B) != zero_zero(X_a) ) ) ),
    file('theBenchmark.p',fact_582_no__zero__divisors) ).

fof(fact_583_divisors__zero,axiom,
    ! [X_a] :
      ( no_zero_divisors(X_a)
     => ! [A_1,B] :
          ( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B) = zero_zero(X_a)
         => ( ti(X_a,B) = zero_zero(X_a)
            | ti(X_a,A_1) = zero_zero(X_a) ) ) ),
    file('theBenchmark.p',fact_583_divisors__zero) ).

fof(fact_584_mult__0,axiom,
    ! [N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),zero_zero(nat)),N) = zero_zero(nat),
    file('theBenchmark.p',fact_584_mult__0) ).

fof(fact_585_mult__0__right,axiom,
    ! [M_1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),zero_zero(nat)) = zero_zero(nat),
    file('theBenchmark.p',fact_585_mult__0__right) ).

fof(fact_586_mult__is__0,axiom,
    ! [M,Na] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na) = zero_zero(nat)
    <=> ( Na = zero_zero(nat)
        | M = zero_zero(nat) ) ),
    file('theBenchmark.p',fact_586_mult__is__0) ).

fof(fact_587_mult__cancel1,axiom,
    ! [K,M,Na] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na)
    <=> ( K = zero_zero(nat)
        | M = Na ) ),
    file('theBenchmark.p',fact_587_mult__cancel1) ).

fof(fact_588_mult__cancel2,axiom,
    ! [M,K,Na] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Na),K)
    <=> ( K = zero_zero(nat)
        | M = Na ) ),
    file('theBenchmark.p',fact_588_mult__cancel2) ).

fof(fact_589_comp__fun__idem,axiom,
    ! [X_b] :
      ( ab_sem1668676832m_mult(X_b)
     => hBOOL(hAPP(fun(X_b,fun(X_b,X_b)),bool,finite_comp_fun_idem(X_b,X_b),times_times(X_b))) ),
    file('theBenchmark.p',fact_589_comp__fun__idem) ).

fof(fact_590_comm__semiring__class_Odistrib,axiom,
    ! [X_a] :
      ( comm_semiring(X_a)
     => ! [A_1,B,C] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),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),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C)) ),
    file('theBenchmark.p',fact_590_comm__semiring__class_Odistrib) ).

fof(fact_591_combine__common__factor,axiom,
    ! [X_a] :
      ( semiring(X_a)
     => ! [A_1,E_1,B,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),times_times(X_a),A_1),E_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),times_times(X_a),B),E_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),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),E_1)),C) ),
    file('theBenchmark.p',fact_591_combine__common__factor) ).

fof(fact_592_mult_Ocomm__neutral,axiom,
    ! [X_a] :
      ( comm_monoid_mult(X_a)
     => ! [A_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),one_one(X_a)) = ti(X_a,A_1) ),
    file('theBenchmark.p',fact_592_mult_Ocomm__neutral) ).

fof(fact_593_mult__1__right,axiom,
    ! [X_a] :
      ( monoid_mult(X_a)
     => ! [A_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),one_one(X_a)) = ti(X_a,A_1) ),
    file('theBenchmark.p',fact_593_mult__1__right) ).

fof(fact_594_mult__1,axiom,
    ! [X_a] :
      ( comm_monoid_mult(X_a)
     => ! [A_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),one_one(X_a)),A_1) = ti(X_a,A_1) ),
    file('theBenchmark.p',fact_594_mult__1) ).

fof(fact_595_mult__1__left,axiom,
    ! [X_a] :
      ( monoid_mult(X_a)
     => ! [A_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),one_one(X_a)),A_1) = ti(X_a,A_1) ),
    file('theBenchmark.p',fact_595_mult__1__left) ).

fof(fact_596_Suc__mult__cancel1,axiom,
    ! [K,M,Na] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),M) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),Na)
    <=> M = Na ),
    file('theBenchmark.p',fact_596_Suc__mult__cancel1) ).

fof(fact_597_add__mult__distrib,axiom,
    ! [M_1,N,K_1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N)),K_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),K_1)),
    file('theBenchmark.p',fact_597_add__mult__distrib) ).

fof(fact_598_add__mult__distrib2,axiom,
    ! [K_1,M_1,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N)),
    file('theBenchmark.p',fact_598_add__mult__distrib2) ).

fof(fact_599_mult__le__mono,axiom,
    ! [K_1,L_1,I_2,J] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),J))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),L_1))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_2),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),L_1))) ) ),
    file('theBenchmark.p',fact_599_mult__le__mono) ).

fof(fact_600_mult__le__mono2,axiom,
    ! [K_1,I_2,J] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),J))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),I_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),J))) ),
    file('theBenchmark.p',fact_600_mult__le__mono2) ).

fof(fact_601_mult__le__mono1,axiom,
    ! [K_1,I_2,J] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),J))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_2),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),K_1))) ),
    file('theBenchmark.p',fact_601_mult__le__mono1) ).

fof(fact_602_le__cube,axiom,
    ! [M_1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),M_1)))),
    file('theBenchmark.p',fact_602_le__cube) ).

fof(fact_603_le__square,axiom,
    ! [M_1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),M_1))),
    file('theBenchmark.p',fact_603_le__square) ).

fof(fact_604_diff__mult__distrib,axiom,
    ! [M_1,N,K_1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N)),K_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),K_1)),
    file('theBenchmark.p',fact_604_diff__mult__distrib) ).

fof(fact_605_diff__mult__distrib2,axiom,
    ! [K_1,M_1,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N)),
    file('theBenchmark.p',fact_605_diff__mult__distrib2) ).

fof(fact_606_times_Oidem,axiom,
    ! [X_a] :
      ( ab_sem1668676832m_mult(X_a)
     => ! [A_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),A_1) = ti(X_a,A_1) ),
    file('theBenchmark.p',fact_606_times_Oidem) ).

fof(fact_607_mult__idem,axiom,
    ! [X_a] :
      ( ab_sem1668676832m_mult(X_a)
     => ! [X] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),X) = ti(X_a,X) ),
    file('theBenchmark.p',fact_607_mult__idem) ).

fof(fact_608_mult__left__idem,axiom,
    ! [X_a] :
      ( ab_sem1668676832m_mult(X_a)
     => ! [A_1,B] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B) ),
    file('theBenchmark.p',fact_608_mult__left__idem) ).

fof(fact_609_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
    ! [X_a] :
      ( ab_semigroup_mult(X_a)
     => ! [A_1,B,C] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C)) ),
    file('theBenchmark.p',fact_609_ab__semigroup__mult__class_Omult__ac_I1_J) ).

fof(fact_610_nat__mult__eq__1__iff,axiom,
    ! [M,Na] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na) = one_one(nat)
    <=> ( Na = one_one(nat)
        & M = one_one(nat) ) ),
    file('theBenchmark.p',fact_610_nat__mult__eq__1__iff) ).

fof(fact_611_nat__mult__1__right,axiom,
    ! [N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),one_one(nat)) = N,
    file('theBenchmark.p',fact_611_nat__mult__1__right) ).

fof(fact_612_nat__1__eq__mult__iff,axiom,
    ! [M,Na] :
      ( one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na)
    <=> ( Na = one_one(nat)
        & M = one_one(nat) ) ),
    file('theBenchmark.p',fact_612_nat__1__eq__mult__iff) ).

fof(fact_613_nat__mult__1,axiom,
    ! [N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),one_one(nat)),N) = N,
    file('theBenchmark.p',fact_613_nat__mult__1) ).

fof(fact_614_less__number__of,axiom,
    ! [X_b] :
      ( ( linordered_idom(X_b)
        & number_ring(X_b) )
     => ! [X_1,Y_2] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(int,X_b,number_number_of(X_b),X_1)),hAPP(int,X_b,number_number_of(X_b),Y_2)))
        <=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Y_2)) ) ),
    file('theBenchmark.p',fact_614_less__number__of) ).

fof(fact_615_Ints__number__of,axiom,
    ! [X_b] :
      ( number_ring(X_b)
     => ! [W_1] : hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(int,X_b,number_number_of(X_b),W_1)),ring_1_Ints(X_b))) ),
    file('theBenchmark.p',fact_615_Ints__number__of) ).

fof(fact_616_number__of__mult,axiom,
    ! [X_a] :
      ( number_ring(X_a)
     => ! [V,W] : hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),W)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),W)) ),
    file('theBenchmark.p',fact_616_number__of__mult) ).

fof(fact_617_number__of__reorient,axiom,
    ! [X_b] :
      ( number(X_b)
     => ! [W_1,X_1] :
          ( hAPP(int,X_b,number_number_of(X_b),W_1) = ti(X_b,X_1)
        <=> ti(X_b,X_1) = hAPP(int,X_b,number_number_of(X_b),W_1) ) ),
    file('theBenchmark.p',fact_617_number__of__reorient) ).

fof(fact_618_arith__simps_I32_J,axiom,
    ! [X_a] :
      ( number_ring(X_a)
     => ! [V,W] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),W)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),W)) ),
    file('theBenchmark.p',fact_618_arith__simps_I32_J) ).

fof(fact_619_eq__number__of,axiom,
    ! [X_b] :
      ( ( ring_char_0(X_b)
        & number_ring(X_b) )
     => ! [X_1,Y_2] :
          ( hAPP(int,X_b,number_number_of(X_b),X_1) = hAPP(int,X_b,number_number_of(X_b),Y_2)
        <=> X_1 = Y_2 ) ),
    file('theBenchmark.p',fact_619_eq__number__of) ).

fof(fact_620_mult__number__of__left,axiom,
    ! [X_a] :
      ( number_ring(X_a)
     => ! [V,W,Z] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),W)),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),W))),Z) ),
    file('theBenchmark.p',fact_620_mult__number__of__left) ).

fof(fact_621_Ints__mult,axiom,
    ! [X_b] :
      ( ring_1(X_b)
     => ! [B_3,A_2] :
          ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),ring_1_Ints(X_b)))
         => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_3),ring_1_Ints(X_b)))
           => 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),times_times(X_b),A_2),B_3)),ring_1_Ints(X_b))) ) ) ),
    file('theBenchmark.p',fact_621_Ints__mult) ).

fof(fact_622_le__number__of,axiom,
    ! [X_b] :
      ( ( linordered_idom(X_b)
        & number_ring(X_b) )
     => ! [X_1,Y_2] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(int,X_b,number_number_of(X_b),X_1)),hAPP(int,X_b,number_number_of(X_b),Y_2)))
        <=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X_1),Y_2)) ) ),
    file('theBenchmark.p',fact_622_le__number__of) ).

fof(fact_623_number__of__diff,axiom,
    ! [X_a] :
      ( number_ring(X_a)
     => ! [V,W] : hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),V),W)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),W)) ),
    file('theBenchmark.p',fact_623_number__of__diff) ).

fof(fact_624_left__diff__distrib__number__of,axiom,
    ! [X_b] :
      ( ( ring(X_b)
        & number(X_b) )
     => ! [A_1,B,V] : hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_1),B)),hAPP(int,X_b,number_number_of(X_b),V)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_1),hAPP(int,X_b,number_number_of(X_b),V))),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B),hAPP(int,X_b,number_number_of(X_b),V))) ),
    file('theBenchmark.p',fact_624_left__diff__distrib__number__of) ).

fof(fact_625_right__diff__distrib__number__of,axiom,
    ! [X_b] :
      ( ( ring(X_b)
        & number(X_b) )
     => ! [V,B,C] : hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),V)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),B),C)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),V)),B)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),V)),C)) ),
    file('theBenchmark.p',fact_625_right__diff__distrib__number__of) ).

fof(fact_626_Ints__add,axiom,
    ! [X_b] :
      ( ring_1(X_b)
     => ! [B_3,A_2] :
          ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),ring_1_Ints(X_b)))
         => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_3),ring_1_Ints(X_b)))
           => 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),plus_plus(X_b),A_2),B_3)),ring_1_Ints(X_b))) ) ) ),
    file('theBenchmark.p',fact_626_Ints__add) ).

fof(fact_627_number__of__add,axiom,
    ! [X_a] :
      ( number_ring(X_a)
     => ! [V,W] : hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),W)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),W)) ),
    file('theBenchmark.p',fact_627_number__of__add) ).

fof(fact_628_add__number__of__eq,axiom,
    ! [X_a] :
      ( number_ring(X_a)
     => ! [V,W] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),W)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),W)) ),
    file('theBenchmark.p',fact_628_add__number__of__eq) ).

fof(fact_629_right__distrib__number__of,axiom,
    ! [X_b] :
      ( ( semiring(X_b)
        & number(X_b) )
     => ! [V,B,C] : hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),V)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),B),C)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),V)),B)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),V)),C)) ),
    file('theBenchmark.p',fact_629_right__distrib__number__of) ).

fof(fact_630_add__number__of__left,axiom,
    ! [X_a] :
      ( number_ring(X_a)
     => ! [V,W,Z] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),W)),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),W))),Z) ),
    file('theBenchmark.p',fact_630_add__number__of__left) ).

fof(fact_631_left__distrib__number__of,axiom,
    ! [X_b] :
      ( ( semiring(X_b)
        & number(X_b) )
     => ! [A_1,B,V] : hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_1),B)),hAPP(int,X_b,number_number_of(X_b),V)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_1),hAPP(int,X_b,number_number_of(X_b),V))),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B),hAPP(int,X_b,number_number_of(X_b),V))) ),
    file('theBenchmark.p',fact_631_left__distrib__number__of) ).

fof(fact_632_Ints__0,axiom,
    ! [X_b] :
      ( ring_1(X_b)
     => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),zero_zero(X_b)),ring_1_Ints(X_b))) ),
    file('theBenchmark.p',fact_632_Ints__0) ).

fof(fact_633_Ints__1,axiom,
    ! [X_b] :
      ( ring_1(X_b)
     => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),one_one(X_b)),ring_1_Ints(X_b))) ),
    file('theBenchmark.p',fact_633_Ints__1) ).

fof(fact_634_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
    ! [X_a] :
      ( comm_semiring_1(X_a)
     => ! [A_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),one_one(X_a)),A_1) = ti(X_a,A_1) ),
    file('theBenchmark.p',fact_634_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).

fof(fact_635_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
    ! [X_a] :
      ( comm_semiring_1(X_a)
     => ! [A_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),one_one(X_a)) = ti(X_a,A_1) ),
    file('theBenchmark.p',fact_635_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).

fof(fact_636_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
    ! [X_a] :
      ( comm_semiring_1(X_a)
     => ! [A_1,B] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),A_1) ),
    file('theBenchmark.p',fact_636_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).

fof(fact_637_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
    ! [X_a] :
      ( comm_semiring_1(X_a)
     => ! [Lx,Rx,Ry] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ry)) ),
    file('theBenchmark.p',fact_637_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).

fof(fact_638_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
    ! [X_a] :
      ( comm_semiring_1(X_a)
     => ! [Lx,Rx,Ry] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Rx)),Ry) ),
    file('theBenchmark.p',fact_638_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).

fof(fact_639_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
    ! [X_a] :
      ( comm_semiring_1(X_a)
     => ! [Lx,Ly,Rx] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),Rx) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ly),Rx)) ),
    file('theBenchmark.p',fact_639_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).

fof(fact_640_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
    ! [X_a] :
      ( comm_semiring_1(X_a)
     => ! [Lx,Ly,Rx] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),Rx) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Rx)),Ly) ),
    file('theBenchmark.p',fact_640_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).

fof(fact_641_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
    ! [X_a] :
      ( comm_semiring_1(X_a)
     => ! [Lx,Ly,Rx,Ry] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ly),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry))) ),
    file('theBenchmark.p',fact_641_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).

fof(fact_642_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
    ! [X_a] :
      ( comm_semiring_1(X_a)
     => ! [Lx,Ly,Rx,Ry] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),Ry)) ),
    file('theBenchmark.p',fact_642_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).

fof(fact_643_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
    ! [X_a] :
      ( comm_semiring_1(X_a)
     => ! [Lx,Ly,Rx,Ry] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Rx)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ly),Ry)) ),
    file('theBenchmark.p',fact_643_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).

fof(fact_644_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
    ! [X_a] :
      ( comm_semiring_1(X_a)
     => ! [X,Y,Z] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Y),Z)) = 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),times_times(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Z)) ),
    file('theBenchmark.p',fact_644_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).

fof(fact_645_crossproduct__noteq,axiom,
    ! [X_b] :
      ( semiri456707255roduct(X_b)
     => ! [C_1,D_1,A_2,B_3] :
          ( ( ti(X_b,C_1) != ti(X_b,D_1)
            & ti(X_b,A_2) != ti(X_b,B_3) )
        <=> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),D_1)) != hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),D_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),C_1)) ) ),
    file('theBenchmark.p',fact_645_crossproduct__noteq) ).

fof(fact_646_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
    ! [X_a] :
      ( comm_semiring_1(X_a)
     => ! [A_1,B,C] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),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),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C)) ),
    file('theBenchmark.p',fact_646_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).

fof(fact_647_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
    ! [X_a] :
      ( comm_semiring_1(X_a)
     => ! [A_1,M_1,B] : 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),times_times(X_a),A_1),M_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),M_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),M_1) ),
    file('theBenchmark.p',fact_647_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).

fof(fact_648_crossproduct__eq,axiom,
    ! [X_b] :
      ( semiri456707255roduct(X_b)
     => ! [W_1,Y_2,X_1,Z_2] :
          ( hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),W_1),Y_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),Z_2)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),W_1),Z_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),Y_2))
        <=> ( ti(X_b,Y_2) = ti(X_b,Z_2)
            | ti(X_b,W_1) = ti(X_b,X_1) ) ) ),
    file('theBenchmark.p',fact_648_crossproduct__eq) ).

fof(fact_649_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
    ! [X_a] :
      ( comm_semiring_1(X_a)
     => ! [A_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),zero_zero(X_a)),A_1) = zero_zero(X_a) ),
    file('theBenchmark.p',fact_649_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).

fof(fact_650_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
    ! [X_a] :
      ( comm_semiring_1(X_a)
     => ! [A_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),zero_zero(X_a)) = zero_zero(X_a) ),
    file('theBenchmark.p',fact_650_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).

fof(fact_651_le__number__of__eq__not__less,axiom,
    ! [X_b] :
      ( ( linorder(X_b)
        & number(X_b) )
     => ! [V_3,W_1] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(int,X_b,number_number_of(X_b),V_3)),hAPP(int,X_b,number_number_of(X_b),W_1)))
        <=> ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(int,X_b,number_number_of(X_b),W_1)),hAPP(int,X_b,number_number_of(X_b),V_3))) ) ),
    file('theBenchmark.p',fact_651_le__number__of__eq__not__less) ).

fof(fact_652_add__number__of__diff1,axiom,
    ! [X_a] :
      ( number_ring(X_a)
     => ! [V,W,C] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),W)),C)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),W))),C) ),
    file('theBenchmark.p',fact_652_add__number__of__diff1) ).

fof(fact_653_split__mult__neg__le,axiom,
    ! [X_a] :
      ( ordere453448008miring(X_a)
     => ! [B,A_1] :
          ( ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B))
              & 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),zero_zero(X_a)))
              & 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),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),zero_zero(X_a))) ) ),
    file('theBenchmark.p',fact_653_split__mult__neg__le) ).

fof(fact_654_split__mult__pos__le,axiom,
    ! [X_a] :
      ( ordered_ring(X_a)
     => ! [B,A_1] :
          ( ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),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))) )
            | ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B))
              & 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)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))) ) ),
    file('theBenchmark.p',fact_654_split__mult__pos__le) ).

fof(fact_655_mult__mono,axiom,
    ! [X_a] :
      ( ordered_semiring(X_a)
     => ! [C,D,A_1,B] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B))
         => ( 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),zero_zero(X_a)),B))
             => ( 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),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D))) ) ) ) ) ),
    file('theBenchmark.p',fact_655_mult__mono) ).

fof(fact_656_mult__mono_H,axiom,
    ! [X_a] :
      ( ordered_semiring(X_a)
     => ! [C,D,A_1,B] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B))
         => ( 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),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)),C))
               => 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),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D))) ) ) ) ) ),
    file('theBenchmark.p',fact_656_mult__mono_H) ).

fof(fact_657_mult__left__mono__neg,axiom,
    ! [X_a] :
      ( ordered_ring(X_a)
     => ! [C,B,A_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),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),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B))) ) ) ),
    file('theBenchmark.p',fact_657_mult__left__mono__neg) ).

fof(fact_658_mult__right__mono__neg,axiom,
    ! [X_a] :
      ( ordered_ring(X_a)
     => ! [C,B,A_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),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),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C))) ) ) ),
    file('theBenchmark.p',fact_658_mult__right__mono__neg) ).

fof(fact_659_comm__mult__left__mono,axiom,
    ! [X_a] :
      ( ordere1490568538miring(X_a)
     => ! [C,A_1,B] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B))
         => ( 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),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B))) ) ) ),
    file('theBenchmark.p',fact_659_comm__mult__left__mono) ).

fof(fact_660_mult__left__mono,axiom,
    ! [X_a] :
      ( ordered_semiring(X_a)
     => ! [C,A_1,B] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B))
         => ( 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),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B))) ) ) ),
    file('theBenchmark.p',fact_660_mult__left__mono) ).

fof(fact_661_mult__right__mono,axiom,
    ! [X_a] :
      ( ordered_semiring(X_a)
     => ! [C,A_1,B] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B))
         => ( 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),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C))) ) ) ),
    file('theBenchmark.p',fact_661_mult__right__mono) ).

fof(fact_662_mult__nonpos__nonpos,axiom,
    ! [X_a] :
      ( ordered_ring(X_a)
     => ! [B,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),zero_zero(X_a)))
           => 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),times_times(X_a),A_1),B))) ) ) ),
    file('theBenchmark.p',fact_662_mult__nonpos__nonpos) ).

fof(fact_663_mult__nonpos__nonneg,axiom,
    ! [X_a] :
      ( ordere453448008miring(X_a)
     => ! [B,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),zero_zero(X_a)),B))
           => 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),times_times(X_a),A_1),B)),zero_zero(X_a))) ) ) ),
    file('theBenchmark.p',fact_663_mult__nonpos__nonneg) ).

fof(fact_664_mult__nonneg__nonpos2,axiom,
    ! [X_a] :
      ( ordere453448008miring(X_a)
     => ! [B,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),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),times_times(X_a),B),A_1)),zero_zero(X_a))) ) ) ),
    file('theBenchmark.p',fact_664_mult__nonneg__nonpos2) ).

fof(fact_665_mult__nonneg__nonpos,axiom,
    ! [X_a] :
      ( ordere453448008miring(X_a)
     => ! [B,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),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),times_times(X_a),A_1),B)),zero_zero(X_a))) ) ) ),
    file('theBenchmark.p',fact_665_mult__nonneg__nonpos) ).

fof(fact_666_mult__nonneg__nonneg,axiom,
    ! [X_a] :
      ( ordere453448008miring(X_a)
     => ! [B,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))
           => 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),times_times(X_a),A_1),B))) ) ) ),
    file('theBenchmark.p',fact_666_mult__nonneg__nonneg) ).

fof(fact_667_mult__le__0__iff,axiom,
    ! [X_b] :
      ( linord581940658strict(X_b)
     => ! [A_2,B_3] :
          ( 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),times_times(X_b),A_2),B_3)),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)),B_3))
              & 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),B_3),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)),A_2)) ) ) ) ),
    file('theBenchmark.p',fact_667_mult__le__0__iff) ).

fof(fact_668_zero__le__mult__iff,axiom,
    ! [X_b] :
      ( linord581940658strict(X_b)
     => ! [A_2,B_3] :
          ( 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),times_times(X_b),A_2),B_3)))
        <=> ( ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),B_3),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),zero_zero(X_b)),B_3))
              & 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_668_zero__le__mult__iff) ).

fof(fact_669_zero__le__square,axiom,
    ! [X_a] :
      ( linordered_ring(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)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),A_1))) ),
    file('theBenchmark.p',fact_669_zero__le__square) ).

fof(fact_670_not__square__less__zero,axiom,
    ! [X_a] :
      ( linordered_ring(X_a)
     => ! [A_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),times_times(X_a),A_1),A_1)),zero_zero(X_a))) ),
    file('theBenchmark.p',fact_670_not__square__less__zero) ).

fof(fact_671_mult__less__cancel__right__disj,axiom,
    ! [X_b] :
      ( linord581940658strict(X_b)
     => ! [A_2,C_1,B_3] :
          ( 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),times_times(X_b),A_2),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),C_1)))
        <=> ( ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),B_3),A_2))
              & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),zero_zero(X_b))) )
            | ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_3))
              & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),C_1)) ) ) ) ),
    file('theBenchmark.p',fact_671_mult__less__cancel__right__disj) ).

fof(fact_672_mult__less__cancel__left__disj,axiom,
    ! [X_b] :
      ( linord581940658strict(X_b)
     => ! [C_1,A_2,B_3] :
          ( 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),times_times(X_b),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),B_3)))
        <=> ( ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),B_3),A_2))
              & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),zero_zero(X_b))) )
            | ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_3))
              & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),C_1)) ) ) ) ),
    file('theBenchmark.p',fact_672_mult__less__cancel__left__disj) ).

fof(fact_673_mult__less__cancel__left__pos,axiom,
    ! [X_b] :
      ( linord581940658strict(X_b)
     => ! [A_2,B_3,C_1] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),C_1))
         => ( 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),times_times(X_b),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),B_3)))
          <=> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_3)) ) ) ),
    file('theBenchmark.p',fact_673_mult__less__cancel__left__pos) ).

fof(fact_674_mult__pos__pos,axiom,
    ! [X_a] :
      ( linord20386208strict(X_a)
     => ! [B,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),zero_zero(X_a)),B))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))) ) ) ),
    file('theBenchmark.p',fact_674_mult__pos__pos) ).

fof(fact_675_mult__pos__neg,axiom,
    ! [X_a] :
      ( linord20386208strict(X_a)
     => ! [B,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),zero_zero(X_a)))
           => 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),times_times(X_a),A_1),B)),zero_zero(X_a))) ) ) ),
    file('theBenchmark.p',fact_675_mult__pos__neg) ).

fof(fact_676_mult__pos__neg2,axiom,
    ! [X_a] :
      ( linord20386208strict(X_a)
     => ! [B,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),zero_zero(X_a)))
           => 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),times_times(X_a),B),A_1)),zero_zero(X_a))) ) ) ),
    file('theBenchmark.p',fact_676_mult__pos__neg2) ).

fof(fact_677_zero__less__mult__pos,axiom,
    ! [X_a] :
      ( linord20386208strict(X_a)
     => ! [A_1,B] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)))
         => ( 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),zero_zero(X_a)),B)) ) ) ),
    file('theBenchmark.p',fact_677_zero__less__mult__pos) ).

fof(fact_678_zero__less__mult__pos2,axiom,
    ! [X_a] :
      ( linord20386208strict(X_a)
     => ! [B,A_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),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),zero_zero(X_a)),B)) ) ) ),
    file('theBenchmark.p',fact_678_zero__less__mult__pos2) ).

fof(fact_679_mult__less__cancel__left__neg,axiom,
    ! [X_b] :
      ( linord581940658strict(X_b)
     => ! [A_2,B_3,C_1] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),zero_zero(X_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),times_times(X_b),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),B_3)))
          <=> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),B_3),A_2)) ) ) ),
    file('theBenchmark.p',fact_679_mult__less__cancel__left__neg) ).

fof(fact_680_mult__neg__pos,axiom,
    ! [X_a] :
      ( linord20386208strict(X_a)
     => ! [B,A_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a)))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B))
           => 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),times_times(X_a),A_1),B)),zero_zero(X_a))) ) ) ),
    file('theBenchmark.p',fact_680_mult__neg__pos) ).

fof(fact_681_mult__neg__neg,axiom,
    ! [X_a] :
      ( linord581940658strict(X_a)
     => ! [B,A_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a)))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a)))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))) ) ) ),
    file('theBenchmark.p',fact_681_mult__neg__neg) ).

fof(fact_682_mult__strict__right__mono,axiom,
    ! [X_a] :
      ( linord20386208strict(X_a)
     => ! [C,A_1,B] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C))
           => 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),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C))) ) ) ),
    file('theBenchmark.p',fact_682_mult__strict__right__mono) ).

fof(fact_683_mult__strict__left__mono,axiom,
    ! [X_a] :
      ( linord20386208strict(X_a)
     => ! [C,A_1,B] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C))
           => 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),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B))) ) ) ),
    file('theBenchmark.p',fact_683_mult__strict__left__mono) ).

fof(fact_684_comm__mult__strict__left__mono,axiom,
    ! [X_a] :
      ( linord893533164strict(X_a)
     => ! [C,A_1,B] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C))
           => 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),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B))) ) ) ),
    file('theBenchmark.p',fact_684_comm__mult__strict__left__mono) ).

fof(fact_685_mult__strict__right__mono__neg,axiom,
    ! [X_a] :
      ( linord581940658strict(X_a)
     => ! [C,B,A_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),zero_zero(X_a)))
           => 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),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C))) ) ) ),
    file('theBenchmark.p',fact_685_mult__strict__right__mono__neg) ).

fof(fact_686_mult__strict__left__mono__neg,axiom,
    ! [X_a] :
      ( linord581940658strict(X_a)
     => ! [C,B,A_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),zero_zero(X_a)))
           => 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),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B))) ) ) ),
    file('theBenchmark.p',fact_686_mult__strict__left__mono__neg) ).

fof(fact_687_add__scale__eq__noteq,axiom,
    ! [X_a] :
      ( semiri456707255roduct(X_a)
     => ! [C,D,A_1,B,R_3] :
          ( ti(X_a,R_3) != zero_zero(X_a)
         => ( ( ti(X_a,C) != ti(X_a,D)
              & ti(X_a,A_1) = ti(X_a,B) )
           => 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),times_times(X_a),R_3),C)) != hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),R_3),D)) ) ) ),
    file('theBenchmark.p',fact_687_add__scale__eq__noteq) ).

fof(fact_688_sum__squares__eq__zero__iff,axiom,
    ! [X_b] :
      ( linord581940658strict(X_b)
     => ! [X_1,Y_2] :
          ( hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),X_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Y_2),Y_2)) = zero_zero(X_b)
        <=> ( ti(X_b,Y_2) = zero_zero(X_b)
            & ti(X_b,X_1) = zero_zero(X_b) ) ) ),
    file('theBenchmark.p',fact_688_sum__squares__eq__zero__iff) ).

fof(fact_689_less__1__mult,axiom,
    ! [X_a] :
      ( linordered_semidom(X_a)
     => ! [N,M_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),M_1))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),N))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),M_1),N))) ) ) ),
    file('theBenchmark.p',fact_689_less__1__mult) ).

fof(fact_690_eq__add__iff2,axiom,
    ! [X_b] :
      ( ring(X_b)
     => ! [A_2,E,C_1,B_3,D_1] :
          ( hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),C_1) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),E)),D_1)
        <=> ti(X_b,C_1) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),B_3),A_2)),E)),D_1) ) ),
    file('theBenchmark.p',fact_690_eq__add__iff2) ).

fof(fact_691_eq__add__iff1,axiom,
    ! [X_b] :
      ( ring(X_b)
     => ! [A_2,E,C_1,B_3,D_1] :
          ( hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),C_1) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),E)),D_1)
        <=> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3)),E)),C_1) = ti(X_b,D_1) ) ),
    file('theBenchmark.p',fact_691_eq__add__iff1) ).

fof(fact_692_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
    ! [X_a] :
      ( comm_semiring_1(X_a)
     => ! [A_1,M_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),times_times(X_a),A_1),M_1)),M_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),one_one(X_a))),M_1) ),
    file('theBenchmark.p',fact_692_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).

fof(fact_693_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
    ! [X_a] :
      ( comm_semiring_1(X_a)
     => ! [M_1,A_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),M_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),M_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),one_one(X_a))),M_1) ),
    file('theBenchmark.p',fact_693_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).

fof(fact_694_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
    ! [X_a] :
      ( comm_semiring_1(X_a)
     => ! [M_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),M_1),M_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),one_one(X_a))),M_1) ),
    file('theBenchmark.p',fact_694_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).

fof(fact_695_mult__eq__1__iff,axiom,
    ! [M,Na] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na) = hAPP(nat,nat,suc,zero_zero(nat))
    <=> ( Na = hAPP(nat,nat,suc,zero_zero(nat))
        & M = hAPP(nat,nat,suc,zero_zero(nat)) ) ),
    file('theBenchmark.p',fact_695_mult__eq__1__iff) ).

fof(fact_696_mult__less__mono2,axiom,
    ! [K_1,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),zero_zero(nat)),K_1))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),I_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),J))) ) ),
    file('theBenchmark.p',fact_696_mult__less__mono2) ).

fof(fact_697_mult__less__mono1,axiom,
    ! [K_1,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),zero_zero(nat)),K_1))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_2),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),K_1))) ) ),
    file('theBenchmark.p',fact_697_mult__less__mono1) ).

fof(fact_698_mult__less__cancel2,axiom,
    ! [M,K,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Na),K)))
    <=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) ) ),
    file('theBenchmark.p',fact_698_mult__less__cancel2) ).

fof(fact_699_mult__less__cancel1,axiom,
    ! [K,M,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na)))
    <=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) ) ),
    file('theBenchmark.p',fact_699_mult__less__cancel1) ).

fof(fact_700_nat__0__less__mult__iff,axiom,
    ! [M,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na)))
    <=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na))
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M)) ) ),
    file('theBenchmark.p',fact_700_nat__0__less__mult__iff) ).

fof(fact_701_Suc__mult__less__cancel1,axiom,
    ! [K,M,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),Na)))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)) ),
    file('theBenchmark.p',fact_701_Suc__mult__less__cancel1) ).

fof(fact_702_mult__Suc__right,axiom,
    ! [M_1,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),hAPP(nat,nat,suc,N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N)),
    file('theBenchmark.p',fact_702_mult__Suc__right) ).

fof(fact_703_mult__Suc,axiom,
    ! [M_1,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,M_1)),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N)),
    file('theBenchmark.p',fact_703_mult__Suc) ).

fof(fact_704_Suc__mult__le__cancel1,axiom,
    ! [K,M,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),Na)))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)) ),
    file('theBenchmark.p',fact_704_Suc__mult__le__cancel1) ).

fof(fact_705_mult__eq__self__implies__10,axiom,
    ! [M_1,N] :
      ( M_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N)
     => ( M_1 = zero_zero(nat)
        | N = one_one(nat) ) ),
    file('theBenchmark.p',fact_705_mult__eq__self__implies__10) ).

fof(fact_706_Ints__double__eq__0__iff,axiom,
    ! [X_b] :
      ( ring_char_0(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),ring_1_Ints(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)
          <=> ti(X_b,A_2) = zero_zero(X_b) ) ) ),
    file('theBenchmark.p',fact_706_Ints__double__eq__0__iff) ).

fof(fact_707_mult__left__le__imp__le,axiom,
    ! [X_a] :
      ( linord20386208strict(X_a)
     => ! [C,A_1,B] :
          ( 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),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B)))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) ) ) ),
    file('theBenchmark.p',fact_707_mult__left__le__imp__le) ).

fof(fact_708_mult__right__le__imp__le,axiom,
    ! [X_a] :
      ( linord20386208strict(X_a)
     => ! [A_1,C,B] :
          ( 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),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C)))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) ) ) ),
    file('theBenchmark.p',fact_708_mult__right__le__imp__le) ).

fof(fact_709_mult__less__imp__less__left,axiom,
    ! [X_a] :
      ( linord20386208strict(X_a)
     => ! [C,A_1,B] :
          ( 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),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B)))
         => ( 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(X_a),A_1),B)) ) ) ),
    file('theBenchmark.p',fact_709_mult__less__imp__less__left) ).

fof(fact_710_mult__left__less__imp__less,axiom,
    ! [X_a] :
      ( linordered_semiring(X_a)
     => ! [C,A_1,B] :
          ( 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),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B)))
         => ( 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(X_a),A_1),B)) ) ) ),
    file('theBenchmark.p',fact_710_mult__left__less__imp__less) ).

fof(fact_711_mult__less__imp__less__right,axiom,
    ! [X_a] :
      ( linord20386208strict(X_a)
     => ! [A_1,C,B] :
          ( 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),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),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(X_a),A_1),B)) ) ) ),
    file('theBenchmark.p',fact_711_mult__less__imp__less__right) ).

fof(fact_712_mult__right__less__imp__less,axiom,
    ! [X_a] :
      ( linordered_semiring(X_a)
     => ! [A_1,C,B] :
          ( 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),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),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(X_a),A_1),B)) ) ) ),
    file('theBenchmark.p',fact_712_mult__right__less__imp__less) ).

fof(fact_713_mult__le__less__imp__less,axiom,
    ! [X_a] :
      ( linord20386208strict(X_a)
     => ! [C,D,A_1,B] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B))
         => ( 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),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)),C))
               => 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),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D))) ) ) ) ) ),
    file('theBenchmark.p',fact_713_mult__le__less__imp__less) ).

fof(fact_714_mult__less__le__imp__less,axiom,
    ! [X_a] :
      ( linord20386208strict(X_a)
     => ! [C,D,A_1,B] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))
         => ( 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),zero_zero(X_a)),A_1))
             => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C))
               => 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),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D))) ) ) ) ) ),
    file('theBenchmark.p',fact_714_mult__less__le__imp__less) ).

fof(fact_715_mult__strict__mono_H,axiom,
    ! [X_a] :
      ( linord20386208strict(X_a)
     => ! [C,D,A_1,B] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))
         => ( 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),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)),C))
               => 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),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D))) ) ) ) ) ),
    file('theBenchmark.p',fact_715_mult__strict__mono_H) ).

fof(fact_716_mult__strict__mono,axiom,
    ! [X_a] :
      ( linord20386208strict(X_a)
     => ! [C,D,A_1,B] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))
         => ( 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),zero_zero(X_a)),B))
             => ( 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(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D))) ) ) ) ) ),
    file('theBenchmark.p',fact_716_mult__strict__mono) ).

fof(fact_717_mult__le__cancel__left__neg,axiom,
    ! [X_b] :
      ( linord581940658strict(X_b)
     => ! [A_2,B_3,C_1] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),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),times_times(X_b),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),B_3)))
          <=> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),B_3),A_2)) ) ) ),
    file('theBenchmark.p',fact_717_mult__le__cancel__left__neg) ).

fof(fact_718_mult__le__cancel__left__pos,axiom,
    ! [X_b] :
      ( linord581940658strict(X_b)
     => ! [A_2,B_3,C_1] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),C_1))
         => ( 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),times_times(X_b),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),B_3)))
          <=> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),B_3)) ) ) ),
    file('theBenchmark.p',fact_718_mult__le__cancel__left__pos) ).

fof(fact_719_sum__squares__le__zero__iff,axiom,
    ! [X_b] :
      ( linord581940658strict(X_b)
     => ! [X_1,Y_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),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),X_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Y_2),Y_2))),zero_zero(X_b)))
        <=> ( ti(X_b,Y_2) = zero_zero(X_b)
            & ti(X_b,X_1) = zero_zero(X_b) ) ) ),
    file('theBenchmark.p',fact_719_sum__squares__le__zero__iff) ).

fof(fact_720_sum__squares__ge__zero,axiom,
    ! [X_a] :
      ( linordered_ring(X_a)
     => ! [X,Y] : 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),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),Y)))) ),
    file('theBenchmark.p',fact_720_sum__squares__ge__zero) ).

fof(fact_721_not__sum__squares__lt__zero,axiom,
    ! [X_a] :
      ( linordered_ring(X_a)
     => ! [X,Y] : ~ 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),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),Y))),zero_zero(X_a))) ),
    file('theBenchmark.p',fact_721_not__sum__squares__lt__zero) ).

fof(fact_722_sum__squares__gt__zero__iff,axiom,
    ! [X_b] :
      ( linord581940658strict(X_b)
     => ! [X_1,Y_2] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),X_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Y_2),Y_2))))
        <=> ( ti(X_b,Y_2) != zero_zero(X_b)
            | ti(X_b,X_1) != zero_zero(X_b) ) ) ),
    file('theBenchmark.p',fact_722_sum__squares__gt__zero__iff) ).

fof(fact_723_mult__left__le__one__le,axiom,
    ! [X_a] :
      ( linordered_idom(X_a)
     => ! [Y,X] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Y))
           => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),one_one(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),times_times(X_a),Y),X)),X)) ) ) ) ),
    file('theBenchmark.p',fact_723_mult__left__le__one__le) ).

fof(fact_724_mult__right__le__one__le,axiom,
    ! [X_a] :
      ( linordered_idom(X_a)
     => ! [Y,X] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Y))
           => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),one_one(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),times_times(X_a),X),Y)),X)) ) ) ) ),
    file('theBenchmark.p',fact_724_mult__right__le__one__le) ).

fof(fact_725_le__add__iff2,axiom,
    ! [X_b] :
      ( ordered_ring(X_b)
     => ! [A_2,E,C_1,B_3,D_1] :
          ( 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),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),E)),D_1)))
        <=> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),C_1),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),B_3),A_2)),E)),D_1))) ) ),
    file('theBenchmark.p',fact_725_le__add__iff2) ).

fof(fact_726_le__add__iff1,axiom,
    ! [X_b] :
      ( ordered_ring(X_b)
     => ! [A_2,E,C_1,B_3,D_1] :
          ( 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),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),E)),D_1)))
        <=> 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),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3)),E)),C_1)),D_1)) ) ),
    file('theBenchmark.p',fact_726_le__add__iff1) ).

fof(fact_727_less__add__iff2,axiom,
    ! [X_b] :
      ( ordered_ring(X_b)
     => ! [A_2,E,C_1,B_3,D_1] :
          ( 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),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),E)),D_1)))
        <=> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),B_3),A_2)),E)),D_1))) ) ),
    file('theBenchmark.p',fact_727_less__add__iff2) ).

fof(fact_728_less__add__iff1,axiom,
    ! [X_b] :
      ( ordered_ring(X_b)
     => ! [A_2,E,C_1,B_3,D_1] :
          ( 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),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),E)),D_1)))
        <=> 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),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3)),E)),C_1)),D_1)) ) ),
    file('theBenchmark.p',fact_728_less__add__iff1) ).

fof(fact_729_n__less__m__mult__n,axiom,
    ! [M_1,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),N))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),M_1))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N))) ) ),
    file('theBenchmark.p',fact_729_n__less__m__mult__n) ).

fof(fact_730_n__less__n__mult__m,axiom,
    ! [M_1,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),N))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),M_1))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),M_1))) ) ),
    file('theBenchmark.p',fact_730_n__less__n__mult__m) ).

fof(fact_731_one__less__mult,axiom,
    ! [M_1,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),N))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),M_1))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N))) ) ),
    file('theBenchmark.p',fact_731_one__less__mult) ).

fof(fact_732_one__le__mult__iff,axiom,
    ! [M,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na)))
    <=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),Na))
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),M)) ) ),
    file('theBenchmark.p',fact_732_one__le__mult__iff) ).

fof(fact_733_mult__le__cancel1,axiom,
    ! [K,M,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na)))
    <=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)) ) ),
    file('theBenchmark.p',fact_733_mult__le__cancel1) ).

fof(fact_734_mult__le__cancel2,axiom,
    ! [M,K,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Na),K)))
    <=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)) ) ),
    file('theBenchmark.p',fact_734_mult__le__cancel2) ).

fof(fact_735_fold__image__insert,axiom,
    ! [X_b,X_c] :
      ( ab_semigroup_mult(X_c)
     => ! [G,Z_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))
           => hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),G),Z_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),A_3)) = hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),times_times(X_c),hAPP(X_b,X_c,G,A_2)),hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),G),Z_2),A_3)) ) ) ),
    file('theBenchmark.p',fact_735_fold__image__insert) ).

fof(fact_736_fold__image__distrib,axiom,
    ! [X_b,X_c] :
      ( comm_monoid_mult(X_c)
     => ! [G,H,A_3] :
          ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))
         => hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),hAPP(fun(X_b,X_c),fun(X_b,X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_b,X_c)),combs(X_b,X_c,X_c),hAPP(fun(X_b,X_c),fun(X_b,fun(X_c,X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_b,fun(X_c,X_c))),combb(X_c,fun(X_c,X_c),X_b),times_times(X_c)),G)),H)),one_one(X_c)),A_3) = hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),times_times(X_c),hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),G),one_one(X_c)),A_3)),hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),H),one_one(X_c)),A_3)) ) ),
    file('theBenchmark.p',fact_736_fold__image__distrib) ).

fof(fact_737_convex__bound__le,axiom,
    ! [X_a] :
      ( linord1278240602ring_1(X_a)
     => ! [V,U_1,Y,X,A_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),A_1))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),A_1))
           => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),U_1))
             => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),V))
               => ( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),U_1),V) = one_one(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),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),U_1),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),V),Y))),A_1)) ) ) ) ) ) ),
    file('theBenchmark.p',fact_737_convex__bound__le) ).

fof(fact_738_mult__eq__if,axiom,
    ! [N,M_1] :
      ( ( M_1 != zero_zero(nat)
       => hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),one_one(nat))),N)) )
      & ( M_1 = zero_zero(nat)
       => hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N) = zero_zero(nat) ) ),
    file('theBenchmark.p',fact_738_mult__eq__if) ).

fof(fact_739_Ints__odd__nonzero,axiom,
    ! [X_b] :
      ( ring_char_0(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),ring_1_Ints(X_b)))
         => hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),one_one(X_b)),A_2)),A_2) != zero_zero(X_b) ) ),
    file('theBenchmark.p',fact_739_Ints__odd__nonzero) ).

fof(fact_740_field__le__mult__one__interval,axiom,
    ! [X_a] :
      ( linord1117847801e_zero(X_a)
     => ! [X,Y] :
          ( ! [Z_3] :
              ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Z_3))
             => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_3),one_one(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),times_times(X_a),Z_3),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_740_field__le__mult__one__interval) ).

fof(fact_741_fold__image__1,axiom,
    ! [X_b,X_c] :
      ( comm_monoid_mult(X_c)
     => ! [F,S] :
          ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),S))
         => ( ! [X_2] :
                ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),S))
               => hAPP(X_b,X_c,F,X_2) = one_one(X_c) )
           => hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),F),one_one(X_c)),S) = one_one(X_c) ) ) ),
    file('theBenchmark.p',fact_741_fold__image__1) ).

fof(fact_742_nat__less__add__iff2,axiom,
    ! [U,M,Na,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,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),Na)))
      <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),I_1)),U)),Na))) ) ),
    file('theBenchmark.p',fact_742_nat__less__add__iff2) ).

fof(fact_743_nat__mult__commute,axiom,
    ! [M_1,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),M_1),
    file('theBenchmark.p',fact_743_nat__mult__commute) ).

fof(fact_744_nat__mult__assoc,axiom,
    ! [M_1,N,K_1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N)),K_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),K_1)),
    file('theBenchmark.p',fact_744_nat__mult__assoc) ).

fof(fact_745_less__number__of__int__code,axiom,
    ! [K,L] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),K)),hAPP(int,int,number_number_of(int),L)))
    <=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L)) ),
    file('theBenchmark.p',fact_745_less__number__of__int__code) ).

fof(fact_746_zmult__1,axiom,
    ! [Z] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),one_one(int)),Z) = Z,
    file('theBenchmark.p',fact_746_zmult__1) ).

fof(fact_747_zmult__1__right,axiom,
    ! [Z] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z),one_one(int)) = Z,
    file('theBenchmark.p',fact_747_zmult__1__right) ).

fof(fact_748_zmult__commute,axiom,
    ! [Z,W] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z),W) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),Z),
    file('theBenchmark.p',fact_748_zmult__commute) ).

fof(fact_749_times__numeral__code_I5_J,axiom,
    ! [V,W] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),V)),hAPP(int,int,number_number_of(int),W)) = hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),W)),
    file('theBenchmark.p',fact_749_times__numeral__code_I5_J) ).

fof(fact_750_zmult__assoc,axiom,
    ! [Z1,Z2,Z3] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z1),Z2)),Z3) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z2),Z3)),
    file('theBenchmark.p',fact_750_zmult__assoc) ).

fof(fact_751_less__eq__number__of__int__code,axiom,
    ! [K,L] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),K)),hAPP(int,int,number_number_of(int),L)))
    <=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),L)) ),
    file('theBenchmark.p',fact_751_less__eq__number__of__int__code) ).

fof(fact_752_zdiff__zmult__distrib,axiom,
    ! [Z1,Z2,W] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z1),Z2)),W) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z1),W)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z2),W)),
    file('theBenchmark.p',fact_752_zdiff__zmult__distrib) ).

fof(fact_753_zdiff__zmult__distrib2,axiom,
    ! [W,Z1,Z2] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z1),Z2)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),Z1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),Z2)),
    file('theBenchmark.p',fact_753_zdiff__zmult__distrib2) ).

fof(fact_754_zadd__zmult__distrib2,axiom,
    ! [W,Z1,Z2] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z1),Z2)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),Z1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),Z2)),
    file('theBenchmark.p',fact_754_zadd__zmult__distrib2) ).

fof(fact_755_plus__numeral__code_I9_J,axiom,
    ! [V,W] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,number_number_of(int),V)),hAPP(int,int,number_number_of(int),W)) = hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),W)),
    file('theBenchmark.p',fact_755_plus__numeral__code_I9_J) ).

fof(fact_756_zadd__zmult__distrib,axiom,
    ! [Z1,Z2,W] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z1),Z2)),W) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z1),W)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z2),W)),
    file('theBenchmark.p',fact_756_zadd__zmult__distrib) ).

fof(fact_757_zmult__zless__mono2,axiom,
    ! [K_1,I_2,J] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_2),J))
     => ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K_1))
       => hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_1),I_2)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_1),J))) ) ),
    file('theBenchmark.p',fact_757_zmult__zless__mono2) ).

fof(fact_758_pos__zmult__eq__1__iff,axiom,
    ! [Na,M] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M))
     => ( hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M),Na) = one_one(int)
      <=> ( Na = one_one(int)
          & M = one_one(int) ) ) ),
    file('theBenchmark.p',fact_758_pos__zmult__eq__1__iff) ).

fof(fact_759_odd__nonzero,axiom,
    ! [Z] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),Z)),Z) != zero_zero(int),
    file('theBenchmark.p',fact_759_odd__nonzero) ).

fof(fact_760_zadd__0__right,axiom,
    ! [Z] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z),zero_zero(int)) = Z,
    file('theBenchmark.p',fact_760_zadd__0__right) ).

fof(fact_761_zadd__0,axiom,
    ! [Z] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),zero_zero(int)),Z) = Z,
    file('theBenchmark.p',fact_761_zadd__0) ).

fof(fact_762_int__0__less__1,axiom,
    hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),one_one(int))),
    file('theBenchmark.p',fact_762_int__0__less__1) ).

fof(fact_763_int__one__le__iff__zero__less,axiom,
    ! [Z_2] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),Z_2))
    <=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z_2)) ),
    file('theBenchmark.p',fact_763_int__one__le__iff__zero__less) ).

fof(fact_764_less__bin__lemma,axiom,
    ! [K,L] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L))
    <=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K),L)),zero_zero(int))) ),
    file('theBenchmark.p',fact_764_less__bin__lemma) ).

fof(fact_765_le__imp__0__less,axiom,
    ! [Z] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z))
     => hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),Z))) ),
    file('theBenchmark.p',fact_765_le__imp__0__less) ).

fof(fact_766_odd__less__0,axiom,
    ! [Z_2] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),Z_2)),Z_2)),zero_zero(int)))
    <=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),zero_zero(int))) ),
    file('theBenchmark.p',fact_766_odd__less__0) ).

fof(fact_767_zadd__left__mono,axiom,
    ! [K_1,I_2,J] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I_2),J))
     => hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_1),I_2)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_1),J))) ),
    file('theBenchmark.p',fact_767_zadd__left__mono) ).

fof(fact_768_zadd__assoc,axiom,
    ! [Z1,Z2,Z3] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z1),Z2)),Z3) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z2),Z3)),
    file('theBenchmark.p',fact_768_zadd__assoc) ).

fof(fact_769_zadd__left__commute,axiom,
    ! [X,Y,Z] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Y),Z)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Y),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),Z)),
    file('theBenchmark.p',fact_769_zadd__left__commute) ).

fof(fact_770_zadd__commute,axiom,
    ! [Z,W] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z),W) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W),Z),
    file('theBenchmark.p',fact_770_zadd__commute) ).

fof(fact_771_zle__refl,axiom,
    ! [W] : hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W),W)),
    file('theBenchmark.p',fact_771_zle__refl) ).

fof(fact_772_zle__linear,axiom,
    ! [Z,W] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W),Z))
      | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z),W)) ),
    file('theBenchmark.p',fact_772_zle__linear) ).

fof(fact_773_zle__trans,axiom,
    ! [K_1,I_2,J] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I_2),J))
     => ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),J),K_1))
       => hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I_2),K_1)) ) ),
    file('theBenchmark.p',fact_773_zle__trans) ).

fof(fact_774_zle__antisym,axiom,
    ! [Z,W] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z),W))
     => ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W),Z))
       => Z = W ) ),
    file('theBenchmark.p',fact_774_zle__antisym) ).

fof(fact_775_zle__diff1__eq,axiom,
    ! [W_1,Z_2] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z_2),one_one(int))))
    <=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_2)) ),
    file('theBenchmark.p',fact_775_zle__diff1__eq) ).

fof(fact_776_zless__linear,axiom,
    ! [X,Y] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y),X))
      | X = Y
      | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),Y)) ),
    file('theBenchmark.p',fact_776_zless__linear) ).

fof(fact_777_zless__le,axiom,
    ! [Z_2,W_1] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),W_1))
    <=> ( Z_2 != W_1
        & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_2),W_1)) ) ),
    file('theBenchmark.p',fact_777_zless__le) ).

fof(fact_778_zadd__strict__right__mono,axiom,
    ! [K_1,I_2,J] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_2),J))
     => hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I_2),K_1)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),J),K_1))) ),
    file('theBenchmark.p',fact_778_zadd__strict__right__mono) ).

fof(fact_779_zadd__zless__mono,axiom,
    ! [Z_4,Z,W_2,W] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_2),W))
     => ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_4),Z))
       => hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_2),Z_4)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W),Z))) ) ),
    file('theBenchmark.p',fact_779_zadd__zless__mono) ).

fof(fact_780_zle__add1__eq__le,axiom,
    ! [W_1,Z_2] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_2),one_one(int))))
    <=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W_1),Z_2)) ),
    file('theBenchmark.p',fact_780_zle__add1__eq__le) ).

fof(fact_781_add1__zle__eq,axiom,
    ! [W_1,Z_2] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_1),one_one(int))),Z_2))
    <=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_2)) ),
    file('theBenchmark.p',fact_781_add1__zle__eq) ).

fof(fact_782_zless__imp__add1__zle,axiom,
    ! [W,Z] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W),Z))
     => hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W),one_one(int))),Z)) ),
    file('theBenchmark.p',fact_782_zless__imp__add1__zle) ).

fof(fact_783_zless__add1__eq,axiom,
    ! [W_1,Z_2] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_2),one_one(int))))
    <=> ( W_1 = Z_2
        | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_2)) ) ),
    file('theBenchmark.p',fact_783_zless__add1__eq) ).

fof(fact_784_nat__mult__eq__cancel__disj,axiom,
    ! [K,M,Na] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na)
    <=> ( M = Na
        | K = zero_zero(nat) ) ),
    file('theBenchmark.p',fact_784_nat__mult__eq__cancel__disj) ).

fof(fact_785_left__add__mult__distrib,axiom,
    ! [I_2,U_1,J,K_1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_2),U_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),U_1)),K_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),J)),U_1)),K_1),
    file('theBenchmark.p',fact_785_left__add__mult__distrib) ).

fof(fact_786_nat__mult__eq__cancel1,axiom,
    ! [M,Na,K] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))
     => ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na)
      <=> M = Na ) ),
    file('theBenchmark.p',fact_786_nat__mult__eq__cancel1) ).

fof(fact_787_nat__mult__less__cancel1,axiom,
    ! [M,Na,K] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na)))
      <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)) ) ),
    file('theBenchmark.p',fact_787_nat__mult__less__cancel1) ).

fof(fact_788_nat__mult__le__cancel1,axiom,
    ! [M,Na,K] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na)))
      <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)) ) ),
    file('theBenchmark.p',fact_788_nat__mult__le__cancel1) ).

fof(fact_789_nat__le__add__iff1,axiom,
    ! [U,M,Na,J_1,I_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J_1),I_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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),Na)))
      <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J_1)),U)),M)),Na)) ) ),
    file('theBenchmark.p',fact_789_nat__le__add__iff1) ).

fof(fact_790_nat__diff__add__eq1,axiom,
    ! [U_1,M_1,N,J,I_2] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J),I_2))
     => hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_2),U_1)),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),U_1)),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_2),J)),U_1)),M_1)),N) ),
    file('theBenchmark.p',fact_790_nat__diff__add__eq1) ).

fof(fact_791_nat__eq__add__iff1,axiom,
    ! [U,M,Na,J_1,I_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J_1),I_1))
     => ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),Na)
      <=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J_1)),U)),M) = Na ) ),
    file('theBenchmark.p',fact_791_nat__eq__add__iff1) ).

fof(fact_792_nat__le__add__iff2,axiom,
    ! [U,M,Na,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,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),Na)))
      <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),I_1)),U)),Na))) ) ),
    file('theBenchmark.p',fact_792_nat__le__add__iff2) ).

fof(fact_793_nat__diff__add__eq2,axiom,
    ! [U_1,M_1,N,I_2,J] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),J))
     => hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_2),U_1)),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),U_1)),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),I_2)),U_1)),N)) ),
    file('theBenchmark.p',fact_793_nat__diff__add__eq2) ).

fof(fact_794_nat__eq__add__iff2,axiom,
    ! [U,M,Na,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),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),Na)
      <=> M = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),I_1)),U)),Na) ) ),
    file('theBenchmark.p',fact_794_nat__eq__add__iff2) ).

fof(fact_795_nat__less__add__iff1,axiom,
    ! [U,M,Na,J_1,I_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J_1),I_1))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),Na)))
      <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J_1)),U)),M)),Na)) ) ),
    file('theBenchmark.p',fact_795_nat__less__add__iff1) ).

fof(fact_796_zdiv__mono2__neg__lemma,axiom,
    ! [B,Q_2,R_3,B_2,Q_1,R_2] :
      ( hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q_2)),R_3) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_2),Q_1)),R_2)
     => ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_2),Q_1)),R_2)),zero_zero(int)))
       => ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_3),B))
         => ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R_2))
           => ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_2))
             => ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_2),B))
               => hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Q_1),Q_2)) ) ) ) ) ) ),
    file('theBenchmark.p',fact_796_zdiv__mono2__neg__lemma) ).

fof(fact_797_unique__quotient__lemma__neg,axiom,
    ! [B,Q_1,R_2,Q_2,R_3] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q_1)),R_2)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q_2)),R_3)))
     => ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),R_3),zero_zero(int)))
       => ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R_3))
         => ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R_2))
           => hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Q_2),Q_1)) ) ) ) ),
    file('theBenchmark.p',fact_797_unique__quotient__lemma__neg) ).

fof(fact_798_number__of__is__id,axiom,
    ! [K_1] : hAPP(int,int,number_number_of(int),K_1) = K_1,
    file('theBenchmark.p',fact_798_number__of__is__id) ).

fof(fact_799_int__0__neq__1,axiom,
    zero_zero(int) != one_one(int),
    file('theBenchmark.p',fact_799_int__0__neq__1) ).

fof(fact_800_self__quotient__aux1,axiom,
    ! [R_3,Q_2,A_1] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))
     => ( A_1 = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),R_3),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),Q_2))
       => ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_3),A_1))
         => hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),Q_2)) ) ) ),
    file('theBenchmark.p',fact_800_self__quotient__aux1) ).

fof(fact_801_self__quotient__aux2,axiom,
    ! [R_3,Q_2,A_1] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))
     => ( A_1 = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),R_3),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),Q_2))
       => ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R_3))
         => hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Q_2),one_one(int))) ) ) ),
    file('theBenchmark.p',fact_801_self__quotient__aux2) ).

fof(fact_802_q__pos__lemma,axiom,
    ! [B_2,Q_1,R_2] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_2),Q_1)),R_2)))
     => ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_2),B_2))
       => ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_2))
         => hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Q_1)) ) ) ),
    file('theBenchmark.p',fact_802_q__pos__lemma) ).

fof(fact_803_q__neg__lemma,axiom,
    ! [B_2,Q_1,R_2] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_2),Q_1)),R_2)),zero_zero(int)))
     => ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R_2))
       => ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_2))
         => hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Q_1),zero_zero(int))) ) ) ),
    file('theBenchmark.p',fact_803_q__neg__lemma) ).

fof(fact_804_unique__quotient__lemma,axiom,
    ! [B,Q_1,R_2,Q_2,R_3] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q_1)),R_2)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q_2)),R_3)))
     => ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R_2))
       => ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_2),B))
         => ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_3),B))
           => hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Q_1),Q_2)) ) ) ) ),
    file('theBenchmark.p',fact_804_unique__quotient__lemma) ).

fof(fact_805_zdiv__mono2__lemma,axiom,
    ! [B,Q_2,R_3,B_2,Q_1,R_2] :
      ( hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q_2)),R_3) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_2),Q_1)),R_2)
     => ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_2),Q_1)),R_2)))
       => ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_2),B_2))
         => ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R_3))
           => ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_2))
             => ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_2),B))
               => hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Q_2),Q_1)) ) ) ) ) ) ),
    file('theBenchmark.p',fact_805_zdiv__mono2__lemma) ).

fof(fact_806_int__less__induct,axiom,
    ! [Pa,I_1,K] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_1),K))
     => ( hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K),one_one(int))))
       => ( ! [I] :
              ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I),K))
             => ( hBOOL(hAPP(int,bool,Pa,I))
               => hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),I),one_one(int)))) ) )
         => hBOOL(hAPP(int,bool,Pa,I_1)) ) ) ),
    file('theBenchmark.p',fact_806_int__less__induct) ).

fof(fact_807_int__le__induct,axiom,
    ! [Pa,I_1,K] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I_1),K))
     => ( hBOOL(hAPP(int,bool,Pa,K))
       => ( ! [I] :
              ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I),K))
             => ( hBOOL(hAPP(int,bool,Pa,I))
               => hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),I),one_one(int)))) ) )
         => hBOOL(hAPP(int,bool,Pa,I_1)) ) ) ),
    file('theBenchmark.p',fact_807_int__le__induct) ).

fof(fact_808_fold__image__cong,axiom,
    ! [X_b,X_c] :
      ( ab_semigroup_mult(X_c)
     => ! [Z_2,G,H,A_3] :
          ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(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))
               => hAPP(X_b,X_c,G,X_2) = hAPP(X_b,X_c,H,X_2) )
           => hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),G),Z_2),A_3) = hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),H),Z_2),A_3) ) ) ),
    file('theBenchmark.p',fact_808_fold__image__cong) ).

fof(fact_809_int__gr__induct,axiom,
    ! [Pa,K,I_1] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),I_1))
     => ( hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K),one_one(int))))
       => ( ! [I] :
              ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),I))
             => ( hBOOL(hAPP(int,bool,Pa,I))
               => hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I),one_one(int)))) ) )
         => hBOOL(hAPP(int,bool,Pa,I_1)) ) ) ),
    file('theBenchmark.p',fact_809_int__gr__induct) ).

fof(fact_810_int__ge__induct,axiom,
    ! [Pa,K,I_1] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),I_1))
     => ( hBOOL(hAPP(int,bool,Pa,K))
       => ( ! [I] :
              ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),I))
             => ( hBOOL(hAPP(int,bool,Pa,I))
               => hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I),one_one(int)))) ) )
         => hBOOL(hAPP(int,bool,Pa,I_1)) ) ) ),
    file('theBenchmark.p',fact_810_int__ge__induct) ).

fof(fact_811_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
    ! [Y,X] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X))
     => ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y))
       => hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),Y))) ) ),
    file('theBenchmark.p',fact_811_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).

fof(fact_812_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
    hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),zero_zero(int))),
    file('theBenchmark.p',fact_812_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).

fof(fact_813_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
    ! [Y,X] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X))
     => ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y))
       => hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),Y))) ) ),
    file('theBenchmark.p',fact_813_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).

fof(fact_814_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
    hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),one_one(int))),
    file('theBenchmark.p',fact_814_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).

fof(fact_815_transfer__nat__int__set__cong,axiom,
    ! [P_1,Pa] :
      ( ! [X_2] :
          ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2))
         => ( hBOOL(hAPP(int,bool,Pa,X_2))
          <=> hBOOL(hAPP(int,bool,P_1,X_2)) ) )
     => hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),Pa)) = hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),P_1)) ),
    file('theBenchmark.p',fact_815_transfer__nat__int__set__cong) ).

fof(fact_816_decr__mult__lemma,axiom,
    ! [K,Pa,D_1] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1))
     => ( ! [X_2] :
            ( hBOOL(hAPP(int,bool,Pa,X_2))
           => hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),D_1))) )
       => ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K))
         => ! [X_2] :
              ( hBOOL(hAPP(int,bool,Pa,X_2))
             => hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),D_1)))) ) ) ) ),
    file('theBenchmark.p',fact_816_decr__mult__lemma) ).

fof(fact_817_conj__le__cong,axiom,
    ! [P_1,Pa,X_1] :
      ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1))
       => ( hBOOL(Pa)
        <=> hBOOL(P_1) ) )
     => ( ( hBOOL(Pa)
          & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) )
      <=> ( hBOOL(P_1)
          & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) ) ) ),
    file('theBenchmark.p',fact_817_conj__le__cong) ).

fof(fact_818_imp__le__cong,axiom,
    ! [P_1,Pa,X_1] :
      ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1))
       => ( hBOOL(Pa)
        <=> hBOOL(P_1) ) )
     => ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1))
         => hBOOL(Pa) )
      <=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1))
         => hBOOL(P_1) ) ) ),
    file('theBenchmark.p',fact_818_imp__le__cong) ).

fof(fact_819_incr__mult__lemma,axiom,
    ! [K,Pa,D_1] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1))
     => ( ! [X_2] :
            ( hBOOL(hAPP(int,bool,Pa,X_2))
           => hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),D_1))) )
       => ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K))
         => ! [X_2] :
              ( hBOOL(hAPP(int,bool,Pa,X_2))
             => hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),D_1)))) ) ) ) ),
    file('theBenchmark.p',fact_819_incr__mult__lemma) ).

fof(fact_820_minf_I8_J,axiom,
    ! [X_a] :
      ( linorder(X_a)
     => ! [T_4] :
        ? [Z_3] :
        ! [X_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Z_3))
         => ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),T_4),X_2)) ) ),
    file('theBenchmark.p',fact_820_minf_I8_J) ).

fof(fact_821_pinf_I6_J,axiom,
    ! [X_a] :
      ( linorder(X_a)
     => ! [T_4] :
        ? [Z_3] :
        ! [X_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_3),X_2))
         => ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),T_4)) ) ),
    file('theBenchmark.p',fact_821_pinf_I6_J) ).

fof(fact_822_minf_I6_J,axiom,
    ! [X_a] :
      ( linorder(X_a)
     => ! [T_4] :
        ? [Z_3] :
        ! [X_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Z_3))
         => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),T_4)) ) ),
    file('theBenchmark.p',fact_822_minf_I6_J) ).

fof(fact_823_pinf_I8_J,axiom,
    ! [X_a] :
      ( linorder(X_a)
     => ! [T_4] :
        ? [Z_3] :
        ! [X_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_3),X_2))
         => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),T_4),X_2)) ) ),
    file('theBenchmark.p',fact_823_pinf_I8_J) ).

fof(fact_824_int__induct,axiom,
    ! [I_1,Pa,K] :
      ( hBOOL(hAPP(int,bool,Pa,K))
     => ( ! [I] :
            ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),I))
           => ( hBOOL(hAPP(int,bool,Pa,I))
             => hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I),one_one(int)))) ) )
       => ( ! [I] :
              ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I),K))
             => ( hBOOL(hAPP(int,bool,Pa,I))
               => hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),I),one_one(int)))) ) )
         => hBOOL(hAPP(int,bool,Pa,I_1)) ) ) ),
    file('theBenchmark.p',fact_824_int__induct) ).

fof(fact_825_minusinfinity,axiom,
    ! [Pa,P1,D_1] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1))
     => ( ! [X_2,K_2] :
            ( hBOOL(hAPP(int,bool,P1,X_2))
          <=> hBOOL(hAPP(int,bool,P1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_2),D_1)))) )
       => ( ? [Z_3] :
            ! [X_2] :
              ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_2),Z_3))
             => ( hBOOL(hAPP(int,bool,Pa,X_2))
              <=> hBOOL(hAPP(int,bool,P1,X_2)) ) )
         => ( ? [X1] : hBOOL(hAPP(int,bool,P1,X1))
           => ? [X1] : hBOOL(hAPP(int,bool,Pa,X1)) ) ) ) ),
    file('theBenchmark.p',fact_825_minusinfinity) ).

fof(fact_826_plusinfinity,axiom,
    ! [Pa,P_1,D_1] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1))
     => ( ! [X_2,K_2] :
            ( hBOOL(hAPP(int,bool,P_1,X_2))
          <=> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_2),D_1)))) )
       => ( ? [Z_3] :
            ! [X_2] :
              ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_3),X_2))
             => ( hBOOL(hAPP(int,bool,Pa,X_2))
              <=> hBOOL(hAPP(int,bool,P_1,X_2)) ) )
         => ( ? [X1] : hBOOL(hAPP(int,bool,P_1,X1))
           => ? [X1] : hBOOL(hAPP(int,bool,Pa,X1)) ) ) ) ),
    file('theBenchmark.p',fact_826_plusinfinity) ).

fof(fact_827_tsub__def,axiom,
    ! [Y,X] :
      ( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Y),X))
       => hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,X),Y) = zero_zero(int) )
      & ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Y),X))
       => hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,X),Y) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X),Y) ) ),
    file('theBenchmark.p',fact_827_tsub__def) ).

fof(fact_828_of__nat__number__of__lemma,axiom,
    ! [X_a] :
      ( number_ring(X_a)
     => ! [V] :
          ( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),V)))
           => hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,number_number_of(nat),V)) = zero_zero(X_a) )
          & ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),V)))
           => hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,number_number_of(nat),V)) = hAPP(int,X_a,number_number_of(X_a),V) ) ) ),
    file('theBenchmark.p',fact_828_of__nat__number__of__lemma) ).

fof(fact_829_number__of__int,axiom,
    ! [X_a] :
      ( number_semiring(X_a)
     => ! [N] : hAPP(int,X_a,number_number_of(X_a),hAPP(nat,int,semiring_1_of_nat(int),N)) = hAPP(nat,X_a,semiring_1_of_nat(X_a),N) ),
    file('theBenchmark.p',fact_829_number__of__int) ).

fof(fact_830_zero__zle__int,axiom,
    ! [N] : hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),N))),
    file('theBenchmark.p',fact_830_zero__zle__int) ).

fof(fact_831_int__less__0__conv,axiom,
    ! [K_1] : ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),K_1)),zero_zero(int))),
    file('theBenchmark.p',fact_831_int__less__0__conv) ).

fof(fact_832_of__nat__0__le__iff,axiom,
    ! [X_a] :
      ( linordered_semidom(X_a)
     => ! [N] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N))) ),
    file('theBenchmark.p',fact_832_of__nat__0__le__iff) ).

fof(fact_833_zero__le__imp__of__nat,axiom,
    ! [X_a] :
      ( linordered_semidom(X_a)
     => ! [M_1] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(nat,X_a,semiring_1_of_nat(X_a),M_1))) ),
    file('theBenchmark.p',fact_833_zero__le__imp__of__nat) ).

fof(fact_834_of__nat__less__0__iff,axiom,
    ! [X_a] :
      ( linordered_semidom(X_a)
     => ! [M_1] : ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M_1)),zero_zero(X_a))) ),
    file('theBenchmark.p',fact_834_of__nat__less__0__iff) ).

fof(fact_835_of__nat__0,axiom,
    ! [X_a] :
      ( semiring_1(X_a)
     => hAPP(nat,X_a,semiring_1_of_nat(X_a),zero_zero(nat)) = zero_zero(X_a) ),
    file('theBenchmark.p',fact_835_of__nat__0) ).

fof(fact_836_of__nat__1,axiom,
    ! [X_a] :
      ( semiring_1(X_a)
     => hAPP(nat,X_a,semiring_1_of_nat(X_a),one_one(nat)) = one_one(X_a) ),
    file('theBenchmark.p',fact_836_of__nat__1) ).

fof(fact_837_int__1,axiom,
    hAPP(nat,int,semiring_1_of_nat(int),one_one(nat)) = one_one(int),
    file('theBenchmark.p',fact_837_int__1) ).

fof(fact_838_int__0,axiom,
    hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat)) = zero_zero(int),
    file('theBenchmark.p',fact_838_int__0) ).

fof(fact_839_int__eq__0__conv,axiom,
    ! [Na] :
      ( hAPP(nat,int,semiring_1_of_nat(int),Na) = zero_zero(int)
    <=> Na = zero_zero(nat) ),
    file('theBenchmark.p',fact_839_int__eq__0__conv) ).

fof(fact_840_Ints__of__nat,axiom,
    ! [X_b] :
      ( ring_1(X_b)
     => ! [Na] : hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(nat,X_b,semiring_1_of_nat(X_b),Na)),ring_1_Ints(X_b))) ),
    file('theBenchmark.p',fact_840_Ints__of__nat) ).

fof(fact_841_of__nat__eq__iff,axiom,
    ! [X_b] :
      ( semiring_char_0(X_b)
     => ! [M,Na] :
          ( hAPP(nat,X_b,semiring_1_of_nat(X_b),M) = hAPP(nat,X_b,semiring_1_of_nat(X_b),Na)
        <=> M = Na ) ),
    file('theBenchmark.p',fact_841_of__nat__eq__iff) ).

fof(fact_842_of__nat__add,axiom,
    ! [X_a] :
      ( semiring_1(X_a)
     => ! [M_1,N] : hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M_1)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N)) ),
    file('theBenchmark.p',fact_842_of__nat__add) ).

fof(fact_843_of__nat__le__iff,axiom,
    ! [X_b] :
      ( linordered_semidom(X_b)
     => ! [M,Na] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(nat,X_b,semiring_1_of_nat(X_b),M)),hAPP(nat,X_b,semiring_1_of_nat(X_b),Na)))
        <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)) ) ),
    file('theBenchmark.p',fact_843_of__nat__le__iff) ).

fof(fact_844_of__nat__less__iff,axiom,
    ! [X_b] :
      ( linordered_semidom(X_b)
     => ! [M,Na] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(nat,X_b,semiring_1_of_nat(X_b),M)),hAPP(nat,X_b,semiring_1_of_nat(X_b),Na)))
        <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)) ) ),
    file('theBenchmark.p',fact_844_of__nat__less__iff) ).

fof(fact_845_less__imp__of__nat__less,axiom,
    ! [X_a] :
      ( linordered_semidom(X_a)
     => ! [M_1,N] :
          ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N))
         => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M_1)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N))) ) ),
    file('theBenchmark.p',fact_845_less__imp__of__nat__less) ).

fof(fact_846_of__nat__less__imp__less,axiom,
    ! [X_a] :
      ( linordered_semidom(X_a)
     => ! [M_1,N] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M_1)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N)))
         => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)) ) ),
    file('theBenchmark.p',fact_846_of__nat__less__imp__less) ).

fof(fact_847_zless__int,axiom,
    ! [M,Na] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(nat,int,semiring_1_of_nat(int),Na)))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)) ),
    file('theBenchmark.p',fact_847_zless__int) ).

fof(fact_848_zle__int,axiom,
    ! [M,Na] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(nat,int,semiring_1_of_nat(int),Na)))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)) ),
    file('theBenchmark.p',fact_848_zle__int) ).

fof(fact_849_zadd__int,axiom,
    ! [M_1,N] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),M_1)),hAPP(nat,int,semiring_1_of_nat(int),N)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N)),
    file('theBenchmark.p',fact_849_zadd__int) ).

fof(fact_850_zadd__int__left,axiom,
    ! [M_1,N,Z] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),M_1)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),N)),Z)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N))),Z),
    file('theBenchmark.p',fact_850_zadd__int__left) ).

fof(fact_851_zle__iff__zadd,axiom,
    ! [W_1,Z_2] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W_1),Z_2))
    <=> ? [N_1] : Z_2 = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_1),hAPP(nat,int,semiring_1_of_nat(int),N_1)) ),
    file('theBenchmark.p',fact_851_zle__iff__zadd) ).

fof(fact_852_zmult__int,axiom,
    ! [M_1,N] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),M_1)),hAPP(nat,int,semiring_1_of_nat(int),N)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N)),
    file('theBenchmark.p',fact_852_zmult__int) ).

fof(fact_853_int__mult,axiom,
    ! [M_1,N] : hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),M_1)),hAPP(nat,int,semiring_1_of_nat(int),N)),
    file('theBenchmark.p',fact_853_int__mult) ).

fof(fact_854_of__nat__mult,axiom,
    ! [X_a] :
      ( semiring_1(X_a)
     => ! [M_1,N] : hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M_1)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N)) ),
    file('theBenchmark.p',fact_854_of__nat__mult) ).

fof(fact_855_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom,
    ! [X,Y] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),X)),hAPP(nat,int,semiring_1_of_nat(int),Y)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X),Y)),
    file('theBenchmark.p',fact_855_Nat__Transfer_Otransfer__int__nat__functions_I2_J) ).

fof(fact_856_transfer__int__nat__relations_I2_J,axiom,
    ! [X_1,Y_2] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(nat,int,semiring_1_of_nat(int),Y_2)))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y_2)) ),
    file('theBenchmark.p',fact_856_transfer__int__nat__relations_I2_J) ).

fof(fact_857_transfer__int__nat__relations_I3_J,axiom,
    ! [X_1,Y_2] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(nat,int,semiring_1_of_nat(int),Y_2)))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X_1),Y_2)) ),
    file('theBenchmark.p',fact_857_transfer__int__nat__relations_I3_J) ).

fof(fact_858_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom,
    ! [X,Y] : hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,hAPP(nat,int,semiring_1_of_nat(int),X)),hAPP(nat,int,semiring_1_of_nat(int),Y)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X),Y)),
    file('theBenchmark.p',fact_858_Nat__Transfer_Otransfer__int__nat__functions_I3_J) ).

fof(fact_859_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom,
    ! [X,Y] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),X)),hAPP(nat,int,semiring_1_of_nat(int),Y)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X),Y)),
    file('theBenchmark.p',fact_859_Nat__Transfer_Otransfer__int__nat__functions_I1_J) ).

fof(fact_860_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom,
    ! [A_3] : hAPP(fun(nat,bool),nat,finite_card(nat),A_3) = hAPP(fun(int,bool),nat,finite_card(int),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3)),
    file('theBenchmark.p',fact_860_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J) ).

fof(fact_861_transfer__nat__int__set__relations_I1_J,axiom,
    ! [A_3] :
      ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),A_3))
    <=> hBOOL(hAPP(fun(int,bool),bool,finite_finite(int),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3))) ),
    file('theBenchmark.p',fact_861_transfer__nat__int__set__relations_I1_J) ).

fof(fact_862_transfer__int__nat__numerals_I2_J,axiom,
    one_one(int) = hAPP(nat,int,semiring_1_of_nat(int),one_one(nat)),
    file('theBenchmark.p',fact_862_transfer__int__nat__numerals_I2_J) ).

fof(fact_863_transfer__int__nat__numerals_I1_J,axiom,
    zero_zero(int) = hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat)),
    file('theBenchmark.p',fact_863_transfer__int__nat__numerals_I1_J) ).

fof(fact_864_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom,
    ! [Pa] : hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),Pa)) = hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,int),fun(nat,bool),hAPP(fun(int,bool),fun(fun(nat,int),fun(nat,bool)),combb(int,bool,nat),Pa),semiring_1_of_nat(int)))),
    file('theBenchmark.p',fact_864_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J) ).

fof(fact_865_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom,
    ! [Z] : hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),Z))),
    file('theBenchmark.p',fact_865_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) ).

fof(fact_866_transfer__int__nat__quantifiers_I2_J,axiom,
    ! [Pa] :
      ( ? [X_2] :
          ( hBOOL(hAPP(int,bool,Pa,X_2))
          & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)) )
    <=> ? [X_2] : hBOOL(hAPP(int,bool,Pa,hAPP(nat,int,semiring_1_of_nat(int),X_2))) ),
    file('theBenchmark.p',fact_866_transfer__int__nat__quantifiers_I2_J) ).

fof(fact_867_transfer__int__nat__quantifiers_I1_J,axiom,
    ! [Pa] :
      ( ! [X_2] :
          ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2))
         => hBOOL(hAPP(int,bool,Pa,X_2)) )
    <=> ! [X_2] : hBOOL(hAPP(int,bool,Pa,hAPP(nat,int,semiring_1_of_nat(int),X_2))) ),
    file('theBenchmark.p',fact_867_transfer__int__nat__quantifiers_I1_J) ).

fof(fact_868_int__le__0__conv,axiom,
    ! [Na] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),Na)),zero_zero(int)))
    <=> Na = zero_zero(nat) ),
    file('theBenchmark.p',fact_868_int__le__0__conv) ).

fof(fact_869_int__Suc0__eq__1,axiom,
    hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,zero_zero(nat))) = one_one(int),
    file('theBenchmark.p',fact_869_int__Suc0__eq__1) ).

fof(fact_870_zless__iff__Suc__zadd,axiom,
    ! [W_1,Z_2] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_2))
    <=> ? [N_1] : Z_2 = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_1),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,N_1))) ),
    file('theBenchmark.p',fact_870_zless__iff__Suc__zadd) ).

fof(fact_871_int__Suc,axiom,
    ! [M_1] : hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,M_1)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),M_1)),
    file('theBenchmark.p',fact_871_int__Suc) ).

fof(fact_872_zdiff__int,axiom,
    ! [N,M_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M_1))
     => hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),M_1)),hAPP(nat,int,semiring_1_of_nat(int),N)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N)) ),
    file('theBenchmark.p',fact_872_zdiff__int) ).

fof(fact_873_of__nat__Suc,axiom,
    ! [X_a] :
      ( semiring_1(X_a)
     => ! [M_1] : hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,suc,M_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),hAPP(nat,X_a,semiring_1_of_nat(X_a),M_1)) ),
    file('theBenchmark.p',fact_873_of__nat__Suc) ).

fof(fact_874_of__nat__diff,axiom,
    ! [X_a] :
      ( ring_1(X_a)
     => ! [N,M_1] :
          ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M_1))
         => hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M_1)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N)) ) ),
    file('theBenchmark.p',fact_874_of__nat__diff) ).

fof(fact_875_zero__less__int__conv,axiom,
    ! [Na] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),Na)))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)) ),
    file('theBenchmark.p',fact_875_zero__less__int__conv) ).

fof(fact_876_zmult__zless__mono2__lemma,axiom,
    ! [K_1,I_2,J] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_2),J))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1))
       => hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),K_1)),I_2)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),K_1)),J))) ) ),
    file('theBenchmark.p',fact_876_zmult__zless__mono2__lemma) ).

fof(fact_877_of__nat__0__less__iff,axiom,
    ! [X_b] :
      ( linordered_semidom(X_b)
     => ! [Na] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),hAPP(nat,X_b,semiring_1_of_nat(X_b),Na)))
        <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)) ) ),
    file('theBenchmark.p',fact_877_of__nat__0__less__iff) ).

fof(fact_878_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom,
    ! [Y,X] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X))
     => ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y))
       => hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,X),Y))) ) ),
    file('theBenchmark.p',fact_878_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J) ).

fof(fact_879_zdiff__int__split,axiom,
    ! [Pa,X_1,Y_2] :
      ( hBOOL(hAPP(int,bool,Pa,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X_1),Y_2))))
    <=> ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y_2))
         => hBOOL(hAPP(int,bool,Pa,zero_zero(int))) )
        & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Y_2),X_1))
         => hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(nat,int,semiring_1_of_nat(int),Y_2)))) ) ) ),
    file('theBenchmark.p',fact_879_zdiff__int__split) ).

fof(fact_880_tsub__eq,axiom,
    ! [Y,X] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Y),X))
     => hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,X),Y) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X),Y) ),
    file('theBenchmark.p',fact_880_tsub__eq) ).

fof(fact_881_zero__less__imp__eq__int,axiom,
    ! [K_1] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K_1))
     => ? [N_1] :
          ( K_1 = hAPP(nat,int,semiring_1_of_nat(int),N_1)
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) ) ),
    file('theBenchmark.p',fact_881_zero__less__imp__eq__int) ).

fof(fact_882_semiring__1__class_Oof__nat__code,axiom,
    ! [X_b] :
      ( semiring_1(X_b)
     => ! [Na] : hAPP(nat,X_b,semiring_1_of_nat(X_b),Na) = hAPP(X_b,X_b,hAPP(nat,fun(X_b,X_b),hAPP(fun(X_b,X_b),fun(nat,fun(X_b,X_b)),semiri532925092at_aux(X_b),hAPP(X_b,fun(X_b,X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(X_b,X_b)),combc(X_b,X_b,X_b),plus_plus(X_b)),one_one(X_b))),Na),zero_zero(X_b)) ),
    file('theBenchmark.p',fact_882_semiring__1__class_Oof__nat__code) ).

fof(fact_883_int__int__eq,axiom,
    ! [M,Na] :
      ( hAPP(nat,int,semiring_1_of_nat(int),M) = hAPP(nat,int,semiring_1_of_nat(int),Na)
    <=> M = Na ),
    file('theBenchmark.p',fact_883_int__int__eq) ).

fof(fact_884_transfer__nat__int__set__relations_I4_J,axiom,
    ! [A_3,B_1] :
      ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less(fun(nat,bool)),A_3),B_1))
    <=> hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less(fun(int,bool)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B_1))) ),
    file('theBenchmark.p',fact_884_transfer__nat__int__set__relations_I4_J) ).

fof(fact_885_transfer__nat__int__set__relations_I5_J,axiom,
    ! [A_3,B_1] :
      ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),A_3),B_1))
    <=> hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B_1))) ),
    file('theBenchmark.p',fact_885_transfer__nat__int__set__relations_I5_J) ).

fof(fact_886_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J,axiom,
    bot_bot(fun(int,bool)) = hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),bot_bot(fun(nat,bool))),
    file('theBenchmark.p',fact_886_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J) ).

fof(fact_887_transfer__nat__int__set__relations_I3_J,axiom,
    ! [A_3,B_1] :
      ( A_3 = B_1
    <=> hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3) = hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B_1) ),
    file('theBenchmark.p',fact_887_transfer__nat__int__set__relations_I3_J) ).

fof(fact_888_transfer__nat__int__set__relations_I2_J,axiom,
    ! [X_1,A_3] :
      ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_1),A_3))
    <=> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3))) ),
    file('theBenchmark.p',fact_888_transfer__nat__int__set__relations_I2_J) ).

fof(fact_889_int__if__cong,axiom,
    ! [X_1,Y_2,Pa] :
      ( ( ~ hBOOL(Pa)
       => hAPP(nat,int,semiring_1_of_nat(int),Y_2) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),Pa),X_1),Y_2)) )
      & ( hBOOL(Pa)
       => hAPP(nat,int,semiring_1_of_nat(int),X_1) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),Pa),X_1),Y_2)) ) ),
    file('theBenchmark.p',fact_889_int__if__cong) ).

fof(fact_890_transfer__int__nat__relations_I1_J,axiom,
    ! [X_1,Y_2] :
      ( hAPP(nat,int,semiring_1_of_nat(int),X_1) = hAPP(nat,int,semiring_1_of_nat(int),Y_2)
    <=> X_1 = Y_2 ),
    file('theBenchmark.p',fact_890_transfer__int__nat__relations_I1_J) ).

fof(fact_891_of__nat__aux_Osimps_I1_J,axiom,
    ! [X_b] :
      ( semiring_1(X_b)
     => ! [Inc,I_1] : hAPP(X_b,X_b,hAPP(nat,fun(X_b,X_b),hAPP(fun(X_b,X_b),fun(nat,fun(X_b,X_b)),semiri532925092at_aux(X_b),Inc),zero_zero(nat)),I_1) = ti(X_b,I_1) ),
    file('theBenchmark.p',fact_891_of__nat__aux_Osimps_I1_J) ).

fof(fact_892_of__nat__aux_Osimps_I2_J,axiom,
    ! [X_b] :
      ( semiring_1(X_b)
     => ! [Inc,Na,I_1] : hAPP(X_b,X_b,hAPP(nat,fun(X_b,X_b),hAPP(fun(X_b,X_b),fun(nat,fun(X_b,X_b)),semiri532925092at_aux(X_b),Inc),hAPP(nat,nat,suc,Na)),I_1) = hAPP(X_b,X_b,hAPP(nat,fun(X_b,X_b),hAPP(fun(X_b,X_b),fun(nat,fun(X_b,X_b)),semiri532925092at_aux(X_b),Inc),Na),hAPP(X_b,X_b,Inc,I_1)) ),
    file('theBenchmark.p',fact_892_of__nat__aux_Osimps_I2_J) ).

fof(fact_893_nonneg__int__cases,axiom,
    ! [K_1] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K_1))
     => ~ ! [N_1] : K_1 != hAPP(nat,int,semiring_1_of_nat(int),N_1) ),
    file('theBenchmark.p',fact_893_nonneg__int__cases) ).

fof(fact_894_nonneg__eq__int,axiom,
    ! [Z] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z))
     => ~ ! [M_2] : Z != hAPP(nat,int,semiring_1_of_nat(int),M_2) ),
    file('theBenchmark.p',fact_894_nonneg__eq__int) ).

fof(fact_895_zero__le__imp__eq__int,axiom,
    ! [K_1] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K_1))
     => ? [N_1] : K_1 = hAPP(nat,int,semiring_1_of_nat(int),N_1) ),
    file('theBenchmark.p',fact_895_zero__le__imp__eq__int) ).

fof(fact_896_int__diff__cases,axiom,
    ! [Z] :
      ~ ! [M_2,N_1] : Z != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),M_2)),hAPP(nat,int,semiring_1_of_nat(int),N_1)),
    file('theBenchmark.p',fact_896_int__diff__cases) ).

fof(fact_897_fold__image__related,axiom,
    ! [X_c,X_b] :
      ( comm_monoid_mult(X_b)
     => ! [H,G,S,R_1,E] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,E),E))
         => ( ! [X1,Y1,X2,Y2] :
                ( ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,Y1),Y2))
                  & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,X1),X2)) )
               => hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X1),Y1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X2),Y2))) )
           => ( hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),S))
             => ( ! [X_2] :
                    ( hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_2),S))
                   => hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,hAPP(X_c,X_b,H,X_2)),hAPP(X_c,X_b,G,X_2))) )
               => hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,hAPP(fun(X_c,bool),X_b,hAPP(X_b,fun(fun(X_c,bool),X_b),hAPP(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b))),finite_fold_image(X_b,X_c),times_times(X_b)),H),E),S)),hAPP(fun(X_c,bool),X_b,hAPP(X_b,fun(fun(X_c,bool),X_b),hAPP(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b))),finite_fold_image(X_b,X_c),times_times(X_b)),G),E),S))) ) ) ) ) ),
    file('theBenchmark.p',fact_897_fold__image__related) ).

fof(fact_898_fold__image__eq__general__inverses,axiom,
    ! [X_c,X_b,X_d] :
      ( comm_monoid_mult(X_d)
     => ! [E,G,F,H,K,T_3,S] :
          ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),S))
         => ( ! [Y_1] :
                ( hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),Y_1),T_3))
               => ( hAPP(X_b,X_c,H,hAPP(X_c,X_b,K,Y_1)) = ti(X_c,Y_1)
                  & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_c,X_b,K,Y_1)),S)) ) )
           => ( ! [X_2] :
                  ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),S))
                 => ( hAPP(X_c,X_d,G,hAPP(X_b,X_c,H,X_2)) = hAPP(X_b,X_d,F,X_2)
                    & hAPP(X_c,X_b,K,hAPP(X_b,X_c,H,X_2)) = ti(X_b,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,H,X_2)),T_3)) ) )
             => hAPP(fun(X_b,bool),X_d,hAPP(X_d,fun(fun(X_b,bool),X_d),hAPP(fun(X_b,X_d),fun(X_d,fun(fun(X_b,bool),X_d)),hAPP(fun(X_d,fun(X_d,X_d)),fun(fun(X_b,X_d),fun(X_d,fun(fun(X_b,bool),X_d))),finite_fold_image(X_d,X_b),times_times(X_d)),F),E),S) = hAPP(fun(X_c,bool),X_d,hAPP(X_d,fun(fun(X_c,bool),X_d),hAPP(fun(X_c,X_d),fun(X_d,fun(fun(X_c,bool),X_d)),hAPP(fun(X_d,fun(X_d,X_d)),fun(fun(X_c,X_d),fun(X_d,fun(fun(X_c,bool),X_d))),finite_fold_image(X_d,X_c),times_times(X_d)),G),E),T_3) ) ) ) ),
    file('theBenchmark.p',fact_898_fold__image__eq__general__inverses) ).

fof(fact_899_of__nat__number__of__eq,axiom,
    ! [X_a] :
      ( number_ring(X_a)
     => ! [V] :
          ( ( ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))
           => hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,number_number_of(nat),V)) = hAPP(int,X_a,number_number_of(X_a),V) )
          & ( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))
           => hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,number_number_of(nat),V)) = zero_zero(X_a) ) ) ),
    file('theBenchmark.p',fact_899_of__nat__number__of__eq) ).

fof(fact_900_decr__lemma,axiom,
    ! [X,Z,D] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D))
     => hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X),Z))),one_one(int))),D))),Z)) ),
    file('theBenchmark.p',fact_900_decr__lemma) ).

fof(fact_901_abs__triangle__ineq4,axiom,
    ! [X_a] :
      ( ordere142940540dd_abs(X_a)
     => ! [A_1,B] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B)))) ),
    file('theBenchmark.p',fact_901_abs__triangle__ineq4) ).

fof(fact_902_abs__diff__triangle__ineq,axiom,
    ! [X_a] :
      ( ordere142940540dd_abs(X_a)
     => ! [A_1,B,C,D] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,abs_abs(X_a),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)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),D)))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),C))),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B),D))))) ),
    file('theBenchmark.p',fact_902_abs__diff__triangle__ineq) ).

fof(fact_903_zabs__less__one__iff,axiom,
    ! [Z_2] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),Z_2)),one_one(int)))
    <=> Z_2 = zero_zero(int) ),
    file('theBenchmark.p',fact_903_zabs__less__one__iff) ).

fof(fact_904_neg__def,axiom,
    ! [Z_1] :
      ( hBOOL(hAPP(int,bool,nat_neg,Z_1))
    <=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_1),zero_zero(int))) ),
    file('theBenchmark.p',fact_904_neg__def) ).

fof(fact_905_not__neg__eq__ge__0,axiom,
    ! [X_1] :
      ( ~ hBOOL(hAPP(int,bool,nat_neg,X_1))
    <=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) ),
    file('theBenchmark.p',fact_905_not__neg__eq__ge__0) ).

fof(fact_906_abs__of__nonneg,axiom,
    ! [X_a] :
      ( ordere142940540dd_abs(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)),A_1))
         => hAPP(X_a,X_a,abs_abs(X_a),A_1) = ti(X_a,A_1) ) ),
    file('theBenchmark.p',fact_906_abs__of__nonneg) ).

fof(fact_907_abs__le__zero__iff,axiom,
    ! [X_b] :
      ( ordere142940540dd_abs(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,abs_abs(X_b),A_2)),zero_zero(X_b)))
        <=> ti(X_b,A_2) = zero_zero(X_b) ) ),
    file('theBenchmark.p',fact_907_abs__le__zero__iff) ).

fof(fact_908_abs__ge__zero,axiom,
    ! [X_a] :
      ( ordere142940540dd_abs(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)),hAPP(X_a,X_a,abs_abs(X_a),A_1))) ),
    file('theBenchmark.p',fact_908_abs__ge__zero) ).

fof(fact_909_abs__not__less__zero,axiom,
    ! [X_a] :
      ( ordere142940540dd_abs(X_a)
     => ! [A_1] : ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),zero_zero(X_a))) ),
    file('theBenchmark.p',fact_909_abs__not__less__zero) ).

fof(fact_910_zero__less__abs__iff,axiom,
    ! [X_b] :
      ( ordere142940540dd_abs(X_b)
     => ! [A_2] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),hAPP(X_b,X_b,abs_abs(X_b),A_2)))
        <=> ti(X_b,A_2) != zero_zero(X_b) ) ),
    file('theBenchmark.p',fact_910_zero__less__abs__iff) ).

fof(fact_911_abs__of__pos,axiom,
    ! [X_a] :
      ( ordere142940540dd_abs(X_a)
     => ! [A_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))
         => hAPP(X_a,X_a,abs_abs(X_a),A_1) = ti(X_a,A_1) ) ),
    file('theBenchmark.p',fact_911_abs__of__pos) ).

fof(fact_912_abs__triangle__ineq3,axiom,
    ! [X_a] :
      ( ordere142940540dd_abs(X_a)
     => ! [A_1,B] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B)))),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)))) ),
    file('theBenchmark.p',fact_912_abs__triangle__ineq3) ).

fof(fact_913_abs__triangle__ineq2,axiom,
    ! [X_a] :
      ( ordere142940540dd_abs(X_a)
     => ! [A_1,B] : 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),minus_minus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B))),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)))) ),
    file('theBenchmark.p',fact_913_abs__triangle__ineq2) ).

fof(fact_914_abs__triangle__ineq2__sym,axiom,
    ! [X_a] :
      ( ordere142940540dd_abs(X_a)
     => ! [A_1,B] : 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),minus_minus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B))),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B),A_1)))) ),
    file('theBenchmark.p',fact_914_abs__triangle__ineq2__sym) ).

fof(fact_915_abs__mult__less,axiom,
    ! [X_a] :
      ( linordered_idom(X_a)
     => ! [B,D,A_1,C] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),C))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,abs_abs(X_a),B)),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),times_times(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),D))) ) ) ),
    file('theBenchmark.p',fact_915_abs__mult__less) ).

fof(fact_916_abs__triangle__ineq,axiom,
    ! [X_a] :
      ( ordere142940540dd_abs(X_a)
     => ! [A_1,B] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B)))) ),
    file('theBenchmark.p',fact_916_abs__triangle__ineq) ).

fof(fact_917_abs__le__D1,axiom,
    ! [X_a] :
      ( ordere142940540dd_abs(X_a)
     => ! [A_1,B] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),B))
         => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) ) ),
    file('theBenchmark.p',fact_917_abs__le__D1) ).

fof(fact_918_abs__ge__self,axiom,
    ! [X_a] :
      ( ordere142940540dd_abs(X_a)
     => ! [A_1] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),hAPP(X_a,X_a,abs_abs(X_a),A_1))) ),
    file('theBenchmark.p',fact_918_abs__ge__self) ).

fof(fact_919_abs__eq__mult,axiom,
    ! [X_a] :
      ( ordered_ring_abs(X_a)
     => ! [B,A_1] :
          ( ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),zero_zero(X_a)))
              | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B)) )
            & ( 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),zero_zero(X_a)),A_1)) ) )
         => hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B)) ) ),
    file('theBenchmark.p',fact_919_abs__eq__mult) ).

fof(fact_920_abs__mult__pos,axiom,
    ! [X_a] :
      ( linordered_idom(X_a)
     => ! [Y,X] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X))
         => hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,abs_abs(X_a),Y)),X) = hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),X)) ) ),
    file('theBenchmark.p',fact_920_abs__mult__pos) ).

fof(fact_921_abs__mult,axiom,
    ! [X_a] :
      ( linordered_idom(X_a)
     => ! [A_1,B] : hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B)) ),
    file('theBenchmark.p',fact_921_abs__mult) ).

fof(fact_922_abs__mult__self,axiom,
    ! [X_a] :
      ( linordered_idom(X_a)
     => ! [A_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),A_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),A_1) ),
    file('theBenchmark.p',fact_922_abs__mult__self) ).

fof(fact_923_abs__minus__commute,axiom,
    ! [X_a] :
      ( ordere142940540dd_abs(X_a)
     => ! [A_1,B] : hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)) = hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B),A_1)) ),
    file('theBenchmark.p',fact_923_abs__minus__commute) ).

fof(fact_924_abs__add__abs,axiom,
    ! [X_a] :
      ( ordere142940540dd_abs(X_a)
     => ! [A_1,B] : hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B)) ),
    file('theBenchmark.p',fact_924_abs__add__abs) ).

fof(fact_925_abs__idempotent,axiom,
    ! [X_a] :
      ( ordere142940540dd_abs(X_a)
     => ! [A_1] : hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)) = hAPP(X_a,X_a,abs_abs(X_a),A_1) ),
    file('theBenchmark.p',fact_925_abs__idempotent) ).

fof(fact_926_not__neg__1,axiom,
    ~ hBOOL(hAPP(int,bool,nat_neg,one_one(int))),
    file('theBenchmark.p',fact_926_not__neg__1) ).

fof(fact_927_abs__one,axiom,
    ! [X_a] :
      ( linordered_idom(X_a)
     => hAPP(X_a,X_a,abs_abs(X_a),one_one(X_a)) = one_one(X_a) ),
    file('theBenchmark.p',fact_927_abs__one) ).

fof(fact_928_not__neg__0,axiom,
    ~ hBOOL(hAPP(int,bool,nat_neg,zero_zero(int))),
    file('theBenchmark.p',fact_928_not__neg__0) ).

fof(fact_929_abs__eq__0,axiom,
    ! [X_b] :
      ( ordere142940540dd_abs(X_b)
     => ! [A_2] :
          ( hAPP(X_b,X_b,abs_abs(X_b),A_2) = zero_zero(X_b)
        <=> ti(X_b,A_2) = zero_zero(X_b) ) ),
    file('theBenchmark.p',fact_929_abs__eq__0) ).

fof(fact_930_abs__zero,axiom,
    ! [X_a] :
      ( ordere142940540dd_abs(X_a)
     => hAPP(X_a,X_a,abs_abs(X_a),zero_zero(X_a)) = zero_zero(X_a) ),
    file('theBenchmark.p',fact_930_abs__zero) ).

fof(fact_931_abs__zmult__eq__1,axiom,
    ! [M_1,N] :
      ( hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M_1),N)) = one_one(int)
     => hAPP(int,int,abs_abs(int),M_1) = one_one(int) ),
    file('theBenchmark.p',fact_931_abs__zmult__eq__1) ).

fof(fact_932_abs__of__nat,axiom,
    ! [X_a] :
      ( linordered_idom(X_a)
     => ! [N] : hAPP(X_a,X_a,abs_abs(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N)) = hAPP(nat,X_a,semiring_1_of_nat(X_a),N) ),
    file('theBenchmark.p',fact_932_abs__of__nat) ).

fof(fact_933_not__neg__int,axiom,
    ! [N] : ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(nat,int,semiring_1_of_nat(int),N))),
    file('theBenchmark.p',fact_933_not__neg__int) ).

fof(fact_934_abs__int__eq,axiom,
    ! [M_1] : hAPP(int,int,abs_abs(int),hAPP(nat,int,semiring_1_of_nat(int),M_1)) = hAPP(nat,int,semiring_1_of_nat(int),M_1),
    file('theBenchmark.p',fact_934_abs__int__eq) ).

fof(fact_935_neg__imp__number__of__eq__0,axiom,
    ! [V] :
      ( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))
     => hAPP(int,nat,number_number_of(nat),V) = zero_zero(nat) ),
    file('theBenchmark.p',fact_935_neg__imp__number__of__eq__0) ).

fof(fact_936_eq__nat__number__of,axiom,
    ! [V_3,V_2] :
      ( hAPP(int,nat,number_number_of(nat),V_3) = hAPP(int,nat,number_number_of(nat),V_2)
    <=> ( ( ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_3)))
         => ( ( ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_2)))
             => V_3 = V_2 )
            & ( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_2)))
             => hAPP(int,int,number_number_of(int),V_3) = zero_zero(int) ) ) )
        & ( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_3)))
         => hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),V_2)),zero_zero(int))) ) ) ),
    file('theBenchmark.p',fact_936_eq__nat__number__of) ).

fof(fact_937_nat__number__of__add__left,axiom,
    ! [V_1,K_1,V] :
      ( ( ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))
       => ( ( ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_1)))
           => hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V_1)),K_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),V_1))),K_1) )
          & ( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_1)))
           => hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V_1)),K_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),K_1) ) ) )
      & ( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))
       => hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V_1)),K_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V_1)),K_1) ) ),
    file('theBenchmark.p',fact_937_nat__number__of__add__left) ).

fof(fact_938_int__nat__number__of,axiom,
    ! [V] :
      ( ( ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))
       => hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),V)) = hAPP(int,int,number_number_of(int),V) )
      & ( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))
       => hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),V)) = zero_zero(int) ) ),
    file('theBenchmark.p',fact_938_int__nat__number__of) ).

fof(fact_939_incr__lemma,axiom,
    ! [Z,X,D] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D))
     => hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X),Z))),one_one(int))),D)))) ),
    file('theBenchmark.p',fact_939_incr__lemma) ).

fof(fact_940_int__val__lemma,axiom,
    ! [K,F,Na] :
      ( ! [I] :
          ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),Na))
         => hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),one_one(nat)))),hAPP(nat,int,F,I)))),one_one(int))) )
     => ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,F,zero_zero(nat))),K))
       => ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),hAPP(nat,int,F,Na)))
         => ? [I] :
              ( hAPP(nat,int,F,I) = K
              & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),Na)) ) ) ) ),
    file('theBenchmark.p',fact_940_int__val__lemma) ).

fof(fact_941_nat0__intermed__int__val,axiom,
    ! [K,F,Na] :
      ( ! [I] :
          ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),Na))
         => hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),one_one(nat)))),hAPP(nat,int,F,I)))),one_one(int))) )
     => ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,F,zero_zero(nat))),K))
       => ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),hAPP(nat,int,F,Na)))
         => ? [I] :
              ( hAPP(nat,int,F,I) = K
              & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),Na)) ) ) ) ),
    file('theBenchmark.p',fact_941_nat0__intermed__int__val) ).

fof(fact_942_nat__intermed__int__val,axiom,
    ! [K,F,Na,M] :
      ( ! [I] :
          ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),Na))
            & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),I)) )
         => hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),one_one(nat)))),hAPP(nat,int,F,I)))),one_one(int))) )
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))
       => ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,F,M)),K))
         => ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),hAPP(nat,int,F,Na)))
           => ? [I] :
                ( hAPP(nat,int,F,I) = K
                & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),Na))
                & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),I)) ) ) ) ) ),
    file('theBenchmark.p',fact_942_nat__intermed__int__val) ).

fof(fact_943_Suc__nat__number__of__add,axiom,
    ! [N,V] :
      ( ( ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))
       => hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,V))),N) )
      & ( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))
       => hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),N) ) ),
    file('theBenchmark.p',fact_943_Suc__nat__number__of__add) ).

fof(fact_944_succ__def,axiom,
    ! [K_1] : hAPP(int,int,succ,K_1) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_1),one_one(int)),
    file('theBenchmark.p',fact_944_succ__def) ).

fof(fact_945_number__of__succ,axiom,
    ! [X_a] :
      ( number_ring(X_a)
     => ! [K_1] : hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,succ,K_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),hAPP(int,X_a,number_number_of(X_a),K_1)) ),
    file('theBenchmark.p',fact_945_number__of__succ) ).

fof(fact_946_Suc__nat__number__of,axiom,
    ! [V] :
      ( ( ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))
       => hAPP(nat,nat,suc,hAPP(int,nat,number_number_of(nat),V)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,V)) )
      & ( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))
       => hAPP(nat,nat,suc,hAPP(int,nat,number_number_of(nat),V)) = one_one(nat) ) ),
    file('theBenchmark.p',fact_946_Suc__nat__number__of) ).

fof(fact_947_nat__number__of__Bit1,axiom,
    ! [W] :
      ( ( ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),W)))
       => hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,W)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),W)),hAPP(int,nat,number_number_of(nat),W))) )
      & ( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),W)))
       => hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,W)) = zero_zero(nat) ) ),
    file('theBenchmark.p',fact_947_nat__number__of__Bit1) ).

fof(fact_948_nat__1__add__number__of,axiom,
    ! [V] :
      ( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls))
       => hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(int,nat,number_number_of(nat),V)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,V)) )
      & ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls))
       => hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(int,nat,number_number_of(nat),V)) = one_one(nat) ) ),
    file('theBenchmark.p',fact_948_nat__1__add__number__of) ).

fof(fact_949_succ__Pls,axiom,
    hAPP(int,int,succ,pls) = hAPP(int,int,bit1,pls),
    file('theBenchmark.p',fact_949_succ__Pls) ).

fof(fact_950_neg__number__of__Bit1,axiom,
    ! [W_1] :
      ( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,W_1))))
    <=> hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),W_1))) ),
    file('theBenchmark.p',fact_950_neg__number__of__Bit1) ).

fof(fact_951_not__neg__number__of__Pls,axiom,
    ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),pls))),
    file('theBenchmark.p',fact_951_not__neg__number__of__Pls) ).

fof(fact_952_transfer__int__nat__numerals_I4_J,axiom,
    hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),
    file('theBenchmark.p',fact_952_transfer__int__nat__numerals_I4_J) ).

fof(fact_953_number__of__Bit1,axiom,
    ! [X_a] :
      ( number_ring(X_a)
     => ! [W] : hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,W)) = 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),one_one(X_a)),hAPP(int,X_a,number_number_of(X_a),W))),hAPP(int,X_a,number_number_of(X_a),W)) ),
    file('theBenchmark.p',fact_953_number__of__Bit1) ).

fof(fact_954_numeral__1__eq__Suc__0,axiom,
    hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,pls)) = hAPP(nat,nat,suc,zero_zero(nat)),
    file('theBenchmark.p',fact_954_numeral__1__eq__Suc__0) ).

fof(fact_955_numeral__3__eq__3,axiom,
    hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))) = hAPP(nat,nat,suc,hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))),
    file('theBenchmark.p',fact_955_numeral__3__eq__3) ).

fof(fact_956_Suc3__eq__add__3,axiom,
    ! [N] : hAPP(nat,nat,suc,hAPP(nat,nat,suc,hAPP(nat,nat,suc,N))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),N),
    file('theBenchmark.p',fact_956_Suc3__eq__add__3) ).

fof(fact_957_semiring__norm_I110_J,axiom,
    ! [X_a] :
      ( number_ring(X_a)
     => one_one(X_a) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,pls)) ),
    file('theBenchmark.p',fact_957_semiring__norm_I110_J) ).

fof(fact_958_Numeral1__eq1__nat,axiom,
    one_one(nat) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,pls)),
    file('theBenchmark.p',fact_958_Numeral1__eq1__nat) ).

fof(fact_959_nat__numeral__1__eq__1,axiom,
    hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,pls)) = one_one(nat),
    file('theBenchmark.p',fact_959_nat__numeral__1__eq__1) ).

fof(fact_960_one__is__num__one,axiom,
    one_one(int) = hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,pls)),
    file('theBenchmark.p',fact_960_one__is__num__one) ).

fof(fact_961_numeral__1__eq__1,axiom,
    ! [X_a] :
      ( number_ring(X_a)
     => hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,pls)) = one_one(X_a) ),
    file('theBenchmark.p',fact_961_numeral__1__eq__1) ).

fof(fact_962_semiring__numeral__1__eq__1,axiom,
    ! [X_a] :
      ( number_semiring(X_a)
     => hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,pls)) = one_one(X_a) ),
    file('theBenchmark.p',fact_962_semiring__numeral__1__eq__1) ).

fof(fact_963_mult__numeral__1__right,axiom,
    ! [X_a] :
      ( number_ring(X_a)
     => ! [A_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,pls))) = ti(X_a,A_1) ),
    file('theBenchmark.p',fact_963_mult__numeral__1__right) ).

fof(fact_964_mult__numeral__1,axiom,
    ! [X_a] :
      ( number_ring(X_a)
     => ! [A_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,pls))),A_1) = ti(X_a,A_1) ),
    file('theBenchmark.p',fact_964_mult__numeral__1) ).

fof(fact_965_add__special_I3_J,axiom,
    ! [X_a] :
      ( number_ring(X_a)
     => ! [V] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),one_one(X_a)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),hAPP(int,int,bit1,pls))) ),
    file('theBenchmark.p',fact_965_add__special_I3_J) ).

fof(fact_966_add__special_I2_J,axiom,
    ! [X_a] :
      ( number_ring(X_a)
     => ! [W] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),hAPP(int,X_a,number_number_of(X_a),W)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit1,pls)),W)) ),
    file('theBenchmark.p',fact_966_add__special_I2_J) ).

fof(fact_967_zero__is__num__zero,axiom,
    zero_zero(int) = hAPP(int,int,number_number_of(int),pls),
    file('theBenchmark.p',fact_967_zero__is__num__zero) ).

fof(fact_968_Bit1__def,axiom,
    ! [K_1] : hAPP(int,int,bit1,K_1) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),K_1)),K_1),
    file('theBenchmark.p',fact_968_Bit1__def) ).

fof(fact_969_semiring__numeral__0__eq__0,axiom,
    ! [X_a] :
      ( number_semiring(X_a)
     => hAPP(int,X_a,number_number_of(X_a),pls) = zero_zero(X_a) ),
    file('theBenchmark.p',fact_969_semiring__numeral__0__eq__0) ).

fof(fact_970_number__of__Pls,axiom,
    ! [X_a] :
      ( number_ring(X_a)
     => hAPP(int,X_a,number_number_of(X_a),pls) = zero_zero(X_a) ),
    file('theBenchmark.p',fact_970_number__of__Pls) ).

fof(fact_971_semiring__norm_I112_J,axiom,
    ! [X_a] :
      ( number_ring(X_a)
     => zero_zero(X_a) = hAPP(int,X_a,number_number_of(X_a),pls) ),
    file('theBenchmark.p',fact_971_semiring__norm_I112_J) ).

fof(fact_972_add__numeral__0,axiom,
    ! [X_a] :
      ( number_ring(X_a)
     => ! [A_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),pls)),A_1) = ti(X_a,A_1) ),
    file('theBenchmark.p',fact_972_add__numeral__0) ).

fof(fact_973_add__numeral__0__right,axiom,
    ! [X_a] :
      ( number_ring(X_a)
     => ! [A_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(int,X_a,number_number_of(X_a),pls)) = ti(X_a,A_1) ),
    file('theBenchmark.p',fact_973_add__numeral__0__right) ).

fof(fact_974_nat__number__of__Pls,axiom,
    hAPP(int,nat,number_number_of(nat),pls) = zero_zero(nat),
    file('theBenchmark.p',fact_974_nat__number__of__Pls) ).

fof(fact_975_semiring__norm_I113_J,axiom,
    zero_zero(nat) = hAPP(int,nat,number_number_of(nat),pls),
    file('theBenchmark.p',fact_975_semiring__norm_I113_J) ).

fof(fact_976_Pls__def,axiom,
    pls = zero_zero(int),
    file('theBenchmark.p',fact_976_Pls__def) ).

fof(fact_977_rel__simps_I51_J,axiom,
    ! [K,L] :
      ( hAPP(int,int,bit1,K) = hAPP(int,int,bit1,L)
    <=> K = L ),
    file('theBenchmark.p',fact_977_rel__simps_I51_J) ).

fof(fact_978_rel__simps_I46_J,axiom,
    ! [K_1] : hAPP(int,int,bit1,K_1) != pls,
    file('theBenchmark.p',fact_978_rel__simps_I46_J) ).

fof(fact_979_rel__simps_I39_J,axiom,
    ! [L_1] : pls != hAPP(int,int,bit1,L_1),
    file('theBenchmark.p',fact_979_rel__simps_I39_J) ).

fof(fact_980_diff__bin__simps_I1_J,axiom,
    ! [K_1] : hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K_1),pls) = K_1,
    file('theBenchmark.p',fact_980_diff__bin__simps_I1_J) ).

fof(fact_981_add__Pls,axiom,
    ! [K_1] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),pls),K_1) = K_1,
    file('theBenchmark.p',fact_981_add__Pls) ).

fof(fact_982_add__Pls__right,axiom,
    ! [K_1] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_1),pls) = K_1,
    file('theBenchmark.p',fact_982_add__Pls__right) ).

fof(fact_983_mult__Pls,axiom,
    ! [W] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),W) = pls,
    file('theBenchmark.p',fact_983_mult__Pls) ).

fof(fact_984_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom,
    hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))))),
    file('theBenchmark.p',fact_984_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J) ).

fof(fact_985_rel__simps_I19_J,axiom,
    hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),pls)),
    file('theBenchmark.p',fact_985_rel__simps_I19_J) ).

fof(fact_986_rel__simps_I22_J,axiom,
    ! [K] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),hAPP(int,int,bit1,K)))
    <=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),K)) ),
    file('theBenchmark.p',fact_986_rel__simps_I22_J) ).

fof(fact_987_rel__simps_I34_J,axiom,
    ! [K,L] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,K)),hAPP(int,int,bit1,L)))
    <=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),L)) ),
    file('theBenchmark.p',fact_987_rel__simps_I34_J) ).

fof(fact_988_less__eq__int__code_I16_J,axiom,
    ! [K1,K2] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,K1)),hAPP(int,int,bit1,K2)))
    <=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K1),K2)) ),
    file('theBenchmark.p',fact_988_less__eq__int__code_I16_J) ).

fof(fact_989_rel__simps_I2_J,axiom,
    ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)),
    file('theBenchmark.p',fact_989_rel__simps_I2_J) ).

fof(fact_990_rel__simps_I12_J,axiom,
    ! [K] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K)),pls))
    <=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),pls)) ),
    file('theBenchmark.p',fact_990_rel__simps_I12_J) ).

fof(fact_991_rel__simps_I17_J,axiom,
    ! [K,L] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K)),hAPP(int,int,bit1,L)))
    <=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L)) ),
    file('theBenchmark.p',fact_991_rel__simps_I17_J) ).

fof(fact_992_less__int__code_I16_J,axiom,
    ! [K1,K2] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K1)),hAPP(int,int,bit1,K2)))
    <=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2)) ),
    file('theBenchmark.p',fact_992_less__int__code_I16_J) ).

fof(fact_993_rel__simps_I29_J,axiom,
    ! [K] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,K)),pls))
    <=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),pls)) ),
    file('theBenchmark.p',fact_993_rel__simps_I29_J) ).

fof(fact_994_rel__simps_I5_J,axiom,
    ! [K] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit1,K)))
    <=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),K)) ),
    file('theBenchmark.p',fact_994_rel__simps_I5_J) ).

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_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc,axiom,
    semiri456707255roduct(int),
    file('theBenchmark.p',arity_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc) ).

fof(arity_Int_Oint___Groups_Oordered__cancel__ab__semigroup__add,axiom,
    ordere223160158up_add(int),
    file('theBenchmark.p',arity_Int_Oint___Groups_Oordered__cancel__ab__semigroup__add) ).

fof(arity_Int_Oint___Groups_Oordered__ab__semigroup__add__imp__le,axiom,
    ordere236663937imp_le(int),
    file('theBenchmark.p',arity_Int_Oint___Groups_Oordered__ab__semigroup__add__imp__le) ).

fof(arity_Int_Oint___Rings_Olinordered__comm__semiring__strict,axiom,
    linord893533164strict(int),
    file('theBenchmark.p',arity_Int_Oint___Rings_Olinordered__comm__semiring__strict) ).

fof(arity_Int_Oint___Rings_Olinordered__semiring__1__strict,axiom,
    linord626643107strict(int),
    file('theBenchmark.p',arity_Int_Oint___Rings_Olinordered__semiring__1__strict) ).

fof(arity_Int_Oint___Rings_Olinordered__semiring__strict,axiom,
    linord20386208strict(int),
    file('theBenchmark.p',arity_Int_Oint___Rings_Olinordered__semiring__strict) ).

fof(arity_Int_Oint___Groups_Oordered__ab__semigroup__add,axiom,
    ordere779506340up_add(int),
    file('theBenchmark.p',arity_Int_Oint___Groups_Oordered__ab__semigroup__add) ).

fof(arity_Int_Oint___Groups_Oordered__ab__group__add__abs,axiom,
    ordere142940540dd_abs(int),
    file('theBenchmark.p',arity_Int_Oint___Groups_Oordered__ab__group__add__abs) ).

fof(arity_Int_Oint___Groups_Oordered__comm__monoid__add,axiom,
    ordere216010020id_add(int),
    file('theBenchmark.p',arity_Int_Oint___Groups_Oordered__comm__monoid__add) ).

fof(arity_Int_Oint___Groups_Olinordered__ab__group__add,axiom,
    linord219039673up_add(int),
    file('theBenchmark.p',arity_Int_Oint___Groups_Olinordered__ab__group__add) ).

fof(arity_Int_Oint___Groups_Ocancel__ab__semigroup__add,axiom,
    cancel146912293up_add(int),
    file('theBenchmark.p',arity_Int_Oint___Groups_Ocancel__ab__semigroup__add) ).

fof(arity_Int_Oint___Rings_Oordered__cancel__semiring,axiom,
    ordere453448008miring(int),
    file('theBenchmark.p',arity_Int_Oint___Rings_Oordered__cancel__semiring) ).

fof(arity_Int_Oint___Rings_Olinordered__ring__strict,axiom,
    linord581940658strict(int),
    file('theBenchmark.p',arity_Int_Oint___Rings_Olinordered__ring__strict) ).

fof(arity_Int_Oint___Rings_Oring__no__zero__divisors,axiom,
    ring_n68954251visors(int),
    file('theBenchmark.p',arity_Int_Oint___Rings_Oring__no__zero__divisors) ).

fof(arity_Int_Oint___Rings_Oordered__comm__semiring,axiom,
    ordere1490568538miring(int),
    file('theBenchmark.p',arity_Int_Oint___Rings_Oordered__comm__semiring) ).

fof(arity_Int_Oint___Rings_Olinordered__semiring__1,axiom,
    linord1278240602ring_1(int),
    file('theBenchmark.p',arity_Int_Oint___Rings_Olinordered__semiring__1) ).

fof(arity_Int_Oint___Groups_Oordered__ab__group__add,axiom,
    ordered_ab_group_add(int),
    file('theBenchmark.p',arity_Int_Oint___Groups_Oordered__ab__group__add) ).

fof(arity_Int_Oint___Groups_Ocancel__semigroup__add,axiom,
    cancel_semigroup_add(int),
    file('theBenchmark.p',arity_Int_Oint___Groups_Ocancel__semigroup__add) ).

fof(arity_Int_Oint___Rings_Olinordered__semiring,axiom,
    linordered_semiring(int),
    file('theBenchmark.p',arity_Int_Oint___Rings_Olinordered__semiring) ).

fof(arity_Int_Oint___Rings_Olinordered__semidom,axiom,
    linordered_semidom(int),
    file('theBenchmark.p',arity_Int_Oint___Rings_Olinordered__semidom) ).

fof(arity_Int_Oint___Groups_Oab__semigroup__mult,axiom,
    ab_semigroup_mult(int),
    file('theBenchmark.p',arity_Int_Oint___Groups_Oab__semigroup__mult) ).

fof(arity_Int_Oint___Groups_Ocomm__monoid__mult,axiom,
    comm_monoid_mult(int),
    file('theBenchmark.p',arity_Int_Oint___Groups_Ocomm__monoid__mult) ).

fof(arity_Int_Oint___Groups_Oab__semigroup__add,axiom,
    ab_semigroup_add(int),
    file('theBenchmark.p',arity_Int_Oint___Groups_Oab__semigroup__add) ).

fof(arity_Int_Oint___Rings_Oordered__semiring,axiom,
    ordered_semiring(int),
    file('theBenchmark.p',arity_Int_Oint___Rings_Oordered__semiring) ).

fof(arity_Int_Oint___Rings_Oordered__ring__abs,axiom,
    ordered_ring_abs(int),
    file('theBenchmark.p',arity_Int_Oint___Rings_Oordered__ring__abs) ).

fof(arity_Int_Oint___Rings_Ono__zero__divisors,axiom,
    no_zero_divisors(int),
    file('theBenchmark.p',arity_Int_Oint___Rings_Ono__zero__divisors) ).

fof(arity_Int_Oint___Groups_Ocomm__monoid__add,axiom,
    comm_monoid_add(int),
    file('theBenchmark.p',arity_Int_Oint___Groups_Ocomm__monoid__add) ).

fof(arity_Int_Oint___Rings_Olinordered__ring,axiom,
    linordered_ring(int),
    file('theBenchmark.p',arity_Int_Oint___Rings_Olinordered__ring) ).

fof(arity_Int_Oint___Rings_Olinordered__idom,axiom,
    linordered_idom(int),
    file('theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).

fof(arity_Int_Oint___Rings_Ocomm__semiring__1,axiom,
    comm_semiring_1(int),
    file('theBenchmark.p',arity_Int_Oint___Rings_Ocomm__semiring__1) ).

fof(arity_Int_Oint___Rings_Ocomm__semiring,axiom,
    comm_semiring(int),
    file('theBenchmark.p',arity_Int_Oint___Rings_Ocomm__semiring) ).

fof(arity_Int_Oint___Nat_Osemiring__char__0,axiom,
    semiring_char_0(int),
    file('theBenchmark.p',arity_Int_Oint___Nat_Osemiring__char__0) ).

fof(arity_Int_Oint___Int_Onumber__semiring,axiom,
    number_semiring(int),
    file('theBenchmark.p',arity_Int_Oint___Int_Onumber__semiring) ).

fof(arity_Int_Oint___Groups_Oab__group__add,axiom,
    ab_group_add(int),
    file('theBenchmark.p',arity_Int_Oint___Groups_Oab__group__add) ).

fof(arity_Int_Oint___Rings_Ozero__neq__one,axiom,
    zero_neq_one(int),
    file('theBenchmark.p',arity_Int_Oint___Rings_Ozero__neq__one) ).

fof(arity_Int_Oint___Rings_Oordered__ring,axiom,
    ordered_ring(int),
    file('theBenchmark.p',arity_Int_Oint___Rings_Oordered__ring) ).

fof(arity_Int_Oint___Orderings_Opreorder,axiom,
    preorder(int),
    file('theBenchmark.p',arity_Int_Oint___Orderings_Opreorder) ).

fof(arity_Int_Oint___Orderings_Olinorder,axiom,
    linorder(int),
    file('theBenchmark.p',arity_Int_Oint___Orderings_Olinorder) ).

fof(arity_Int_Oint___Groups_Omonoid__mult,axiom,
    monoid_mult(int),
    file('theBenchmark.p',arity_Int_Oint___Groups_Omonoid__mult) ).

fof(arity_Int_Oint___Groups_Omonoid__add,axiom,
    monoid_add(int),
    file('theBenchmark.p',arity_Int_Oint___Groups_Omonoid__add) ).

fof(arity_Int_Oint___Rings_Osemiring__1,axiom,
    semiring_1(int),
    file('theBenchmark.p',arity_Int_Oint___Rings_Osemiring__1) ).

fof(arity_Int_Oint___Groups_Ogroup__add,axiom,
    group_add(int),
    file('theBenchmark.p',arity_Int_Oint___Groups_Ogroup__add) ).

fof(arity_Int_Oint___Rings_Omult__zero,axiom,
    mult_zero(int),
    file('theBenchmark.p',arity_Int_Oint___Rings_Omult__zero) ).

fof(arity_Int_Oint___Orderings_Oorder,axiom,
    order(int),
    file('theBenchmark.p',arity_Int_Oint___Orderings_Oorder) ).

fof(arity_Int_Oint___Int_Oring__char__0,axiom,
    ring_char_0(int),
    file('theBenchmark.p',arity_Int_Oint___Int_Oring__char__0) ).

fof(arity_Int_Oint___Int_Onumber__ring,axiom,
    number_ring(int),
    file('theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).

fof(arity_Int_Oint___Rings_Osemiring,axiom,
    semiring(int),
    file('theBenchmark.p',arity_Int_Oint___Rings_Osemiring) ).

fof(arity_Int_Oint___Orderings_Oord,axiom,
    ord(int),
    file('theBenchmark.p',arity_Int_Oint___Orderings_Oord) ).

fof(arity_Int_Oint___Rings_Oring__1,axiom,
    ring_1(int),
    file('theBenchmark.p',arity_Int_Oint___Rings_Oring__1) ).

fof(arity_Int_Oint___Groups_Ominus,axiom,
    minus(int),
    file('theBenchmark.p',arity_Int_Oint___Groups_Ominus) ).

fof(arity_Int_Oint___Groups_Ozero,axiom,
    zero(int),
    file('theBenchmark.p',arity_Int_Oint___Groups_Ozero) ).

fof(arity_Int_Oint___Rings_Oring,axiom,
    ring(int),
    file('theBenchmark.p',arity_Int_Oint___Rings_Oring) ).

fof(arity_Int_Oint___Int_Onumber,axiom,
    number(int),
    file('theBenchmark.p',arity_Int_Oint___Int_Onumber) ).

fof(arity_Int_Oint___Groups_Oone,axiom,
    one(int),
    file('theBenchmark.p',arity_Int_Oint___Groups_Oone) ).

fof(arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc,axiom,
    semiri456707255roduct(nat),
    file('theBenchmark.p',arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc) ).

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___Rings_Olinordered__comm__semiring__strict,axiom,
    linord893533164strict(nat),
    file('theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__comm__semiring__strict) ).

fof(arity_Nat_Onat___Rings_Olinordered__semiring__strict,axiom,
    linord20386208strict(nat),
    file('theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__semiring__strict) ).

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___Rings_Oordered__cancel__semiring,axiom,
    ordere453448008miring(nat),
    file('theBenchmark.p',arity_Nat_Onat___Rings_Oordered__cancel__semiring) ).

fof(arity_Nat_Onat___Rings_Oordered__comm__semiring,axiom,
    ordere1490568538miring(nat),
    file('theBenchmark.p',arity_Nat_Onat___Rings_Oordered__comm__semiring) ).

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__semiring,axiom,
    linordered_semiring(nat),
    file('theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__semiring) ).

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__mult,axiom,
    ab_semigroup_mult(nat),
    file('theBenchmark.p',arity_Nat_Onat___Groups_Oab__semigroup__mult) ).

fof(arity_Nat_Onat___Groups_Ocomm__monoid__mult,axiom,
    comm_monoid_mult(nat),
    file('theBenchmark.p',arity_Nat_Onat___Groups_Ocomm__monoid__mult) ).

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___Rings_Oordered__semiring,axiom,
    ordered_semiring(nat),
    file('theBenchmark.p',arity_Nat_Onat___Rings_Oordered__semiring) ).

fof(arity_Nat_Onat___Rings_Ono__zero__divisors,axiom,
    no_zero_divisors(nat),
    file('theBenchmark.p',arity_Nat_Onat___Rings_Ono__zero__divisors) ).

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_Ocomm__semiring__1,axiom,
    comm_semiring_1(nat),
    file('theBenchmark.p',arity_Nat_Onat___Rings_Ocomm__semiring__1) ).

fof(arity_Nat_Onat___Rings_Ocomm__semiring,axiom,
    comm_semiring(nat),
    file('theBenchmark.p',arity_Nat_Onat___Rings_Ocomm__semiring) ).

fof(arity_Nat_Onat___Nat_Osemiring__char__0,axiom,
    semiring_char_0(nat),
    file('theBenchmark.p',arity_Nat_Onat___Nat_Osemiring__char__0) ).

fof(arity_Nat_Onat___Int_Onumber__semiring,axiom,
    number_semiring(nat),
    file('theBenchmark.p',arity_Nat_Onat___Int_Onumber__semiring) ).

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__mult,axiom,
    monoid_mult(nat),
    file('theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__mult) ).

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

fof(arity_Nat_Onat___Rings_Osemiring__1,axiom,
    semiring_1(nat),
    file('theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).

fof(arity_Nat_Onat___Rings_Omult__zero,axiom,
    mult_zero(nat),
    file('theBenchmark.p',arity_Nat_Onat___Rings_Omult__zero) ).

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

fof(arity_Nat_Onat___Rings_Osemiring,axiom,
    semiring(nat),
    file('theBenchmark.p',arity_Nat_Onat___Rings_Osemiring) ).

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___Int_Onumber,axiom,
    number(nat),
    file('theBenchmark.p',arity_Nat_Onat___Int_Onumber) ).

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_If_1_1_T,axiom,
    ! [X_a,X,Y] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),hAPP(bool,fun(X_a,fun(X_a,X_a)),if(X_a),fTrue),X),Y) = ti(X_a,X),
    file('theBenchmark.p',help_If_1_1_T) ).

fof(help_If_2_1_T,axiom,
    ! [X_a,X,Y] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),hAPP(bool,fun(X_a,fun(X_a,X_a)),if(X_a),fFalse),X),Y) = ti(X_a,Y),
    file('theBenchmark.p',help_If_2_1_T) ).

fof(help_If_3_1_T,axiom,
    ! [P] :
      ( ti(bool,P) = fFalse
      | ti(bool,P) = fTrue ),
    file('theBenchmark.p',help_If_3_1_T) ).

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_5,U_3,U_4] : 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_8,U_7] : 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_10,U_9,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_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(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(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b)))),finite_fold_image(X_b,X_c)) = finite_fold_image(X_b,X_c),
    inference(fof_nnf,[status(thm)],[tsy_c_Finite__Set_Ofold__image_res]) ).

fof(f_10_2,plain,
    ! [U_17,U_16] : ti(fun(fun(U_17,fun(U_17,U_17)),fun(fun(U_16,U_17),fun(U_17,fun(fun(U_16,bool),U_17)))),finite_fold_image(U_17,U_16)) = finite_fold_image(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(fun(U_16,U_17),fun(U_17,fun(fun(U_16,bool),U_17)))),finite_fold_image(U_17,U_16)) = finite_fold_image(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(fun(U_16,U_17),fun(U_17,fun(fun(U_16,bool),U_17)))),finite_fold_image(U_17,U_16)) = finite_fold_image(U_17,U_16),
    inference(clausify,[status(thm)],[f_10_3]) ).

fof(f_11_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_11_2,plain,
    ! [U_19,U_18] : ti(fun(fun(U_19,fun(U_19,U_19)),fun(U_19,fun(fun(U_18,U_19),fun(fun(fun(U_18,bool),U_19),bool)))),finite1357897459simple(U_19,U_18)) = finite1357897459simple(U_19,U_18),
    inference(variable_rename,[status(thm)],[f_11_1]) ).

fof(f_11_3,plain,
    ! [U_18,U_19] : ti(fun(fun(U_19,fun(U_19,U_19)),fun(U_19,fun(fun(U_18,U_19),fun(fun(fun(U_18,bool),U_19),bool)))),finite1357897459simple(U_19,U_18)) = finite1357897459simple(U_19,U_18),
    inference(definitional_conversion,[status(esa)],[f_11_2]) ).

cnf(f_11_4,plain,
    ti(fun(fun(U_19,fun(U_19,U_19)),fun(U_19,fun(fun(U_18,U_19),fun(fun(fun(U_18,bool),U_19),bool)))),finite1357897459simple(U_19,U_18)) = finite1357897459simple(U_19,U_18),
    inference(clausify,[status(thm)],[f_11_3]) ).

fof(f_12_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)))),finite908156982e_idem(X_b,X_c)) = finite908156982e_idem(X_b,X_c),
    inference(fof_nnf,[status(thm)],[tsy_c_Finite__Set_Ofolding__image__simple__idem_res]) ).

fof(f_12_2,plain,
    ! [U_21,U_20] : ti(fun(fun(U_21,fun(U_21,U_21)),fun(U_21,fun(fun(U_20,U_21),fun(fun(fun(U_20,bool),U_21),bool)))),finite908156982e_idem(U_21,U_20)) = finite908156982e_idem(U_21,U_20),
    inference(variable_rename,[status(thm)],[f_12_1]) ).

fof(f_12_3,plain,
    ! [U_20,U_21] : ti(fun(fun(U_21,fun(U_21,U_21)),fun(U_21,fun(fun(U_20,U_21),fun(fun(fun(U_20,bool),U_21),bool)))),finite908156982e_idem(U_21,U_20)) = finite908156982e_idem(U_21,U_20),
    inference(definitional_conversion,[status(esa)],[f_12_2]) ).

cnf(f_12_4,plain,
    ti(fun(fun(U_21,fun(U_21,U_21)),fun(U_21,fun(fun(U_20,U_21),fun(fun(fun(U_20,bool),U_21),bool)))),finite908156982e_idem(U_21,U_20)) = finite908156982e_idem(U_21,U_20),
    inference(clausify,[status(thm)],[f_12_3]) ).

fof(f_13_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_13_2,plain,
    ! [U_22] : ti(fun(fun(U_22,fun(U_22,U_22)),fun(fun(fun(U_22,bool),U_22),bool)),finite_folding_one(U_22)) = finite_folding_one(U_22),
    inference(variable_rename,[status(thm)],[f_13_1]) ).

fof(f_13_3,plain,
    ! [U_22] : ti(fun(fun(U_22,fun(U_22,U_22)),fun(fun(fun(U_22,bool),U_22),bool)),finite_folding_one(U_22)) = finite_folding_one(U_22),
    inference(definitional_conversion,[status(esa)],[f_13_2]) ).

cnf(f_13_4,plain,
    ti(fun(fun(U_22,fun(U_22,U_22)),fun(fun(fun(U_22,bool),U_22),bool)),finite_folding_one(U_22)) = finite_folding_one(U_22),
    inference(clausify,[status(thm)],[f_13_3]) ).

fof(f_14_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_14_2,plain,
    ! [U_23] : ti(fun(fun(U_23,fun(U_23,U_23)),fun(fun(fun(U_23,bool),U_23),bool)),finite2073411215e_idem(U_23)) = finite2073411215e_idem(U_23),
    inference(variable_rename,[status(thm)],[f_14_1]) ).

fof(f_14_3,plain,
    ! [U_23] : ti(fun(fun(U_23,fun(U_23,U_23)),fun(fun(fun(U_23,bool),U_23),bool)),finite2073411215e_idem(U_23)) = finite2073411215e_idem(U_23),
    inference(definitional_conversion,[status(esa)],[f_14_2]) ).

cnf(f_14_4,plain,
    ti(fun(fun(U_23,fun(U_23,U_23)),fun(fun(fun(U_23,bool),U_23),bool)),finite2073411215e_idem(U_23)) = finite2073411215e_idem(U_23),
    inference(clausify,[status(thm)],[f_14_3]) ).

fof(f_15_1,plain,
    ! [X_a] :
      ( ti(fun(X_a,X_a),abs_abs(X_a)) = abs_abs(X_a)
      | ~ ordere142940540dd_abs(X_a) ),
    inference(fof_nnf,[status(thm)],[tsy_c_Groups_Oabs__class_Oabs_res]) ).

fof(f_15_2,plain,
    ! [U_24] :
      ( ti(fun(U_24,U_24),abs_abs(U_24)) = abs_abs(U_24)
      | ~ ordere142940540dd_abs(U_24) ),
    inference(variable_rename,[status(thm)],[f_15_1]) ).

fof(f_15_3,plain,
    ! [U_24] :
      ( ti(fun(U_24,U_24),abs_abs(U_24)) = abs_abs(U_24)
      | ~ ordere142940540dd_abs(U_24) ),
    inference(definitional_conversion,[status(esa)],[f_15_2]) ).

cnf(f_15_4,plain,
    ( ti(fun(U_24,U_24),abs_abs(U_24)) = abs_abs(U_24)
    | ~ ordere142940540dd_abs(U_24) ),
    inference(clausify,[status(thm)],[f_15_3]) ).

fof(f_16_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_16_2,plain,
    ! [U_25] :
      ( ti(fun(U_25,fun(U_25,U_25)),minus_minus(U_25)) = minus_minus(U_25)
      | ~ minus(U_25) ),
    inference(variable_rename,[status(thm)],[f_16_1]) ).

fof(f_16_3,plain,
    ! [U_25] :
      ( ti(fun(U_25,fun(U_25,U_25)),minus_minus(U_25)) = minus_minus(U_25)
      | ~ minus(U_25) ),
    inference(definitional_conversion,[status(esa)],[f_16_2]) ).

cnf(f_16_4,plain,
    ( ti(fun(U_25,fun(U_25,U_25)),minus_minus(U_25)) = minus_minus(U_25)
    | ~ minus(U_25) ),
    inference(clausify,[status(thm)],[f_16_3]) ).

fof(f_17_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_17_2,plain,
    ! [U_26] :
      ( ti(U_26,one_one(U_26)) = one_one(U_26)
      | ~ one(U_26) ),
    inference(variable_rename,[status(thm)],[f_17_1]) ).

fof(f_17_3,plain,
    ! [U_26] :
      ( ti(U_26,one_one(U_26)) = one_one(U_26)
      | ~ one(U_26) ),
    inference(definitional_conversion,[status(esa)],[f_17_2]) ).

cnf(f_17_4,plain,
    ( ti(U_26,one_one(U_26)) = one_one(U_26)
    | ~ one(U_26) ),
    inference(clausify,[status(thm)],[f_17_3]) ).

fof(f_18_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_18_2,plain,
    ! [U_27] :
      ( ti(fun(U_27,fun(U_27,U_27)),plus_plus(U_27)) = plus_plus(U_27)
      | ~ monoid_add(U_27) ),
    inference(variable_rename,[status(thm)],[f_18_1]) ).

fof(f_18_3,plain,
    ! [U_27] :
      ( ti(fun(U_27,fun(U_27,U_27)),plus_plus(U_27)) = plus_plus(U_27)
      | ~ monoid_add(U_27) ),
    inference(definitional_conversion,[status(esa)],[f_18_2]) ).

cnf(f_18_4,plain,
    ( ti(fun(U_27,fun(U_27,U_27)),plus_plus(U_27)) = plus_plus(U_27)
    | ~ monoid_add(U_27) ),
    inference(clausify,[status(thm)],[f_18_3]) ).

fof(f_19_1,plain,
    ! [X_b] :
      ( ti(fun(X_b,fun(X_b,X_b)),plus_plus(X_b)) = plus_plus(X_b)
      | ~ cancel_semigroup_add(X_b) ),
    inference(fof_nnf,[status(thm)],[tsy_c_Groups_Oplus__class_Oplus_1_res]) ).

fof(f_19_2,plain,
    ! [U_28] :
      ( ti(fun(U_28,fun(U_28,U_28)),plus_plus(U_28)) = plus_plus(U_28)
      | ~ cancel_semigroup_add(U_28) ),
    inference(variable_rename,[status(thm)],[f_19_1]) ).

fof(f_19_3,plain,
    ! [U_28] :
      ( ti(fun(U_28,fun(U_28,U_28)),plus_plus(U_28)) = plus_plus(U_28)
      | ~ cancel_semigroup_add(U_28) ),
    inference(definitional_conversion,[status(esa)],[f_19_2]) ).

cnf(f_19_4,plain,
    ( ti(fun(U_28,fun(U_28,U_28)),plus_plus(U_28)) = plus_plus(U_28)
    | ~ cancel_semigroup_add(U_28) ),
    inference(clausify,[status(thm)],[f_19_3]) ).

fof(f_20_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_2_res]) ).

fof(f_20_2,plain,
    ! [U_29] :
      ( ti(fun(U_29,fun(U_29,U_29)),plus_plus(U_29)) = plus_plus(U_29)
      | ~ ab_semigroup_add(U_29) ),
    inference(variable_rename,[status(thm)],[f_20_1]) ).

fof(f_20_3,plain,
    ! [U_29] :
      ( ti(fun(U_29,fun(U_29,U_29)),plus_plus(U_29)) = plus_plus(U_29)
      | ~ ab_semigroup_add(U_29) ),
    inference(definitional_conversion,[status(esa)],[f_20_2]) ).

cnf(f_20_4,plain,
    ( ti(fun(U_29,fun(U_29,U_29)),plus_plus(U_29)) = plus_plus(U_29)
    | ~ ab_semigroup_add(U_29) ),
    inference(clausify,[status(thm)],[f_20_3]) ).

fof(f_21_1,plain,
    ! [X_a] :
      ( ti(fun(X_a,fun(X_a,X_a)),times_times(X_a)) = times_times(X_a)
      | ~ ab_semigroup_mult(X_a) ),
    inference(fof_nnf,[status(thm)],[tsy_c_Groups_Otimes__class_Otimes_0_res]) ).

fof(f_21_2,plain,
    ! [U_30] :
      ( ti(fun(U_30,fun(U_30,U_30)),times_times(U_30)) = times_times(U_30)
      | ~ ab_semigroup_mult(U_30) ),
    inference(variable_rename,[status(thm)],[f_21_1]) ).

fof(f_21_3,plain,
    ! [U_30] :
      ( ti(fun(U_30,fun(U_30,U_30)),times_times(U_30)) = times_times(U_30)
      | ~ ab_semigroup_mult(U_30) ),
    inference(definitional_conversion,[status(esa)],[f_21_2]) ).

cnf(f_21_4,plain,
    ( ti(fun(U_30,fun(U_30,U_30)),times_times(U_30)) = times_times(U_30)
    | ~ ab_semigroup_mult(U_30) ),
    inference(clausify,[status(thm)],[f_21_3]) ).

fof(f_22_1,plain,
    ! [X_a] :
      ( ti(fun(X_a,fun(X_a,X_a)),times_times(X_a)) = times_times(X_a)
      | ~ monoid_mult(X_a) ),
    inference(fof_nnf,[status(thm)],[tsy_c_Groups_Otimes__class_Otimes_1_res]) ).

fof(f_22_2,plain,
    ! [U_31] :
      ( ti(fun(U_31,fun(U_31,U_31)),times_times(U_31)) = times_times(U_31)
      | ~ monoid_mult(U_31) ),
    inference(variable_rename,[status(thm)],[f_22_1]) ).

fof(f_22_3,plain,
    ! [U_31] :
      ( ti(fun(U_31,fun(U_31,U_31)),times_times(U_31)) = times_times(U_31)
      | ~ monoid_mult(U_31) ),
    inference(definitional_conversion,[status(esa)],[f_22_2]) ).

cnf(f_22_4,plain,
    ( ti(fun(U_31,fun(U_31,U_31)),times_times(U_31)) = times_times(U_31)
    | ~ monoid_mult(U_31) ),
    inference(clausify,[status(thm)],[f_22_3]) ).

fof(f_23_1,plain,
    ! [X_a] :
      ( ti(fun(X_a,fun(X_a,X_a)),times_times(X_a)) = times_times(X_a)
      | ~ semiring(X_a) ),
    inference(fof_nnf,[status(thm)],[tsy_c_Groups_Otimes__class_Otimes_2_res]) ).

fof(f_23_2,plain,
    ! [U_32] :
      ( ti(fun(U_32,fun(U_32,U_32)),times_times(U_32)) = times_times(U_32)
      | ~ semiring(U_32) ),
    inference(variable_rename,[status(thm)],[f_23_1]) ).

fof(f_23_3,plain,
    ! [U_32] :
      ( ti(fun(U_32,fun(U_32,U_32)),times_times(U_32)) = times_times(U_32)
      | ~ semiring(U_32) ),
    inference(definitional_conversion,[status(esa)],[f_23_2]) ).

cnf(f_23_4,plain,
    ( ti(fun(U_32,fun(U_32,U_32)),times_times(U_32)) = times_times(U_32)
    | ~ semiring(U_32) ),
    inference(clausify,[status(thm)],[f_23_3]) ).

fof(f_24_1,plain,
    ! [X_a] :
      ( ti(fun(X_a,fun(X_a,X_a)),times_times(X_a)) = times_times(X_a)
      | ~ no_zero_divisors(X_a) ),
    inference(fof_nnf,[status(thm)],[tsy_c_Groups_Otimes__class_Otimes_3_res]) ).

fof(f_24_2,plain,
    ! [U_33] :
      ( ti(fun(U_33,fun(U_33,U_33)),times_times(U_33)) = times_times(U_33)
      | ~ no_zero_divisors(U_33) ),
    inference(variable_rename,[status(thm)],[f_24_1]) ).

fof(f_24_3,plain,
    ! [U_33] :
      ( ti(fun(U_33,fun(U_33,U_33)),times_times(U_33)) = times_times(U_33)
      | ~ no_zero_divisors(U_33) ),
    inference(definitional_conversion,[status(esa)],[f_24_2]) ).

cnf(f_24_4,plain,
    ( ti(fun(U_33,fun(U_33,U_33)),times_times(U_33)) = times_times(U_33)
    | ~ no_zero_divisors(U_33) ),
    inference(clausify,[status(thm)],[f_24_3]) ).

fof(f_25_1,plain,
    ! [X_a] :
      ( ti(fun(X_a,fun(X_a,X_a)),times_times(X_a)) = times_times(X_a)
      | ~ mult_zero(X_a) ),
    inference(fof_nnf,[status(thm)],[tsy_c_Groups_Otimes__class_Otimes_4_res]) ).

fof(f_25_2,plain,
    ! [U_34] :
      ( ti(fun(U_34,fun(U_34,U_34)),times_times(U_34)) = times_times(U_34)
      | ~ mult_zero(U_34) ),
    inference(variable_rename,[status(thm)],[f_25_1]) ).

fof(f_25_3,plain,
    ! [U_34] :
      ( ti(fun(U_34,fun(U_34,U_34)),times_times(U_34)) = times_times(U_34)
      | ~ mult_zero(U_34) ),
    inference(definitional_conversion,[status(esa)],[f_25_2]) ).

cnf(f_25_4,plain,
    ( ti(fun(U_34,fun(U_34,U_34)),times_times(U_34)) = times_times(U_34)
    | ~ mult_zero(U_34) ),
    inference(clausify,[status(thm)],[f_25_3]) ).

fof(f_26_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_26_2,plain,
    ! [U_35] :
      ( ti(U_35,zero_zero(U_35)) = zero_zero(U_35)
      | ~ zero(U_35) ),
    inference(variable_rename,[status(thm)],[f_26_1]) ).

fof(f_26_3,plain,
    ! [U_35] :
      ( ti(U_35,zero_zero(U_35)) = zero_zero(U_35)
      | ~ zero(U_35) ),
    inference(definitional_conversion,[status(esa)],[f_26_2]) ).

cnf(f_26_4,plain,
    ( ti(U_35,zero_zero(U_35)) = zero_zero(U_35)
    | ~ zero(U_35) ),
    inference(clausify,[status(thm)],[f_26_3]) ).

fof(f_27_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_27_2,plain,
    ! [U_36] : ti(fun(fun(U_36,bool),U_36),the(U_36)) = the(U_36),
    inference(variable_rename,[status(thm)],[f_27_1]) ).

fof(f_27_3,plain,
    ! [U_36] : ti(fun(fun(U_36,bool),U_36),the(U_36)) = the(U_36),
    inference(definitional_conversion,[status(esa)],[f_27_2]) ).

cnf(f_27_4,plain,
    ti(fun(fun(U_36,bool),U_36),the(U_36)) = the(U_36),
    inference(clausify,[status(thm)],[f_27_3]) ).

fof(f_28_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_28_2,plain,
    ! [U_37] : ti(U_37,undefined(U_37)) = undefined(U_37),
    inference(variable_rename,[status(thm)],[f_28_1]) ).

fof(f_28_3,plain,
    ! [U_37] : ti(U_37,undefined(U_37)) = undefined(U_37),
    inference(definitional_conversion,[status(esa)],[f_28_2]) ).

cnf(f_28_4,plain,
    ti(U_37,undefined(U_37)) = undefined(U_37),
    inference(clausify,[status(thm)],[f_28_3]) ).

fof(f_29_1,plain,
    ! [X_a] : ti(fun(bool,fun(X_a,fun(X_a,X_a))),if(X_a)) = if(X_a),
    inference(fof_nnf,[status(thm)],[tsy_c_If_res]) ).

fof(f_29_2,plain,
    ! [U_38] : ti(fun(bool,fun(U_38,fun(U_38,U_38))),if(U_38)) = if(U_38),
    inference(variable_rename,[status(thm)],[f_29_1]) ).

fof(f_29_3,plain,
    ! [U_38] : ti(fun(bool,fun(U_38,fun(U_38,U_38))),if(U_38)) = if(U_38),
    inference(definitional_conversion,[status(esa)],[f_29_2]) ).

cnf(f_29_4,plain,
    ti(fun(bool,fun(U_38,fun(U_38,U_38))),if(U_38)) = if(U_38),
    inference(clausify,[status(thm)],[f_29_3]) ).

fof(f_30_1,plain,
    ti(fun(int,int),bit1) = bit1,
    inference(fof_nnf,[status(thm)],[tsy_c_Int_OBit1_res]) ).

fof(f_30_2,plain,
    ti(fun(int,int),bit1) = bit1,
    inference(definitional_conversion,[status(esa)],[f_30_1]) ).

cnf(f_30_3,plain,
    ti(fun(int,int),bit1) = bit1,
    inference(clausify,[status(thm)],[f_30_2]) ).

fof(f_31_1,plain,
    ti(int,pls) = pls,
    inference(fof_nnf,[status(thm)],[tsy_c_Int_OPls_res]) ).

fof(f_31_2,plain,
    ti(int,pls) = pls,
    inference(definitional_conversion,[status(esa)],[f_31_1]) ).

cnf(f_31_3,plain,
    ti(int,pls) = pls,
    inference(clausify,[status(thm)],[f_31_2]) ).

fof(f_32_1,plain,
    ! [X_b] :
      ( ti(fun(int,X_b),number_number_of(X_b)) = number_number_of(X_b)
      | ~ number(X_b) ),
    inference(fof_nnf,[status(thm)],[tsy_c_Int_Onumber__class_Onumber__of_res]) ).

fof(f_32_2,plain,
    ! [U_39] :
      ( ti(fun(int,U_39),number_number_of(U_39)) = number_number_of(U_39)
      | ~ number(U_39) ),
    inference(variable_rename,[status(thm)],[f_32_1]) ).

fof(f_32_3,plain,
    ! [U_39] :
      ( ti(fun(int,U_39),number_number_of(U_39)) = number_number_of(U_39)
      | ~ number(U_39) ),
    inference(definitional_conversion,[status(esa)],[f_32_2]) ).

cnf(f_32_4,plain,
    ( ti(fun(int,U_39),number_number_of(U_39)) = number_number_of(U_39)
    | ~ number(U_39) ),
    inference(clausify,[status(thm)],[f_32_3]) ).

fof(f_33_1,plain,
    ! [X_b] :
      ( ti(fun(X_b,bool),ring_1_Ints(X_b)) = ring_1_Ints(X_b)
      | ~ ring_1(X_b) ),
    inference(fof_nnf,[status(thm)],[tsy_c_Int_Oring__1__class_OInts_res]) ).

fof(f_33_2,plain,
    ! [U_40] :
      ( ti(fun(U_40,bool),ring_1_Ints(U_40)) = ring_1_Ints(U_40)
      | ~ ring_1(U_40) ),
    inference(variable_rename,[status(thm)],[f_33_1]) ).

fof(f_33_3,plain,
    ! [U_40] :
      ( ti(fun(U_40,bool),ring_1_Ints(U_40)) = ring_1_Ints(U_40)
      | ~ ring_1(U_40) ),
    inference(definitional_conversion,[status(esa)],[f_33_2]) ).

cnf(f_33_4,plain,
    ( ti(fun(U_40,bool),ring_1_Ints(U_40)) = ring_1_Ints(U_40)
    | ~ ring_1(U_40) ),
    inference(clausify,[status(thm)],[f_33_3]) ).

fof(f_34_1,plain,
    ti(fun(int,int),succ) = succ,
    inference(fof_nnf,[status(thm)],[tsy_c_Int_Osucc_res]) ).

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

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

fof(f_35_1,plain,
    ti(fun(nat,nat),suc) = suc,
    inference(fof_nnf,[status(thm)],[tsy_c_Nat_OSuc_res]) ).

fof(f_35_2,plain,
    ti(fun(nat,nat),suc) = suc,
    inference(definitional_conversion,[status(esa)],[f_35_1]) ).

cnf(f_35_3,plain,
    ti(fun(nat,nat),suc) = suc,
    inference(clausify,[status(thm)],[f_35_2]) ).

fof(f_36_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_36_2,plain,
    ! [U_41] : ti(fun(U_41,fun(fun(nat,U_41),fun(nat,U_41))),nat_case(U_41)) = nat_case(U_41),
    inference(variable_rename,[status(thm)],[f_36_1]) ).

fof(f_36_3,plain,
    ! [U_41] : ti(fun(U_41,fun(fun(nat,U_41),fun(nat,U_41))),nat_case(U_41)) = nat_case(U_41),
    inference(definitional_conversion,[status(esa)],[f_36_2]) ).

cnf(f_36_4,plain,
    ti(fun(U_41,fun(fun(nat,U_41),fun(nat,U_41))),nat_case(U_41)) = nat_case(U_41),
    inference(clausify,[status(thm)],[f_36_3]) ).

fof(f_37_1,plain,
    ! [X_a] :
      ( ti(fun(nat,X_a),semiring_1_of_nat(X_a)) = semiring_1_of_nat(X_a)
      | ~ semiring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[tsy_c_Nat_Osemiring__1__class_Oof__nat_res]) ).

fof(f_37_2,plain,
    ! [U_42] :
      ( ti(fun(nat,U_42),semiring_1_of_nat(U_42)) = semiring_1_of_nat(U_42)
      | ~ semiring_1(U_42) ),
    inference(variable_rename,[status(thm)],[f_37_1]) ).

fof(f_37_3,plain,
    ! [U_42] :
      ( ti(fun(nat,U_42),semiring_1_of_nat(U_42)) = semiring_1_of_nat(U_42)
      | ~ semiring_1(U_42) ),
    inference(definitional_conversion,[status(esa)],[f_37_2]) ).

cnf(f_37_4,plain,
    ( ti(fun(nat,U_42),semiring_1_of_nat(U_42)) = semiring_1_of_nat(U_42)
    | ~ semiring_1(U_42) ),
    inference(clausify,[status(thm)],[f_37_3]) ).

fof(f_38_1,plain,
    ! [X_b] :
      ( ti(fun(fun(X_b,X_b),fun(nat,fun(X_b,X_b))),semiri532925092at_aux(X_b)) = semiri532925092at_aux(X_b)
      | ~ semiring_1(X_b) ),
    inference(fof_nnf,[status(thm)],[tsy_c_Nat_Osemiring__1__class_Oof__nat__aux_res]) ).

fof(f_38_2,plain,
    ! [U_43] :
      ( ti(fun(fun(U_43,U_43),fun(nat,fun(U_43,U_43))),semiri532925092at_aux(U_43)) = semiri532925092at_aux(U_43)
      | ~ semiring_1(U_43) ),
    inference(variable_rename,[status(thm)],[f_38_1]) ).

fof(f_38_3,plain,
    ! [U_43] :
      ( ti(fun(fun(U_43,U_43),fun(nat,fun(U_43,U_43))),semiri532925092at_aux(U_43)) = semiri532925092at_aux(U_43)
      | ~ semiring_1(U_43) ),
    inference(definitional_conversion,[status(esa)],[f_38_2]) ).

cnf(f_38_4,plain,
    ( ti(fun(fun(U_43,U_43),fun(nat,fun(U_43,U_43))),semiri532925092at_aux(U_43)) = semiri532925092at_aux(U_43)
    | ~ semiring_1(U_43) ),
    inference(clausify,[status(thm)],[f_38_3]) ).

fof(f_39_1,plain,
    ti(fun(int,bool),nat_neg) = nat_neg,
    inference(fof_nnf,[status(thm)],[tsy_c_Nat__Numeral_Oneg_res]) ).

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

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

fof(f_40_1,plain,
    ti(fun(int,fun(int,int)),nat_tsub) = nat_tsub,
    inference(fof_nnf,[status(thm)],[tsy_c_Nat__Transfer_Otsub_res]) ).

fof(f_40_2,plain,
    ti(fun(int,fun(int,int)),nat_tsub) = nat_tsub,
    inference(definitional_conversion,[status(esa)],[f_40_1]) ).

cnf(f_40_3,plain,
    ti(fun(int,fun(int,int)),nat_tsub) = nat_tsub,
    inference(clausify,[status(thm)],[f_40_2]) ).

fof(f_41_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_41_2,plain,
    ti(fun(option(com),com),the_1(com)) = the_1(com),
    inference(definitional_conversion,[status(esa)],[f_41_1]) ).

cnf(f_41_3,plain,
    ti(fun(option(com),com),the_1(com)) = the_1(com),
    inference(clausify,[status(thm)],[f_41_2]) ).

fof(f_42_1,plain,
    ! [X_b] :
      ( ti(X_b,bot_bot(X_b)) = bot_bot(X_b)
      | ~ bot(X_b) ),
    inference(fof_nnf,[status(thm)],[tsy_c_Orderings_Obot__class_Obot_res]) ).

fof(f_42_2,plain,
    ! [U_44] :
      ( ti(U_44,bot_bot(U_44)) = bot_bot(U_44)
      | ~ bot(U_44) ),
    inference(variable_rename,[status(thm)],[f_42_1]) ).

fof(f_42_3,plain,
    ! [U_44] :
      ( ti(U_44,bot_bot(U_44)) = bot_bot(U_44)
      | ~ bot(U_44) ),
    inference(definitional_conversion,[status(esa)],[f_42_2]) ).

cnf(f_42_4,plain,
    ( ti(U_44,bot_bot(U_44)) = bot_bot(U_44)
    | ~ bot(U_44) ),
    inference(clausify,[status(thm)],[f_42_3]) ).

fof(f_43_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_43_2,plain,
    ! [U_45] :
      ( ti(fun(U_45,fun(U_45,bool)),ord_less(U_45)) = ord_less(U_45)
      | ~ ord(U_45) ),
    inference(variable_rename,[status(thm)],[f_43_1]) ).

fof(f_43_3,plain,
    ! [U_45] :
      ( ti(fun(U_45,fun(U_45,bool)),ord_less(U_45)) = ord_less(U_45)
      | ~ ord(U_45) ),
    inference(definitional_conversion,[status(esa)],[f_43_2]) ).

cnf(f_43_4,plain,
    ( ti(fun(U_45,fun(U_45,bool)),ord_less(U_45)) = ord_less(U_45)
    | ~ ord(U_45) ),
    inference(clausify,[status(thm)],[f_43_3]) ).

fof(f_44_1,plain,
    ! [X_a] :
      ( ti(fun(X_a,fun(X_a,bool)),ord_less_eq(X_a)) = ord_less_eq(X_a)
      | ~ ord(X_a) ),
    inference(fof_nnf,[status(thm)],[tsy_c_Orderings_Oord__class_Oless__eq_res]) ).

fof(f_44_2,plain,
    ! [U_46] :
      ( ti(fun(U_46,fun(U_46,bool)),ord_less_eq(U_46)) = ord_less_eq(U_46)
      | ~ ord(U_46) ),
    inference(variable_rename,[status(thm)],[f_44_1]) ).

fof(f_44_3,plain,
    ! [U_46] :
      ( ti(fun(U_46,fun(U_46,bool)),ord_less_eq(U_46)) = ord_less_eq(U_46)
      | ~ ord(U_46) ),
    inference(definitional_conversion,[status(esa)],[f_44_2]) ).

cnf(f_44_4,plain,
    ( ti(fun(U_46,fun(U_46,bool)),ord_less_eq(U_46)) = ord_less_eq(U_46)
    | ~ ord(U_46) ),
    inference(clausify,[status(thm)],[f_44_3]) ).

fof(f_45_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_45_2,plain,
    ! [U_47] : ti(fun(U_47,fun(fun(U_47,bool),U_47)),partial_flat_lub(U_47)) = partial_flat_lub(U_47),
    inference(variable_rename,[status(thm)],[f_45_1]) ).

fof(f_45_3,plain,
    ! [U_47] : ti(fun(U_47,fun(fun(U_47,bool),U_47)),partial_flat_lub(U_47)) = partial_flat_lub(U_47),
    inference(definitional_conversion,[status(esa)],[f_45_2]) ).

cnf(f_45_4,plain,
    ti(fun(U_47,fun(fun(U_47,bool),U_47)),partial_flat_lub(U_47)) = partial_flat_lub(U_47),
    inference(clausify,[status(thm)],[f_45_3]) ).

fof(f_46_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_46_2,plain,
    ! [U_48] : ti(fun(fun(U_48,bool),fun(U_48,bool)),collect(U_48)) = collect(U_48),
    inference(variable_rename,[status(thm)],[f_46_1]) ).

fof(f_46_3,plain,
    ! [U_48] : ti(fun(fun(U_48,bool),fun(U_48,bool)),collect(U_48)) = collect(U_48),
    inference(definitional_conversion,[status(esa)],[f_46_2]) ).

cnf(f_46_4,plain,
    ti(fun(fun(U_48,bool),fun(U_48,bool)),collect(U_48)) = collect(U_48),
    inference(clausify,[status(thm)],[f_46_3]) ).

fof(f_47_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_47_2,plain,
    ! [U_50,U_49] : ti(fun(fun(U_50,U_49),fun(fun(U_50,bool),fun(U_49,bool))),image(U_50,U_49)) = image(U_50,U_49),
    inference(variable_rename,[status(thm)],[f_47_1]) ).

fof(f_47_3,plain,
    ! [U_49,U_50] : ti(fun(fun(U_50,U_49),fun(fun(U_50,bool),fun(U_49,bool))),image(U_50,U_49)) = image(U_50,U_49),
    inference(definitional_conversion,[status(esa)],[f_47_2]) ).

cnf(f_47_4,plain,
    ti(fun(fun(U_50,U_49),fun(fun(U_50,bool),fun(U_49,bool))),image(U_50,U_49)) = image(U_50,U_49),
    inference(clausify,[status(thm)],[f_47_3]) ).

fof(f_48_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_48_2,plain,
    ! [U_51] : ti(fun(U_51,fun(fun(U_51,bool),fun(U_51,bool))),insert(U_51)) = insert(U_51),
    inference(variable_rename,[status(thm)],[f_48_1]) ).

fof(f_48_3,plain,
    ! [U_51] : ti(fun(U_51,fun(fun(U_51,bool),fun(U_51,bool))),insert(U_51)) = insert(U_51),
    inference(definitional_conversion,[status(esa)],[f_48_2]) ).

cnf(f_48_4,plain,
    ti(fun(U_51,fun(fun(U_51,bool),fun(U_51,bool))),insert(U_51)) = insert(U_51),
    inference(clausify,[status(thm)],[f_48_3]) ).

fof(f_49_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_49_2,plain,
    ! [U_52] : ti(fun(fun(U_52,bool),U_52),the_elem(U_52)) = the_elem(U_52),
    inference(variable_rename,[status(thm)],[f_49_1]) ).

fof(f_49_3,plain,
    ! [U_52] : ti(fun(fun(U_52,bool),U_52),the_elem(U_52)) = the_elem(U_52),
    inference(definitional_conversion,[status(esa)],[f_49_2]) ).

cnf(f_49_4,plain,
    ti(fun(fun(U_52,bool),U_52),the_elem(U_52)) = the_elem(U_52),
    inference(clausify,[status(thm)],[f_49_3]) ).

fof(f_50_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_50_2,plain,
    ! [U_54,U_53] : ti(fun(fun(U_54,bool),fun(fun(U_53,bool),fun(sum_sum(U_54,U_53),bool))),sum_Plus(U_54,U_53)) = sum_Plus(U_54,U_53),
    inference(variable_rename,[status(thm)],[f_50_1]) ).

fof(f_50_3,plain,
    ! [U_53,U_54] : ti(fun(fun(U_54,bool),fun(fun(U_53,bool),fun(sum_sum(U_54,U_53),bool))),sum_Plus(U_54,U_53)) = sum_Plus(U_54,U_53),
    inference(definitional_conversion,[status(esa)],[f_50_2]) ).

cnf(f_50_4,plain,
    ti(fun(fun(U_54,bool),fun(fun(U_53,bool),fun(sum_sum(U_54,U_53),bool))),sum_Plus(U_54,U_53)) = sum_Plus(U_54,U_53),
    inference(clausify,[status(thm)],[f_50_3]) ).

fof(f_51_1,plain,
    ti(bool,fFalse) = fFalse,
    inference(fof_nnf,[status(thm)],[tsy_c_fFalse_res]) ).

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

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

fof(f_52_1,plain,
    ti(fun(bool,bool),fNot) = fNot,
    inference(fof_nnf,[status(thm)],[tsy_c_fNot_res]) ).

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

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

fof(f_53_1,plain,
    ti(bool,fTrue) = fTrue,
    inference(fof_nnf,[status(thm)],[tsy_c_fTrue_res]) ).

fof(f_53_2,plain,
    ti(bool,fTrue) = fTrue,
    inference(definitional_conversion,[status(esa)],[f_53_1]) ).

cnf(f_53_3,plain,
    ti(bool,fTrue) = fTrue,
    inference(clausify,[status(thm)],[f_53_2]) ).

fof(f_54_1,plain,
    ti(fun(bool,fun(bool,bool)),fconj) = fconj,
    inference(fof_nnf,[status(thm)],[tsy_c_fconj_res]) ).

fof(f_54_2,plain,
    ti(fun(bool,fun(bool,bool)),fconj) = fconj,
    inference(definitional_conversion,[status(esa)],[f_54_1]) ).

cnf(f_54_3,plain,
    ti(fun(bool,fun(bool,bool)),fconj) = fconj,
    inference(clausify,[status(thm)],[f_54_2]) ).

fof(f_55_1,plain,
    ti(fun(bool,fun(bool,bool)),fdisj) = fdisj,
    inference(fof_nnf,[status(thm)],[tsy_c_fdisj_res]) ).

fof(f_55_2,plain,
    ti(fun(bool,fun(bool,bool)),fdisj) = fdisj,
    inference(definitional_conversion,[status(esa)],[f_55_1]) ).

cnf(f_55_3,plain,
    ti(fun(bool,fun(bool,bool)),fdisj) = fdisj,
    inference(clausify,[status(thm)],[f_55_2]) ).

fof(f_56_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_56_2,plain,
    ! [U_55] : ti(fun(U_55,fun(U_55,bool)),fequal(U_55)) = fequal(U_55),
    inference(variable_rename,[status(thm)],[f_56_1]) ).

fof(f_56_3,plain,
    ! [U_55] : ti(fun(U_55,fun(U_55,bool)),fequal(U_55)) = fequal(U_55),
    inference(definitional_conversion,[status(esa)],[f_56_2]) ).

cnf(f_56_4,plain,
    ti(fun(U_55,fun(U_55,bool)),fequal(U_55)) = fequal(U_55),
    inference(clausify,[status(thm)],[f_56_3]) ).

fof(f_57_1,plain,
    ti(fun(bool,fun(bool,bool)),fimplies) = fimplies,
    inference(fof_nnf,[status(thm)],[tsy_c_fimplies_res]) ).

fof(f_57_2,plain,
    ti(fun(bool,fun(bool,bool)),fimplies) = fimplies,
    inference(definitional_conversion,[status(esa)],[f_57_1]) ).

cnf(f_57_3,plain,
    ti(fun(bool,fun(bool,bool)),fimplies) = fimplies,
    inference(clausify,[status(thm)],[f_57_2]) ).

fof(f_58_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_58_2,plain,
    ! [U_59,U_58,U_57,U_56] : hAPP(U_59,U_58,ti(fun(U_59,U_58),U_57),U_56) = hAPP(U_59,U_58,U_57,U_56),
    inference(variable_rename,[status(thm)],[f_58_1]) ).

fof(f_58_3,plain,
    ! [U_56,U_57,U_58,U_59] : hAPP(U_59,U_58,ti(fun(U_59,U_58),U_57),U_56) = hAPP(U_59,U_58,U_57,U_56),
    inference(definitional_conversion,[status(esa)],[f_58_2]) ).

cnf(f_58_4,plain,
    hAPP(U_59,U_58,ti(fun(U_59,U_58),U_57),U_56) = hAPP(U_59,U_58,U_57,U_56),
    inference(clausify,[status(thm)],[f_58_3]) ).

fof(f_59_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_59_2,plain,
    ! [U_63,U_62,U_61,U_60] : hAPP(U_63,U_62,U_61,ti(U_63,U_60)) = hAPP(U_63,U_62,U_61,U_60),
    inference(variable_rename,[status(thm)],[f_59_1]) ).

fof(f_59_3,plain,
    ! [U_60,U_62,U_61,U_63] : hAPP(U_63,U_62,U_61,ti(U_63,U_60)) = hAPP(U_63,U_62,U_61,U_60),
    inference(definitional_conversion,[status(esa)],[f_59_2]) ).

cnf(f_59_4,plain,
    hAPP(U_63,U_62,U_61,ti(U_63,U_60)) = hAPP(U_63,U_62,U_61,U_60),
    inference(clausify,[status(thm)],[f_59_3]) ).

fof(f_60_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_60_2,plain,
    ! [U_67,U_66,U_65,U_64] : ti(U_67,hAPP(U_66,U_67,U_65,U_64)) = hAPP(U_66,U_67,U_65,U_64),
    inference(variable_rename,[status(thm)],[f_60_1]) ).

fof(f_60_3,plain,
    ! [U_65,U_64,U_66,U_67] : ti(U_67,hAPP(U_66,U_67,U_65,U_64)) = hAPP(U_66,U_67,U_65,U_64),
    inference(definitional_conversion,[status(esa)],[f_60_2]) ).

cnf(f_60_4,plain,
    ti(U_67,hAPP(U_66,U_67,U_65,U_64)) = hAPP(U_66,U_67,U_65,U_64),
    inference(clausify,[status(thm)],[f_60_3]) ).

fof(f_61_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_61_2,plain,
    ! [U_68] :
      ( ( hBOOL(ti(bool,U_68))
        | ~ hBOOL(U_68) )
      & ( hBOOL(U_68)
        | ~ hBOOL(ti(bool,U_68)) ) ),
    inference(variable_rename,[status(thm)],[f_61_1]) ).

fof(f_61_3,plain,
    ( ! [U_70] :
        ( hBOOL(ti(bool,U_70))
        | ~ hBOOL(U_70) )
    & ! [U_69] :
        ( hBOOL(U_69)
        | ~ hBOOL(ti(bool,U_69)) ) ),
    inference(miniscope,[status(thm)],[f_61_2]) ).

fof(f_61_4,plain,
    ( ! [U_70] :
        ( hBOOL(ti(bool,U_70))
        | ~ hBOOL(U_70) )
    & ! [U_69] :
        ( hBOOL(U_69)
        | ~ hBOOL(ti(bool,U_69)) ) ),
    inference(definitional_conversion,[status(esa)],[f_61_3]) ).

cnf(f_61_5,plain,
    ( hBOOL(U_69)
    | ~ hBOOL(ti(bool,U_69)) ),
    inference(clausify,[status(thm)],[f_61_4]) ).

cnf(f_61_6,plain,
    ( hBOOL(ti(bool,U_70))
    | ~ hBOOL(U_70) ),
    inference(clausify,[status(thm)],[f_61_4]) ).

fof(f_62_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_62_2,plain,
    ! [U_71] : ti(fun(U_71,fun(fun(U_71,bool),bool)),member(U_71)) = member(U_71),
    inference(variable_rename,[status(thm)],[f_62_1]) ).

fof(f_62_3,plain,
    ! [U_71] : ti(fun(U_71,fun(fun(U_71,bool),bool)),member(U_71)) = member(U_71),
    inference(definitional_conversion,[status(esa)],[f_62_2]) ).

cnf(f_62_4,plain,
    ti(fun(U_71,fun(fun(U_71,bool),bool)),member(U_71)) = member(U_71),
    inference(clausify,[status(thm)],[f_62_3]) ).

fof(f_63_1,plain,
    ti(fun(x_a,bool),g) = g,
    inference(fof_nnf,[status(thm)],[tsy_v_G_res]) ).

fof(f_63_2,plain,
    ti(fun(x_a,bool),g) = g,
    inference(definitional_conversion,[status(esa)],[f_63_1]) ).

cnf(f_63_3,plain,
    ti(fun(x_a,bool),g) = g,
    inference(clausify,[status(thm)],[f_63_2]) ).

fof(f_64_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_64_2,plain,
    ti(fun(fun(x_a,bool),fun(fun(x_a,bool),bool)),p) = p,
    inference(definitional_conversion,[status(esa)],[f_64_1]) ).

cnf(f_64_3,plain,
    ti(fun(fun(x_a,bool),fun(fun(x_a,bool),bool)),p) = p,
    inference(clausify,[status(thm)],[f_64_2]) ).

fof(f_65_1,plain,
    ti(fun(pname,bool),u) = u,
    inference(fof_nnf,[status(thm)],[tsy_v_U_res]) ).

fof(f_65_2,plain,
    ti(fun(pname,bool),u) = u,
    inference(definitional_conversion,[status(esa)],[f_65_1]) ).

cnf(f_65_3,plain,
    ti(fun(pname,bool),u) = u,
    inference(clausify,[status(thm)],[f_65_2]) ).

fof(f_66_1,plain,
    ti(fun(com,x_a),mgt) = mgt,
    inference(fof_nnf,[status(thm)],[tsy_v_mgt_res]) ).

fof(f_66_2,plain,
    ti(fun(com,x_a),mgt) = mgt,
    inference(definitional_conversion,[status(esa)],[f_66_1]) ).

cnf(f_66_3,plain,
    ti(fun(com,x_a),mgt) = mgt,
    inference(clausify,[status(thm)],[f_66_2]) ).

fof(f_67_1,plain,
    ti(fun(pname,x_a),mgt_call) = mgt_call,
    inference(fof_nnf,[status(thm)],[tsy_v_mgt__call_res]) ).

fof(f_67_2,plain,
    ti(fun(pname,x_a),mgt_call) = mgt_call,
    inference(definitional_conversion,[status(esa)],[f_67_1]) ).

cnf(f_67_3,plain,
    ti(fun(pname,x_a),mgt_call) = mgt_call,
    inference(clausify,[status(thm)],[f_67_2]) ).

fof(f_68_1,plain,
    ti(nat,na) = na,
    inference(fof_nnf,[status(thm)],[tsy_v_na_res]) ).

fof(f_68_2,plain,
    ti(nat,na) = na,
    inference(definitional_conversion,[status(esa)],[f_68_1]) ).

cnf(f_68_3,plain,
    ti(nat,na) = na,
    inference(clausify,[status(thm)],[f_68_2]) ).

fof(f_69_1,plain,
    ti(pname,pn) = pn,
    inference(fof_nnf,[status(thm)],[tsy_v_pn_res]) ).

fof(f_69_2,plain,
    ti(pname,pn) = pn,
    inference(definitional_conversion,[status(esa)],[f_69_1]) ).

cnf(f_69_3,plain,
    ti(pname,pn) = pn,
    inference(clausify,[status(thm)],[f_69_2]) ).

fof(f_70_1,plain,
    ti(fun(com,bool),wt) = wt,
    inference(fof_nnf,[status(thm)],[tsy_v_wt_res]) ).

fof(f_70_2,plain,
    ti(fun(com,bool),wt) = wt,
    inference(definitional_conversion,[status(esa)],[f_70_1]) ).

cnf(f_70_3,plain,
    ti(fun(com,bool),wt) = wt,
    inference(clausify,[status(thm)],[f_70_2]) ).

fof(f_71_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_71_2,plain,
    ! [U_73,U_72] :
      ( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,U_72),U_73))
      | ~ 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_73),U_72)) ),
    inference(variable_rename,[status(thm)],[f_71_1]) ).

fof(f_71_3,plain,
    ! [U_72,U_73] :
      ( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,U_72),U_73))
      | ~ 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_73),U_72)) ),
    inference(definitional_conversion,[status(esa)],[f_71_2]) ).

cnf(f_71_4,plain,
    ( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,U_72),U_73))
    | ~ 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_73),U_72)) ),
    inference(clausify,[status(thm)],[f_71_3]) ).

fof(f_72_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_72_2,plain,
    ! [U_75,U_74] :
      ( hBOOL(hAPP(fun(fun(U_75,bool),bool),bool,finite_finite(fun(U_75,bool)),hAPP(fun(fun(U_75,bool),bool),fun(fun(U_75,bool),bool),collect(fun(U_75,bool)),hAPP(fun(U_75,bool),fun(fun(U_75,bool),bool),hAPP(fun(fun(U_75,bool),fun(fun(U_75,bool),bool)),fun(fun(U_75,bool),fun(fun(U_75,bool),bool)),combc(fun(U_75,bool),fun(U_75,bool),bool),ord_less_eq(fun(U_75,bool))),U_74))))
      | ~ hBOOL(hAPP(fun(U_75,bool),bool,finite_finite(U_75),U_74)) ),
    inference(variable_rename,[status(thm)],[f_72_1]) ).

fof(f_72_3,plain,
    ! [U_75,U_74] :
      ( hBOOL(hAPP(fun(fun(U_75,bool),bool),bool,finite_finite(fun(U_75,bool)),hAPP(fun(fun(U_75,bool),bool),fun(fun(U_75,bool),bool),collect(fun(U_75,bool)),hAPP(fun(U_75,bool),fun(fun(U_75,bool),bool),hAPP(fun(fun(U_75,bool),fun(fun(U_75,bool),bool)),fun(fun(U_75,bool),fun(fun(U_75,bool),bool)),combc(fun(U_75,bool),fun(U_75,bool),bool),ord_less_eq(fun(U_75,bool))),U_74))))
      | ~ hBOOL(hAPP(fun(U_75,bool),bool,finite_finite(U_75),U_74)) ),
    inference(definitional_conversion,[status(esa)],[f_72_2]) ).

cnf(f_72_4,plain,
    ( hBOOL(hAPP(fun(fun(U_75,bool),bool),bool,finite_finite(fun(U_75,bool)),hAPP(fun(fun(U_75,bool),bool),fun(fun(U_75,bool),bool),collect(fun(U_75,bool)),hAPP(fun(U_75,bool),fun(fun(U_75,bool),bool),hAPP(fun(fun(U_75,bool),fun(fun(U_75,bool),bool)),fun(fun(U_75,bool),fun(fun(U_75,bool),bool)),combc(fun(U_75,bool),fun(U_75,bool),bool),ord_less_eq(fun(U_75,bool))),U_74))))
    | ~ hBOOL(hAPP(fun(U_75,bool),bool,finite_finite(U_75),U_74)) ),
    inference(clausify,[status(thm)],[f_72_3]) ).

fof(f_73_1,plain,
    ! [X_c,X_b,H,F_1] :
      ( 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_1)))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_2_finite__imageI]) ).

fof(f_73_2,plain,
    ! [U_79,U_78,U_77,U_76] :
      ( hBOOL(hAPP(fun(U_79,bool),bool,finite_finite(U_79),hAPP(fun(U_78,bool),fun(U_79,bool),hAPP(fun(U_78,U_79),fun(fun(U_78,bool),fun(U_79,bool)),image(U_78,U_79),U_77),U_76)))
      | ~ hBOOL(hAPP(fun(U_78,bool),bool,finite_finite(U_78),U_76)) ),
    inference(variable_rename,[status(thm)],[f_73_1]) ).

fof(f_73_3,plain,
    ! [U_76,U_78,U_77,U_79] :
      ( hBOOL(hAPP(fun(U_79,bool),bool,finite_finite(U_79),hAPP(fun(U_78,bool),fun(U_79,bool),hAPP(fun(U_78,U_79),fun(fun(U_78,bool),fun(U_79,bool)),image(U_78,U_79),U_77),U_76)))
      | ~ hBOOL(hAPP(fun(U_78,bool),bool,finite_finite(U_78),U_76)) ),
    inference(definitional_conversion,[status(esa)],[f_73_2]) ).

cnf(f_73_4,plain,
    ( hBOOL(hAPP(fun(U_79,bool),bool,finite_finite(U_79),hAPP(fun(U_78,bool),fun(U_79,bool),hAPP(fun(U_78,U_79),fun(fun(U_78,bool),fun(U_79,bool)),image(U_78,U_79),U_77),U_76)))
    | ~ hBOOL(hAPP(fun(U_78,bool),bool,finite_finite(U_78),U_76)) ),
    inference(clausify,[status(thm)],[f_73_3]) ).

fof(f_74_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_74_2,plain,
    ! [U_82,U_81,U_80] :
      ( hBOOL(hAPP(fun(U_82,bool),bool,finite_finite(U_82),hAPP(fun(U_82,bool),fun(U_82,bool),hAPP(U_82,fun(fun(U_82,bool),fun(U_82,bool)),insert(U_82),U_81),U_80)))
      | ~ hBOOL(hAPP(fun(U_82,bool),bool,finite_finite(U_82),U_80)) ),
    inference(variable_rename,[status(thm)],[f_74_1]) ).

fof(f_74_3,plain,
    ! [U_80,U_82,U_81] :
      ( hBOOL(hAPP(fun(U_82,bool),bool,finite_finite(U_82),hAPP(fun(U_82,bool),fun(U_82,bool),hAPP(U_82,fun(fun(U_82,bool),fun(U_82,bool)),insert(U_82),U_81),U_80)))
      | ~ hBOOL(hAPP(fun(U_82,bool),bool,finite_finite(U_82),U_80)) ),
    inference(definitional_conversion,[status(esa)],[f_74_2]) ).

cnf(f_74_4,plain,
    ( hBOOL(hAPP(fun(U_82,bool),bool,finite_finite(U_82),hAPP(fun(U_82,bool),fun(U_82,bool),hAPP(U_82,fun(fun(U_82,bool),fun(U_82,bool)),insert(U_82),U_81),U_80)))
    | ~ hBOOL(hAPP(fun(U_82,bool),bool,finite_finite(U_82),U_80)) ),
    inference(clausify,[status(thm)],[f_74_3]) ).

fof(f_75_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_75_2,plain,
    ! [U_86,U_85,U_84,U_83] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(U_86,bool),nat,finite_card(U_86),hAPP(fun(U_85,bool),fun(U_86,bool),hAPP(fun(U_85,U_86),fun(fun(U_85,bool),fun(U_86,bool)),image(U_85,U_86),U_84),U_83))),hAPP(fun(U_85,bool),nat,finite_card(U_85),U_83)))
      | ~ hBOOL(hAPP(fun(U_85,bool),bool,finite_finite(U_85),U_83)) ),
    inference(variable_rename,[status(thm)],[f_75_1]) ).

fof(f_75_3,plain,
    ! [U_83,U_85,U_84,U_86] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(U_86,bool),nat,finite_card(U_86),hAPP(fun(U_85,bool),fun(U_86,bool),hAPP(fun(U_85,U_86),fun(fun(U_85,bool),fun(U_86,bool)),image(U_85,U_86),U_84),U_83))),hAPP(fun(U_85,bool),nat,finite_card(U_85),U_83)))
      | ~ hBOOL(hAPP(fun(U_85,bool),bool,finite_finite(U_85),U_83)) ),
    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),hAPP(fun(U_86,bool),nat,finite_card(U_86),hAPP(fun(U_85,bool),fun(U_86,bool),hAPP(fun(U_85,U_86),fun(fun(U_85,bool),fun(U_86,bool)),image(U_85,U_86),U_84),U_83))),hAPP(fun(U_85,bool),nat,finite_card(U_85),U_83)))
    | ~ hBOOL(hAPP(fun(U_85,bool),bool,finite_finite(U_85),U_83)) ),
    inference(clausify,[status(thm)],[f_75_3]) ).

fof(f_76_1,plain,
    ! [X_b,A_3,B_1] :
      ( 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_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),B_1))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_1)) ),
    inference(fof_nnf,[status(thm)],[fact_5_card__mono]) ).

fof(f_76_2,plain,
    ! [U_89,U_88,U_87] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(U_89,bool),nat,finite_card(U_89),U_88)),hAPP(fun(U_89,bool),nat,finite_card(U_89),U_87)))
      | ~ hBOOL(hAPP(fun(U_89,bool),bool,hAPP(fun(U_89,bool),fun(fun(U_89,bool),bool),ord_less_eq(fun(U_89,bool)),U_88),U_87))
      | ~ hBOOL(hAPP(fun(U_89,bool),bool,finite_finite(U_89),U_87)) ),
    inference(variable_rename,[status(thm)],[f_76_1]) ).

fof(f_76_3,plain,
    ! [U_87,U_88,U_89] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(U_89,bool),nat,finite_card(U_89),U_88)),hAPP(fun(U_89,bool),nat,finite_card(U_89),U_87)))
      | ~ hBOOL(hAPP(fun(U_89,bool),bool,hAPP(fun(U_89,bool),fun(fun(U_89,bool),bool),ord_less_eq(fun(U_89,bool)),U_88),U_87))
      | ~ hBOOL(hAPP(fun(U_89,bool),bool,finite_finite(U_89),U_87)) ),
    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),hAPP(fun(U_89,bool),nat,finite_card(U_89),U_88)),hAPP(fun(U_89,bool),nat,finite_card(U_89),U_87)))
    | ~ hBOOL(hAPP(fun(U_89,bool),bool,hAPP(fun(U_89,bool),fun(fun(U_89,bool),bool),ord_less_eq(fun(U_89,bool)),U_88),U_87))
    | ~ hBOOL(hAPP(fun(U_89,bool),bool,finite_finite(U_89),U_87)) ),
    inference(clausify,[status(thm)],[f_76_3]) ).

fof(f_77_1,plain,
    ! [X_b,A_3,B_1] :
      ( ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_1)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_1)),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_1))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_1)) ),
    inference(fof_nnf,[status(thm)],[fact_6_card__seteq]) ).

fof(f_77_2,plain,
    ! [U_92,U_91,U_90] :
      ( ti(fun(U_92,bool),U_91) = ti(fun(U_92,bool),U_90)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(U_92,bool),nat,finite_card(U_92),U_90)),hAPP(fun(U_92,bool),nat,finite_card(U_92),U_91)))
      | ~ hBOOL(hAPP(fun(U_92,bool),bool,hAPP(fun(U_92,bool),fun(fun(U_92,bool),bool),ord_less_eq(fun(U_92,bool)),U_91),U_90))
      | ~ hBOOL(hAPP(fun(U_92,bool),bool,finite_finite(U_92),U_90)) ),
    inference(variable_rename,[status(thm)],[f_77_1]) ).

fof(f_77_3,plain,
    ! [U_90,U_91,U_92] :
      ( ti(fun(U_92,bool),U_91) = ti(fun(U_92,bool),U_90)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(U_92,bool),nat,finite_card(U_92),U_90)),hAPP(fun(U_92,bool),nat,finite_card(U_92),U_91)))
      | ~ hBOOL(hAPP(fun(U_92,bool),bool,hAPP(fun(U_92,bool),fun(fun(U_92,bool),bool),ord_less_eq(fun(U_92,bool)),U_91),U_90))
      | ~ hBOOL(hAPP(fun(U_92,bool),bool,finite_finite(U_92),U_90)) ),
    inference(definitional_conversion,[status(esa)],[f_77_2]) ).

cnf(f_77_4,plain,
    ( ti(fun(U_92,bool),U_91) = ti(fun(U_92,bool),U_90)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(U_92,bool),nat,finite_card(U_92),U_90)),hAPP(fun(U_92,bool),nat,finite_card(U_92),U_91)))
    | ~ hBOOL(hAPP(fun(U_92,bool),bool,hAPP(fun(U_92,bool),fun(fun(U_92,bool),bool),ord_less_eq(fun(U_92,bool)),U_91),U_90))
    | ~ hBOOL(hAPP(fun(U_92,bool),bool,finite_finite(U_92),U_90)) ),
    inference(clausify,[status(thm)],[f_77_3]) ).

fof(f_78_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_78_2,plain,
    ! [U_95,U_94,U_93] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(U_95,bool),nat,finite_card(U_95),U_93)),hAPP(fun(U_95,bool),nat,finite_card(U_95),hAPP(fun(U_95,bool),fun(U_95,bool),hAPP(U_95,fun(fun(U_95,bool),fun(U_95,bool)),insert(U_95),U_94),U_93))))
      | ~ hBOOL(hAPP(fun(U_95,bool),bool,finite_finite(U_95),U_93)) ),
    inference(variable_rename,[status(thm)],[f_78_1]) ).

fof(f_78_3,plain,
    ! [U_95,U_93,U_94] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(U_95,bool),nat,finite_card(U_95),U_93)),hAPP(fun(U_95,bool),nat,finite_card(U_95),hAPP(fun(U_95,bool),fun(U_95,bool),hAPP(U_95,fun(fun(U_95,bool),fun(U_95,bool)),insert(U_95),U_94),U_93))))
      | ~ hBOOL(hAPP(fun(U_95,bool),bool,finite_finite(U_95),U_93)) ),
    inference(definitional_conversion,[status(esa)],[f_78_2]) ).

cnf(f_78_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(U_95,bool),nat,finite_card(U_95),U_93)),hAPP(fun(U_95,bool),nat,finite_card(U_95),hAPP(fun(U_95,bool),fun(U_95,bool),hAPP(U_95,fun(fun(U_95,bool),fun(U_95,bool)),insert(U_95),U_94),U_93))))
    | ~ hBOOL(hAPP(fun(U_95,bool),bool,finite_finite(U_95),U_93)) ),
    inference(clausify,[status(thm)],[f_78_3]) ).

fof(f_79_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_79_2,plain,
    ! [U_98,U_97,U_96] :
      ( ( ( hAPP(fun(U_98,bool),nat,finite_card(U_98),hAPP(fun(U_98,bool),fun(U_98,bool),hAPP(U_98,fun(fun(U_98,bool),fun(U_98,bool)),insert(U_98),U_97),U_96)) = hAPP(nat,nat,suc,hAPP(fun(U_98,bool),nat,finite_card(U_98),U_96))
          | hBOOL(hAPP(fun(U_98,bool),bool,hAPP(U_98,fun(fun(U_98,bool),bool),member(U_98),U_97),U_96)) )
        & ( hAPP(fun(U_98,bool),nat,finite_card(U_98),hAPP(fun(U_98,bool),fun(U_98,bool),hAPP(U_98,fun(fun(U_98,bool),fun(U_98,bool)),insert(U_98),U_97),U_96)) = hAPP(fun(U_98,bool),nat,finite_card(U_98),U_96)
          | ~ hBOOL(hAPP(fun(U_98,bool),bool,hAPP(U_98,fun(fun(U_98,bool),bool),member(U_98),U_97),U_96)) ) )
      | ~ hBOOL(hAPP(fun(U_98,bool),bool,finite_finite(U_98),U_96)) ),
    inference(variable_rename,[status(thm)],[f_79_1]) ).

fof(f_79_3,plain,
    ( ! [U_97,U_96,U_98] :
        ( hAPP(fun(U_98,bool),nat,finite_card(U_98),hAPP(fun(U_98,bool),fun(U_98,bool),hAPP(U_98,fun(fun(U_98,bool),fun(U_98,bool)),insert(U_98),U_97),U_96)) = hAPP(nat,nat,suc,hAPP(fun(U_98,bool),nat,finite_card(U_98),U_96))
        | hBOOL(hAPP(fun(U_98,bool),bool,hAPP(U_98,fun(fun(U_98,bool),bool),member(U_98),U_97),U_96))
        | ~ sP0(U_97,U_96,U_98) )
    & ! [U_97,U_96,U_98] :
        ( hAPP(fun(U_98,bool),nat,finite_card(U_98),hAPP(fun(U_98,bool),fun(U_98,bool),hAPP(U_98,fun(fun(U_98,bool),fun(U_98,bool)),insert(U_98),U_97),U_96)) = hAPP(fun(U_98,bool),nat,finite_card(U_98),U_96)
        | ~ hBOOL(hAPP(fun(U_98,bool),bool,hAPP(U_98,fun(fun(U_98,bool),bool),member(U_98),U_97),U_96))
        | ~ sP0(U_97,U_96,U_98) )
    & ! [U_97,U_96,U_98] :
        ( sP0(U_97,U_96,U_98)
        | ~ hBOOL(hAPP(fun(U_98,bool),bool,finite_finite(U_98),U_96)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_79_2]) ).

cnf(f_79_4,plain,
    ( sP0(U_97,U_96,U_98)
    | ~ hBOOL(hAPP(fun(U_98,bool),bool,finite_finite(U_98),U_96)) ),
    inference(clausify,[status(thm)],[f_79_3]) ).

cnf(f_79_5,plain,
    ( hAPP(fun(U_98,bool),nat,finite_card(U_98),hAPP(fun(U_98,bool),fun(U_98,bool),hAPP(U_98,fun(fun(U_98,bool),fun(U_98,bool)),insert(U_98),U_97),U_96)) = hAPP(fun(U_98,bool),nat,finite_card(U_98),U_96)
    | ~ hBOOL(hAPP(fun(U_98,bool),bool,hAPP(U_98,fun(fun(U_98,bool),bool),member(U_98),U_97),U_96))
    | ~ sP0(U_97,U_96,U_98) ),
    inference(clausify,[status(thm)],[f_79_3]) ).

cnf(f_79_6,plain,
    ( hAPP(fun(U_98,bool),nat,finite_card(U_98),hAPP(fun(U_98,bool),fun(U_98,bool),hAPP(U_98,fun(fun(U_98,bool),fun(U_98,bool)),insert(U_98),U_97),U_96)) = hAPP(nat,nat,suc,hAPP(fun(U_98,bool),nat,finite_card(U_98),U_96))
    | hBOOL(hAPP(fun(U_98,bool),bool,hAPP(U_98,fun(fun(U_98,bool),bool),member(U_98),U_97),U_96))
    | ~ sP0(U_97,U_96,U_98) ),
    inference(clausify,[status(thm)],[f_79_3]) ).

fof(f_80_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_80_2,plain,
    ! [U_101,U_100,U_99] :
      ( hAPP(fun(U_101,bool),nat,finite_card(U_101),hAPP(fun(U_101,bool),fun(U_101,bool),hAPP(U_101,fun(fun(U_101,bool),fun(U_101,bool)),insert(U_101),U_100),U_99)) = hAPP(nat,nat,suc,hAPP(fun(U_101,bool),nat,finite_card(U_101),U_99))
      | hBOOL(hAPP(fun(U_101,bool),bool,hAPP(U_101,fun(fun(U_101,bool),bool),member(U_101),U_100),U_99))
      | ~ hBOOL(hAPP(fun(U_101,bool),bool,finite_finite(U_101),U_99)) ),
    inference(variable_rename,[status(thm)],[f_80_1]) ).

fof(f_80_3,plain,
    ! [U_99,U_100,U_101] :
      ( hAPP(fun(U_101,bool),nat,finite_card(U_101),hAPP(fun(U_101,bool),fun(U_101,bool),hAPP(U_101,fun(fun(U_101,bool),fun(U_101,bool)),insert(U_101),U_100),U_99)) = hAPP(nat,nat,suc,hAPP(fun(U_101,bool),nat,finite_card(U_101),U_99))
      | hBOOL(hAPP(fun(U_101,bool),bool,hAPP(U_101,fun(fun(U_101,bool),bool),member(U_101),U_100),U_99))
      | ~ hBOOL(hAPP(fun(U_101,bool),bool,finite_finite(U_101),U_99)) ),
    inference(definitional_conversion,[status(esa)],[f_80_2]) ).

cnf(f_80_4,plain,
    ( hAPP(fun(U_101,bool),nat,finite_card(U_101),hAPP(fun(U_101,bool),fun(U_101,bool),hAPP(U_101,fun(fun(U_101,bool),fun(U_101,bool)),insert(U_101),U_100),U_99)) = hAPP(nat,nat,suc,hAPP(fun(U_101,bool),nat,finite_card(U_101),U_99))
    | hBOOL(hAPP(fun(U_101,bool),bool,hAPP(U_101,fun(fun(U_101,bool),bool),member(U_101),U_100),U_99))
    | ~ hBOOL(hAPP(fun(U_101,bool),bool,finite_finite(U_101),U_99)) ),
    inference(clausify,[status(thm)],[f_80_3]) ).

fof(f_81_1,plain,
    ! [X_b,Q_3,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_3))))
      | ( ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Q_3)))
        & ~ 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_81_2,plain,
    ! [U_104,U_103,U_102] :
      ( hBOOL(hAPP(fun(U_104,bool),bool,finite_finite(U_104),hAPP(fun(U_104,bool),fun(U_104,bool),collect(U_104),hAPP(fun(U_104,bool),fun(U_104,bool),hAPP(fun(U_104,fun(bool,bool)),fun(fun(U_104,bool),fun(U_104,bool)),combs(U_104,bool,bool),hAPP(fun(U_104,bool),fun(U_104,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_104,bool),fun(U_104,fun(bool,bool))),combb(bool,fun(bool,bool),U_104),fconj),U_102)),U_103))))
      | ( ~ hBOOL(hAPP(fun(U_104,bool),bool,finite_finite(U_104),hAPP(fun(U_104,bool),fun(U_104,bool),collect(U_104),U_103)))
        & ~ hBOOL(hAPP(fun(U_104,bool),bool,finite_finite(U_104),hAPP(fun(U_104,bool),fun(U_104,bool),collect(U_104),U_102))) ) ),
    inference(variable_rename,[status(thm)],[f_81_1]) ).

fof(f_81_3,plain,
    ( ! [U_104,U_102,U_103] :
        ( ~ hBOOL(hAPP(fun(U_104,bool),bool,finite_finite(U_104),hAPP(fun(U_104,bool),fun(U_104,bool),collect(U_104),U_103)))
        | ~ sP1(U_104,U_102,U_103) )
    & ! [U_104,U_102,U_103] :
        ( ~ hBOOL(hAPP(fun(U_104,bool),bool,finite_finite(U_104),hAPP(fun(U_104,bool),fun(U_104,bool),collect(U_104),U_102)))
        | ~ sP1(U_104,U_102,U_103) )
    & ! [U_104,U_102,U_103] :
        ( hBOOL(hAPP(fun(U_104,bool),bool,finite_finite(U_104),hAPP(fun(U_104,bool),fun(U_104,bool),collect(U_104),hAPP(fun(U_104,bool),fun(U_104,bool),hAPP(fun(U_104,fun(bool,bool)),fun(fun(U_104,bool),fun(U_104,bool)),combs(U_104,bool,bool),hAPP(fun(U_104,bool),fun(U_104,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_104,bool),fun(U_104,fun(bool,bool))),combb(bool,fun(bool,bool),U_104),fconj),U_102)),U_103))))
        | sP1(U_104,U_102,U_103) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1])],[f_81_2]) ).

cnf(f_81_4,plain,
    ( hBOOL(hAPP(fun(U_104,bool),bool,finite_finite(U_104),hAPP(fun(U_104,bool),fun(U_104,bool),collect(U_104),hAPP(fun(U_104,bool),fun(U_104,bool),hAPP(fun(U_104,fun(bool,bool)),fun(fun(U_104,bool),fun(U_104,bool)),combs(U_104,bool,bool),hAPP(fun(U_104,bool),fun(U_104,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_104,bool),fun(U_104,fun(bool,bool))),combb(bool,fun(bool,bool),U_104),fconj),U_102)),U_103))))
    | sP1(U_104,U_102,U_103) ),
    inference(clausify,[status(thm)],[f_81_3]) ).

cnf(f_81_5,plain,
    ( ~ hBOOL(hAPP(fun(U_104,bool),bool,finite_finite(U_104),hAPP(fun(U_104,bool),fun(U_104,bool),collect(U_104),U_102)))
    | ~ sP1(U_104,U_102,U_103) ),
    inference(clausify,[status(thm)],[f_81_3]) ).

cnf(f_81_6,plain,
    ( ~ hBOOL(hAPP(fun(U_104,bool),bool,finite_finite(U_104),hAPP(fun(U_104,bool),fun(U_104,bool),collect(U_104),U_103)))
    | ~ sP1(U_104,U_102,U_103) ),
    inference(clausify,[status(thm)],[f_81_3]) ).

fof(f_82_1,plain,
    ! [N,M_1] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M_1)),N) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M_1)) ),
    inference(fof_nnf,[status(thm)],[fact_11_Suc__diff__le]) ).

fof(f_82_2,plain,
    ! [U_106,U_105] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,U_105)),U_106) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_105),U_106))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_106),U_105)) ),
    inference(variable_rename,[status(thm)],[f_82_1]) ).

fof(f_82_3,plain,
    ! [U_106,U_105] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,U_105)),U_106) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_105),U_106))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_106),U_105)) ),
    inference(definitional_conversion,[status(esa)],[f_82_2]) ).

cnf(f_82_4,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,U_105)),U_106) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_105),U_106))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_106),U_105)) ),
    inference(clausify,[status(thm)],[f_82_3]) ).

fof(f_83_1,plain,
    ! [K] : 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)))),
    inference(fof_nnf,[status(thm)],[fact_12_finite__Collect__le__nat]) ).

fof(f_83_2,plain,
    ! [U_107] : 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_107)))),
    inference(variable_rename,[status(thm)],[f_83_1]) ).

fof(f_83_3,plain,
    ! [U_107] : 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_107)))),
    inference(definitional_conversion,[status(esa)],[f_83_2]) ).

cnf(f_83_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_107)))),
    inference(clausify,[status(thm)],[f_83_3]) ).

fof(f_84_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_84_2,plain,
    ! [U_108] : 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_108))) = hAPP(nat,nat,suc,U_108),
    inference(variable_rename,[status(thm)],[f_84_1]) ).

fof(f_84_3,plain,
    ! [U_108] : 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_108))) = hAPP(nat,nat,suc,U_108),
    inference(definitional_conversion,[status(esa)],[f_84_2]) ).

cnf(f_84_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_108))) = hAPP(nat,nat,suc,U_108),
    inference(clausify,[status(thm)],[f_84_3]) ).

fof(f_85_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_85_2,plain,
    ! [U_110] :
      ( ! [U_109] : hBOOL(hAPP(fun(U_110,bool),bool,finite_finite(U_110),U_109))
      | ~ finite_finite_1(U_110) ),
    inference(variable_rename,[status(thm)],[f_85_1]) ).

fof(f_85_3,plain,
    ! [U_109,U_110] :
      ( hBOOL(hAPP(fun(U_110,bool),bool,finite_finite(U_110),U_109))
      | ~ finite_finite_1(U_110) ),
    inference(definitional_conversion,[status(esa)],[f_85_2]) ).

cnf(f_85_4,plain,
    ( hBOOL(hAPP(fun(U_110,bool),bool,finite_finite(U_110),U_109))
    | ~ finite_finite_1(U_110) ),
    inference(clausify,[status(thm)],[f_85_3]) ).

fof(f_86_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_86_2,plain,
    ! [U_112] :
      ( ! [U_111] : hBOOL(hAPP(fun(U_112,bool),bool,finite_finite(U_112),U_111))
      | ~ finite_finite_1(U_112) ),
    inference(variable_rename,[status(thm)],[f_86_1]) ).

fof(f_86_3,plain,
    ! [U_111,U_112] :
      ( hBOOL(hAPP(fun(U_112,bool),bool,finite_finite(U_112),U_111))
      | ~ finite_finite_1(U_112) ),
    inference(definitional_conversion,[status(esa)],[f_86_2]) ).

cnf(f_86_4,plain,
    ( hBOOL(hAPP(fun(U_112,bool),bool,finite_finite(U_112),U_111))
    | ~ finite_finite_1(U_112) ),
    inference(clausify,[status(thm)],[f_86_3]) ).

fof(f_87_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_87_2,plain,
    ! [U_114,U_113] :
      ( U_114 = U_113
      | hAPP(nat,nat,suc,U_114) != hAPP(nat,nat,suc,U_113) ),
    inference(variable_rename,[status(thm)],[f_87_1]) ).

fof(f_87_3,plain,
    ! [U_113,U_114] :
      ( U_114 = U_113
      | hAPP(nat,nat,suc,U_114) != hAPP(nat,nat,suc,U_113) ),
    inference(definitional_conversion,[status(esa)],[f_87_2]) ).

cnf(f_87_4,plain,
    ( U_114 = U_113
    | hAPP(nat,nat,suc,U_114) != hAPP(nat,nat,suc,U_113) ),
    inference(clausify,[status(thm)],[f_87_3]) ).

fof(f_88_1,plain,
    ! [Nat_3,Nat_4] :
      ( ( hAPP(nat,nat,suc,Nat_3) = hAPP(nat,nat,suc,Nat_4)
        | Nat_3 != Nat_4 )
      & ( Nat_3 = Nat_4
        | hAPP(nat,nat,suc,Nat_3) != hAPP(nat,nat,suc,Nat_4) ) ),
    inference(fof_nnf,[status(thm)],[fact_17_nat_Oinject]) ).

fof(f_88_2,plain,
    ! [U_116,U_115] :
      ( ( hAPP(nat,nat,suc,U_116) = hAPP(nat,nat,suc,U_115)
        | U_116 != U_115 )
      & ( U_116 = U_115
        | hAPP(nat,nat,suc,U_116) != hAPP(nat,nat,suc,U_115) ) ),
    inference(variable_rename,[status(thm)],[f_88_1]) ).

fof(f_88_3,plain,
    ( ! [U_120,U_118] :
        ( hAPP(nat,nat,suc,U_120) = hAPP(nat,nat,suc,U_118)
        | U_120 != U_118 )
    & ! [U_119,U_117] :
        ( U_119 = U_117
        | hAPP(nat,nat,suc,U_119) != hAPP(nat,nat,suc,U_117) ) ),
    inference(miniscope,[status(thm)],[f_88_2]) ).

fof(f_88_4,plain,
    ( ! [U_120,U_118] :
        ( hAPP(nat,nat,suc,U_120) = hAPP(nat,nat,suc,U_118)
        | U_120 != U_118 )
    & ! [U_117,U_119] :
        ( U_119 = U_117
        | hAPP(nat,nat,suc,U_119) != hAPP(nat,nat,suc,U_117) ) ),
    inference(definitional_conversion,[status(esa)],[f_88_3]) ).

cnf(f_88_5,plain,
    ( U_119 = U_117
    | hAPP(nat,nat,suc,U_119) != hAPP(nat,nat,suc,U_117) ),
    inference(clausify,[status(thm)],[f_88_4]) ).

cnf(f_88_6,plain,
    ( hAPP(nat,nat,suc,U_120) = hAPP(nat,nat,suc,U_118)
    | U_120 != U_118 ),
    inference(clausify,[status(thm)],[f_88_4]) ).

fof(f_89_1,plain,
    ! [N] : hAPP(nat,nat,suc,N) != N,
    inference(fof_nnf,[status(thm)],[fact_18_Suc__n__not__n]) ).

fof(f_89_2,plain,
    ! [U_121] : hAPP(nat,nat,suc,U_121) != U_121,
    inference(variable_rename,[status(thm)],[f_89_1]) ).

fof(f_89_3,plain,
    ! [U_121] : hAPP(nat,nat,suc,U_121) != U_121,
    inference(definitional_conversion,[status(esa)],[f_89_2]) ).

cnf(f_89_4,plain,
    hAPP(nat,nat,suc,U_121) != U_121,
    inference(clausify,[status(thm)],[f_89_3]) ).

fof(f_90_1,plain,
    ! [N] : N != hAPP(nat,nat,suc,N),
    inference(fof_nnf,[status(thm)],[fact_19_n__not__Suc__n]) ).

fof(f_90_2,plain,
    ! [U_122] : U_122 != hAPP(nat,nat,suc,U_122),
    inference(variable_rename,[status(thm)],[f_90_1]) ).

fof(f_90_3,plain,
    ! [U_122] : U_122 != hAPP(nat,nat,suc,U_122),
    inference(definitional_conversion,[status(esa)],[f_90_2]) ).

cnf(f_90_4,plain,
    U_122 != hAPP(nat,nat,suc,U_122),
    inference(clausify,[status(thm)],[f_90_3]) ).

fof(f_91_1,plain,
    ! [M_1,N] :
      ( M_1 = N
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M_1))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)) ),
    inference(fof_nnf,[status(thm)],[fact_20_le__antisym]) ).

fof(f_91_2,plain,
    ! [U_124,U_123] :
      ( U_124 = U_123
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_123),U_124))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_124),U_123)) ),
    inference(variable_rename,[status(thm)],[f_91_1]) ).

fof(f_91_3,plain,
    ! [U_123,U_124] :
      ( U_124 = U_123
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_123),U_124))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_124),U_123)) ),
    inference(definitional_conversion,[status(esa)],[f_91_2]) ).

cnf(f_91_4,plain,
    ( U_124 = U_123
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_123),U_124))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_124),U_123)) ),
    inference(clausify,[status(thm)],[f_91_3]) ).

fof(f_92_1,plain,
    ! [K_1,I_2,J] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),K_1))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J),K_1))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),J)) ),
    inference(fof_nnf,[status(thm)],[fact_21_le__trans]) ).

fof(f_92_2,plain,
    ! [U_127,U_126,U_125] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_126),U_127))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_125),U_127))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_126),U_125)) ),
    inference(variable_rename,[status(thm)],[f_92_1]) ).

fof(f_92_3,plain,
    ! [U_126,U_125,U_127] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_126),U_127))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_125),U_127))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_126),U_125)) ),
    inference(definitional_conversion,[status(esa)],[f_92_2]) ).

cnf(f_92_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_126),U_127))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_125),U_127))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_126),U_125)) ),
    inference(clausify,[status(thm)],[f_92_3]) ).

fof(f_93_1,plain,
    ! [M_1,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N))
      | M_1 != N ),
    inference(fof_nnf,[status(thm)],[fact_22_eq__imp__le]) ).

fof(f_93_2,plain,
    ! [U_129,U_128] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_129),U_128))
      | U_129 != U_128 ),
    inference(variable_rename,[status(thm)],[f_93_1]) ).

fof(f_93_3,plain,
    ! [U_128,U_129] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_129),U_128))
      | U_129 != U_128 ),
    inference(definitional_conversion,[status(esa)],[f_93_2]) ).

cnf(f_93_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_129),U_128))
    | U_129 != U_128 ),
    inference(clausify,[status(thm)],[f_93_3]) ).

fof(f_94_1,plain,
    ! [M_1,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M_1))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)) ),
    inference(fof_nnf,[status(thm)],[fact_23_nat__le__linear]) ).

fof(f_94_2,plain,
    ! [U_131,U_130] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_130),U_131))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_131),U_130)) ),
    inference(variable_rename,[status(thm)],[f_94_1]) ).

fof(f_94_3,plain,
    ! [U_130,U_131] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_130),U_131))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_131),U_130)) ),
    inference(definitional_conversion,[status(esa)],[f_94_2]) ).

cnf(f_94_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_130),U_131))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_131),U_130)) ),
    inference(clausify,[status(thm)],[f_94_3]) ).

fof(f_95_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_95_2,plain,
    ! [U_132] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_132),U_132)),
    inference(variable_rename,[status(thm)],[f_95_1]) ).

fof(f_95_3,plain,
    ! [U_132] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_132),U_132)),
    inference(definitional_conversion,[status(esa)],[f_95_2]) ).

cnf(f_95_4,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_132),U_132)),
    inference(clausify,[status(thm)],[f_95_3]) ).

fof(f_96_1,plain,
    ! [I_2,J,K_1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_2),J)),K_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_2),K_1)),J),
    inference(fof_nnf,[status(thm)],[fact_25_diff__commute]) ).

fof(f_96_2,plain,
    ! [U_135,U_134,U_133] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_135),U_134)),U_133) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_135),U_133)),U_134),
    inference(variable_rename,[status(thm)],[f_96_1]) ).

fof(f_96_3,plain,
    ! [U_135,U_134,U_133] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_135),U_134)),U_133) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_135),U_133)),U_134),
    inference(definitional_conversion,[status(esa)],[f_96_2]) ).

cnf(f_96_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_135),U_134)),U_133) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_135),U_133)),U_134),
    inference(clausify,[status(thm)],[f_96_3]) ).

fof(f_97_1,plain,
    ! [X_b,Pa,Q_3] :
      ( ( 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_3))))
        | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Q_3)))
        | ~ 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_3)))
          & 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_3)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_26_finite__Collect__disjI]) ).

fof(f_97_2,plain,
    ! [U_138,U_137,U_136] :
      ( ( hBOOL(hAPP(fun(U_138,bool),bool,finite_finite(U_138),hAPP(fun(U_138,bool),fun(U_138,bool),collect(U_138),hAPP(fun(U_138,bool),fun(U_138,bool),hAPP(fun(U_138,fun(bool,bool)),fun(fun(U_138,bool),fun(U_138,bool)),combs(U_138,bool,bool),hAPP(fun(U_138,bool),fun(U_138,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_138,bool),fun(U_138,fun(bool,bool))),combb(bool,fun(bool,bool),U_138),fdisj),U_137)),U_136))))
        | ~ hBOOL(hAPP(fun(U_138,bool),bool,finite_finite(U_138),hAPP(fun(U_138,bool),fun(U_138,bool),collect(U_138),U_136)))
        | ~ hBOOL(hAPP(fun(U_138,bool),bool,finite_finite(U_138),hAPP(fun(U_138,bool),fun(U_138,bool),collect(U_138),U_137))) )
      & ( ( hBOOL(hAPP(fun(U_138,bool),bool,finite_finite(U_138),hAPP(fun(U_138,bool),fun(U_138,bool),collect(U_138),U_136)))
          & hBOOL(hAPP(fun(U_138,bool),bool,finite_finite(U_138),hAPP(fun(U_138,bool),fun(U_138,bool),collect(U_138),U_137))) )
        | ~ hBOOL(hAPP(fun(U_138,bool),bool,finite_finite(U_138),hAPP(fun(U_138,bool),fun(U_138,bool),collect(U_138),hAPP(fun(U_138,bool),fun(U_138,bool),hAPP(fun(U_138,fun(bool,bool)),fun(fun(U_138,bool),fun(U_138,bool)),combs(U_138,bool,bool),hAPP(fun(U_138,bool),fun(U_138,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_138,bool),fun(U_138,fun(bool,bool))),combb(bool,fun(bool,bool),U_138),fdisj),U_137)),U_136)))) ) ),
    inference(variable_rename,[status(thm)],[f_97_1]) ).

fof(f_97_3,plain,
    ( ! [U_144,U_142,U_140] :
        ( hBOOL(hAPP(fun(U_144,bool),bool,finite_finite(U_144),hAPP(fun(U_144,bool),fun(U_144,bool),collect(U_144),hAPP(fun(U_144,bool),fun(U_144,bool),hAPP(fun(U_144,fun(bool,bool)),fun(fun(U_144,bool),fun(U_144,bool)),combs(U_144,bool,bool),hAPP(fun(U_144,bool),fun(U_144,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_144,bool),fun(U_144,fun(bool,bool))),combb(bool,fun(bool,bool),U_144),fdisj),U_142)),U_140))))
        | ~ hBOOL(hAPP(fun(U_144,bool),bool,finite_finite(U_144),hAPP(fun(U_144,bool),fun(U_144,bool),collect(U_144),U_140)))
        | ~ hBOOL(hAPP(fun(U_144,bool),bool,finite_finite(U_144),hAPP(fun(U_144,bool),fun(U_144,bool),collect(U_144),U_142))) )
    & ! [U_143,U_141,U_139] :
        ( ( hBOOL(hAPP(fun(U_143,bool),bool,finite_finite(U_143),hAPP(fun(U_143,bool),fun(U_143,bool),collect(U_143),U_139)))
          & hBOOL(hAPP(fun(U_143,bool),bool,finite_finite(U_143),hAPP(fun(U_143,bool),fun(U_143,bool),collect(U_143),U_141))) )
        | ~ hBOOL(hAPP(fun(U_143,bool),bool,finite_finite(U_143),hAPP(fun(U_143,bool),fun(U_143,bool),collect(U_143),hAPP(fun(U_143,bool),fun(U_143,bool),hAPP(fun(U_143,fun(bool,bool)),fun(fun(U_143,bool),fun(U_143,bool)),combs(U_143,bool,bool),hAPP(fun(U_143,bool),fun(U_143,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_143,bool),fun(U_143,fun(bool,bool))),combb(bool,fun(bool,bool),U_143),fdisj),U_141)),U_139)))) ) ),
    inference(miniscope,[status(thm)],[f_97_2]) ).

fof(f_97_4,plain,
    ( ! [U_143,U_139,U_141] :
        ( hBOOL(hAPP(fun(U_143,bool),bool,finite_finite(U_143),hAPP(fun(U_143,bool),fun(U_143,bool),collect(U_143),U_139)))
        | ~ sP2(U_143,U_139,U_141) )
    & ! [U_143,U_139,U_141] :
        ( hBOOL(hAPP(fun(U_143,bool),bool,finite_finite(U_143),hAPP(fun(U_143,bool),fun(U_143,bool),collect(U_143),U_141)))
        | ~ sP2(U_143,U_139,U_141) )
    & ! [U_144,U_142,U_140] :
        ( hBOOL(hAPP(fun(U_144,bool),bool,finite_finite(U_144),hAPP(fun(U_144,bool),fun(U_144,bool),collect(U_144),hAPP(fun(U_144,bool),fun(U_144,bool),hAPP(fun(U_144,fun(bool,bool)),fun(fun(U_144,bool),fun(U_144,bool)),combs(U_144,bool,bool),hAPP(fun(U_144,bool),fun(U_144,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_144,bool),fun(U_144,fun(bool,bool))),combb(bool,fun(bool,bool),U_144),fdisj),U_142)),U_140))))
        | ~ hBOOL(hAPP(fun(U_144,bool),bool,finite_finite(U_144),hAPP(fun(U_144,bool),fun(U_144,bool),collect(U_144),U_140)))
        | ~ hBOOL(hAPP(fun(U_144,bool),bool,finite_finite(U_144),hAPP(fun(U_144,bool),fun(U_144,bool),collect(U_144),U_142))) )
    & ! [U_143,U_139,U_141] :
        ( sP2(U_143,U_139,U_141)
        | ~ hBOOL(hAPP(fun(U_143,bool),bool,finite_finite(U_143),hAPP(fun(U_143,bool),fun(U_143,bool),collect(U_143),hAPP(fun(U_143,bool),fun(U_143,bool),hAPP(fun(U_143,fun(bool,bool)),fun(fun(U_143,bool),fun(U_143,bool)),combs(U_143,bool,bool),hAPP(fun(U_143,bool),fun(U_143,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_143,bool),fun(U_143,fun(bool,bool))),combb(bool,fun(bool,bool),U_143),fdisj),U_141)),U_139)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP2])],[f_97_3]) ).

cnf(f_97_5,plain,
    ( sP2(U_143,U_139,U_141)
    | ~ hBOOL(hAPP(fun(U_143,bool),bool,finite_finite(U_143),hAPP(fun(U_143,bool),fun(U_143,bool),collect(U_143),hAPP(fun(U_143,bool),fun(U_143,bool),hAPP(fun(U_143,fun(bool,bool)),fun(fun(U_143,bool),fun(U_143,bool)),combs(U_143,bool,bool),hAPP(fun(U_143,bool),fun(U_143,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_143,bool),fun(U_143,fun(bool,bool))),combb(bool,fun(bool,bool),U_143),fdisj),U_141)),U_139)))) ),
    inference(clausify,[status(thm)],[f_97_4]) ).

cnf(f_97_6,plain,
    ( hBOOL(hAPP(fun(U_144,bool),bool,finite_finite(U_144),hAPP(fun(U_144,bool),fun(U_144,bool),collect(U_144),hAPP(fun(U_144,bool),fun(U_144,bool),hAPP(fun(U_144,fun(bool,bool)),fun(fun(U_144,bool),fun(U_144,bool)),combs(U_144,bool,bool),hAPP(fun(U_144,bool),fun(U_144,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_144,bool),fun(U_144,fun(bool,bool))),combb(bool,fun(bool,bool),U_144),fdisj),U_142)),U_140))))
    | ~ hBOOL(hAPP(fun(U_144,bool),bool,finite_finite(U_144),hAPP(fun(U_144,bool),fun(U_144,bool),collect(U_144),U_140)))
    | ~ hBOOL(hAPP(fun(U_144,bool),bool,finite_finite(U_144),hAPP(fun(U_144,bool),fun(U_144,bool),collect(U_144),U_142))) ),
    inference(clausify,[status(thm)],[f_97_4]) ).

cnf(f_97_7,plain,
    ( hBOOL(hAPP(fun(U_143,bool),bool,finite_finite(U_143),hAPP(fun(U_143,bool),fun(U_143,bool),collect(U_143),U_141)))
    | ~ sP2(U_143,U_139,U_141) ),
    inference(clausify,[status(thm)],[f_97_4]) ).

cnf(f_97_8,plain,
    ( hBOOL(hAPP(fun(U_143,bool),bool,finite_finite(U_143),hAPP(fun(U_143,bool),fun(U_143,bool),collect(U_143),U_139)))
    | ~ sP2(U_143,U_139,U_141) ),
    inference(clausify,[status(thm)],[f_97_4]) ).

fof(f_98_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_98_2,plain,
    ! [U_147,U_146,U_145] :
      ( ( hBOOL(hAPP(fun(U_147,bool),bool,finite_finite(U_147),hAPP(fun(U_147,bool),fun(U_147,bool),hAPP(U_147,fun(fun(U_147,bool),fun(U_147,bool)),insert(U_147),U_146),U_145)))
        | ~ hBOOL(hAPP(fun(U_147,bool),bool,finite_finite(U_147),U_145)) )
      & ( hBOOL(hAPP(fun(U_147,bool),bool,finite_finite(U_147),U_145))
        | ~ hBOOL(hAPP(fun(U_147,bool),bool,finite_finite(U_147),hAPP(fun(U_147,bool),fun(U_147,bool),hAPP(U_147,fun(fun(U_147,bool),fun(U_147,bool)),insert(U_147),U_146),U_145))) ) ),
    inference(variable_rename,[status(thm)],[f_98_1]) ).

fof(f_98_3,plain,
    ( ! [U_153,U_151,U_149] :
        ( hBOOL(hAPP(fun(U_153,bool),bool,finite_finite(U_153),hAPP(fun(U_153,bool),fun(U_153,bool),hAPP(U_153,fun(fun(U_153,bool),fun(U_153,bool)),insert(U_153),U_151),U_149)))
        | ~ hBOOL(hAPP(fun(U_153,bool),bool,finite_finite(U_153),U_149)) )
    & ! [U_152,U_150,U_148] :
        ( hBOOL(hAPP(fun(U_152,bool),bool,finite_finite(U_152),U_148))
        | ~ hBOOL(hAPP(fun(U_152,bool),bool,finite_finite(U_152),hAPP(fun(U_152,bool),fun(U_152,bool),hAPP(U_152,fun(fun(U_152,bool),fun(U_152,bool)),insert(U_152),U_150),U_148))) ) ),
    inference(miniscope,[status(thm)],[f_98_2]) ).

fof(f_98_4,plain,
    ( ! [U_149,U_153,U_151] :
        ( hBOOL(hAPP(fun(U_153,bool),bool,finite_finite(U_153),hAPP(fun(U_153,bool),fun(U_153,bool),hAPP(U_153,fun(fun(U_153,bool),fun(U_153,bool)),insert(U_153),U_151),U_149)))
        | ~ hBOOL(hAPP(fun(U_153,bool),bool,finite_finite(U_153),U_149)) )
    & ! [U_150,U_148,U_152] :
        ( hBOOL(hAPP(fun(U_152,bool),bool,finite_finite(U_152),U_148))
        | ~ hBOOL(hAPP(fun(U_152,bool),bool,finite_finite(U_152),hAPP(fun(U_152,bool),fun(U_152,bool),hAPP(U_152,fun(fun(U_152,bool),fun(U_152,bool)),insert(U_152),U_150),U_148))) ) ),
    inference(definitional_conversion,[status(esa)],[f_98_3]) ).

cnf(f_98_5,plain,
    ( hBOOL(hAPP(fun(U_152,bool),bool,finite_finite(U_152),U_148))
    | ~ hBOOL(hAPP(fun(U_152,bool),bool,finite_finite(U_152),hAPP(fun(U_152,bool),fun(U_152,bool),hAPP(U_152,fun(fun(U_152,bool),fun(U_152,bool)),insert(U_152),U_150),U_148))) ),
    inference(clausify,[status(thm)],[f_98_4]) ).

cnf(f_98_6,plain,
    ( hBOOL(hAPP(fun(U_153,bool),bool,finite_finite(U_153),hAPP(fun(U_153,bool),fun(U_153,bool),hAPP(U_153,fun(fun(U_153,bool),fun(U_153,bool)),insert(U_153),U_151),U_149)))
    | ~ hBOOL(hAPP(fun(U_153,bool),bool,finite_finite(U_153),U_149)) ),
    inference(clausify,[status(thm)],[f_98_4]) ).

fof(f_99_1,plain,
    ! [X_b,A_3,B_1] :
      ( 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_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),B_1)) ),
    inference(fof_nnf,[status(thm)],[fact_28_finite__subset]) ).

fof(f_99_2,plain,
    ! [U_156,U_155,U_154] :
      ( hBOOL(hAPP(fun(U_156,bool),bool,finite_finite(U_156),U_155))
      | ~ hBOOL(hAPP(fun(U_156,bool),bool,finite_finite(U_156),U_154))
      | ~ hBOOL(hAPP(fun(U_156,bool),bool,hAPP(fun(U_156,bool),fun(fun(U_156,bool),bool),ord_less_eq(fun(U_156,bool)),U_155),U_154)) ),
    inference(variable_rename,[status(thm)],[f_99_1]) ).

fof(f_99_3,plain,
    ! [U_154,U_155,U_156] :
      ( hBOOL(hAPP(fun(U_156,bool),bool,finite_finite(U_156),U_155))
      | ~ hBOOL(hAPP(fun(U_156,bool),bool,finite_finite(U_156),U_154))
      | ~ hBOOL(hAPP(fun(U_156,bool),bool,hAPP(fun(U_156,bool),fun(fun(U_156,bool),bool),ord_less_eq(fun(U_156,bool)),U_155),U_154)) ),
    inference(definitional_conversion,[status(esa)],[f_99_2]) ).

cnf(f_99_4,plain,
    ( hBOOL(hAPP(fun(U_156,bool),bool,finite_finite(U_156),U_155))
    | ~ hBOOL(hAPP(fun(U_156,bool),bool,finite_finite(U_156),U_154))
    | ~ hBOOL(hAPP(fun(U_156,bool),bool,hAPP(fun(U_156,bool),fun(fun(U_156,bool),bool),ord_less_eq(fun(U_156,bool)),U_155),U_154)) ),
    inference(clausify,[status(thm)],[f_99_3]) ).

fof(f_100_1,plain,
    ! [X_b,A_3,B_1] :
      ( 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_1))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_1)) ),
    inference(fof_nnf,[status(thm)],[fact_29_rev__finite__subset]) ).

fof(f_100_2,plain,
    ! [U_159,U_158,U_157] :
      ( hBOOL(hAPP(fun(U_159,bool),bool,finite_finite(U_159),U_158))
      | ~ hBOOL(hAPP(fun(U_159,bool),bool,hAPP(fun(U_159,bool),fun(fun(U_159,bool),bool),ord_less_eq(fun(U_159,bool)),U_158),U_157))
      | ~ hBOOL(hAPP(fun(U_159,bool),bool,finite_finite(U_159),U_157)) ),
    inference(variable_rename,[status(thm)],[f_100_1]) ).

fof(f_100_3,plain,
    ! [U_157,U_159,U_158] :
      ( hBOOL(hAPP(fun(U_159,bool),bool,finite_finite(U_159),U_158))
      | ~ hBOOL(hAPP(fun(U_159,bool),bool,hAPP(fun(U_159,bool),fun(fun(U_159,bool),bool),ord_less_eq(fun(U_159,bool)),U_158),U_157))
      | ~ hBOOL(hAPP(fun(U_159,bool),bool,finite_finite(U_159),U_157)) ),
    inference(definitional_conversion,[status(esa)],[f_100_2]) ).

cnf(f_100_4,plain,
    ( hBOOL(hAPP(fun(U_159,bool),bool,finite_finite(U_159),U_158))
    | ~ hBOOL(hAPP(fun(U_159,bool),bool,hAPP(fun(U_159,bool),fun(fun(U_159,bool),bool),ord_less_eq(fun(U_159,bool)),U_158),U_157))
    | ~ hBOOL(hAPP(fun(U_159,bool),bool,finite_finite(U_159),U_157)) ),
    inference(clausify,[status(thm)],[f_100_3]) ).

fof(f_101_1,plain,
    ! [M_1,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M_1)),N)) ),
    inference(fof_nnf,[status(thm)],[fact_30_Suc__leD]) ).

fof(f_101_2,plain,
    ! [U_161,U_160] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_161),U_160))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_161)),U_160)) ),
    inference(variable_rename,[status(thm)],[f_101_1]) ).

fof(f_101_3,plain,
    ! [U_160,U_161] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_161),U_160))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_161)),U_160)) ),
    inference(definitional_conversion,[status(esa)],[f_101_2]) ).

cnf(f_101_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_161),U_160))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_161)),U_160)) ),
    inference(clausify,[status(thm)],[f_101_3]) ).

fof(f_102_1,plain,
    ! [M_1,N] :
      ( M_1 = hAPP(nat,nat,suc,N)
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),hAPP(nat,nat,suc,N))) ),
    inference(fof_nnf,[status(thm)],[fact_31_le__SucE]) ).

fof(f_102_2,plain,
    ! [U_163,U_162] :
      ( U_163 = hAPP(nat,nat,suc,U_162)
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_163),U_162))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_163),hAPP(nat,nat,suc,U_162))) ),
    inference(variable_rename,[status(thm)],[f_102_1]) ).

fof(f_102_3,plain,
    ! [U_163,U_162] :
      ( U_163 = hAPP(nat,nat,suc,U_162)
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_163),U_162))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_163),hAPP(nat,nat,suc,U_162))) ),
    inference(definitional_conversion,[status(esa)],[f_102_2]) ).

cnf(f_102_4,plain,
    ( U_163 = hAPP(nat,nat,suc,U_162)
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_163),U_162))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_163),hAPP(nat,nat,suc,U_162))) ),
    inference(clausify,[status(thm)],[f_102_3]) ).

fof(f_103_1,plain,
    ! [M_1,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),hAPP(nat,nat,suc,N)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)) ),
    inference(fof_nnf,[status(thm)],[fact_32_le__SucI]) ).

fof(f_103_2,plain,
    ! [U_165,U_164] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_165),hAPP(nat,nat,suc,U_164)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_165),U_164)) ),
    inference(variable_rename,[status(thm)],[f_103_1]) ).

fof(f_103_3,plain,
    ! [U_164,U_165] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_165),hAPP(nat,nat,suc,U_164)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_165),U_164)) ),
    inference(definitional_conversion,[status(esa)],[f_103_2]) ).

cnf(f_103_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_165),hAPP(nat,nat,suc,U_164)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_165),U_164)) ),
    inference(clausify,[status(thm)],[f_103_3]) ).

fof(f_104_1,plain,
    ! [Na,M] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Na)),hAPP(nat,nat,suc,M)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Na),M)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Na),M))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Na)),hAPP(nat,nat,suc,M))) ) ),
    inference(fof_nnf,[status(thm)],[fact_33_Suc__le__mono]) ).

fof(f_104_2,plain,
    ! [U_167,U_166] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_167)),hAPP(nat,nat,suc,U_166)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_167),U_166)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_167),U_166))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_167)),hAPP(nat,nat,suc,U_166))) ) ),
    inference(variable_rename,[status(thm)],[f_104_1]) ).

fof(f_104_3,plain,
    ( ! [U_171,U_169] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_171)),hAPP(nat,nat,suc,U_169)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_171),U_169)) )
    & ! [U_170,U_168] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_170),U_168))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_170)),hAPP(nat,nat,suc,U_168))) ) ),
    inference(miniscope,[status(thm)],[f_104_2]) ).

fof(f_104_4,plain,
    ( ! [U_169,U_171] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_171)),hAPP(nat,nat,suc,U_169)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_171),U_169)) )
    & ! [U_168,U_170] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_170),U_168))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_170)),hAPP(nat,nat,suc,U_168))) ) ),
    inference(definitional_conversion,[status(esa)],[f_104_3]) ).

cnf(f_104_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_170),U_168))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_170)),hAPP(nat,nat,suc,U_168))) ),
    inference(clausify,[status(thm)],[f_104_4]) ).

cnf(f_104_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_171)),hAPP(nat,nat,suc,U_169)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_171),U_169)) ),
    inference(clausify,[status(thm)],[f_104_4]) ).

fof(f_105_1,plain,
    ! [M,Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,suc,Na)))
        | ( M != hAPP(nat,nat,suc,Na)
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)) ) )
      & ( M = hAPP(nat,nat,suc,Na)
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,suc,Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_34_le__Suc__eq]) ).

fof(f_105_2,plain,
    ! [U_173,U_172] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_173),hAPP(nat,nat,suc,U_172)))
        | ( U_173 != hAPP(nat,nat,suc,U_172)
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_173),U_172)) ) )
      & ( U_173 = hAPP(nat,nat,suc,U_172)
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_173),U_172))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_173),hAPP(nat,nat,suc,U_172))) ) ),
    inference(variable_rename,[status(thm)],[f_105_1]) ).

fof(f_105_3,plain,
    ( ! [U_177,U_175] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_177),hAPP(nat,nat,suc,U_175)))
        | ( U_177 != hAPP(nat,nat,suc,U_175)
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_177),U_175)) ) )
    & ! [U_176,U_174] :
        ( U_176 = hAPP(nat,nat,suc,U_174)
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_176),U_174))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_176),hAPP(nat,nat,suc,U_174))) ) ),
    inference(miniscope,[status(thm)],[f_105_2]) ).

fof(f_105_4,plain,
    ( ! [U_177,U_175] :
        ( U_177 != hAPP(nat,nat,suc,U_175)
        | ~ sP3(U_177,U_175) )
    & ! [U_177,U_175] :
        ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_177),U_175))
        | ~ sP3(U_177,U_175) )
    & ! [U_177,U_175] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_177),hAPP(nat,nat,suc,U_175)))
        | sP3(U_177,U_175) )
    & ! [U_176,U_174] :
        ( U_176 = hAPP(nat,nat,suc,U_174)
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_176),U_174))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_176),hAPP(nat,nat,suc,U_174))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP3])],[f_105_3]) ).

cnf(f_105_5,plain,
    ( U_176 = hAPP(nat,nat,suc,U_174)
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_176),U_174))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_176),hAPP(nat,nat,suc,U_174))) ),
    inference(clausify,[status(thm)],[f_105_4]) ).

cnf(f_105_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_177),hAPP(nat,nat,suc,U_175)))
    | sP3(U_177,U_175) ),
    inference(clausify,[status(thm)],[f_105_4]) ).

cnf(f_105_7,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_177),U_175))
    | ~ sP3(U_177,U_175) ),
    inference(clausify,[status(thm)],[f_105_4]) ).

cnf(f_105_8,plain,
    ( U_177 != hAPP(nat,nat,suc,U_175)
    | ~ sP3(U_177,U_175) ),
    inference(clausify,[status(thm)],[f_105_4]) ).

fof(f_106_1,plain,
    ! [M,Na] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Na)),M)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Na)),M))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_35_not__less__eq__eq]) ).

fof(f_106_2,plain,
    ! [U_179,U_178] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_179),U_178))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_178)),U_179)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_178)),U_179))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_179),U_178)) ) ),
    inference(variable_rename,[status(thm)],[f_106_1]) ).

fof(f_106_3,plain,
    ( ! [U_183,U_181] :
        ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_183),U_181))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_181)),U_183)) )
    & ! [U_182,U_180] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_180)),U_182))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_182),U_180)) ) ),
    inference(miniscope,[status(thm)],[f_106_2]) ).

fof(f_106_4,plain,
    ( ! [U_183,U_181] :
        ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_183),U_181))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_181)),U_183)) )
    & ! [U_182,U_180] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_180)),U_182))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_182),U_180)) ) ),
    inference(definitional_conversion,[status(esa)],[f_106_3]) ).

cnf(f_106_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_180)),U_182))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_182),U_180)) ),
    inference(clausify,[status(thm)],[f_106_4]) ).

cnf(f_106_6,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_183),U_181))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_181)),U_183)) ),
    inference(clausify,[status(thm)],[f_106_4]) ).

fof(f_107_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_107_2,plain,
    ! [U_184] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_184)),U_184)),
    inference(variable_rename,[status(thm)],[f_107_1]) ).

fof(f_107_3,plain,
    ! [U_184] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_184)),U_184)),
    inference(definitional_conversion,[status(esa)],[f_107_2]) ).

cnf(f_107_4,plain,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_184)),U_184)),
    inference(clausify,[status(thm)],[f_107_3]) ).

fof(f_108_1,plain,
    ! [M_1,N,K_1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M_1)),N)),hAPP(nat,nat,suc,K_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N)),K_1),
    inference(fof_nnf,[status(thm)],[fact_37_Suc__diff__diff]) ).

fof(f_108_2,plain,
    ! [U_187,U_186,U_185] : 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_187)),U_186)),hAPP(nat,nat,suc,U_185)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_187),U_186)),U_185),
    inference(variable_rename,[status(thm)],[f_108_1]) ).

fof(f_108_3,plain,
    ! [U_185,U_186,U_187] : 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_187)),U_186)),hAPP(nat,nat,suc,U_185)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_187),U_186)),U_185),
    inference(definitional_conversion,[status(esa)],[f_108_2]) ).

cnf(f_108_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_187)),U_186)),hAPP(nat,nat,suc,U_185)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_187),U_186)),U_185),
    inference(clausify,[status(thm)],[f_108_3]) ).

fof(f_109_1,plain,
    ! [M_1,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M_1)),hAPP(nat,nat,suc,N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N),
    inference(fof_nnf,[status(thm)],[fact_38_diff__Suc__Suc]) ).

fof(f_109_2,plain,
    ! [U_189,U_188] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,U_189)),hAPP(nat,nat,suc,U_188)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_189),U_188),
    inference(variable_rename,[status(thm)],[f_109_1]) ).

fof(f_109_3,plain,
    ! [U_188,U_189] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,U_189)),hAPP(nat,nat,suc,U_188)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_189),U_188),
    inference(definitional_conversion,[status(esa)],[f_109_2]) ).

cnf(f_109_4,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,U_189)),hAPP(nat,nat,suc,U_188)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_189),U_188),
    inference(clausify,[status(thm)],[f_109_3]) ).

fof(f_110_1,plain,
    ! [Na,K,M] :
      ( ( ( 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),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Na),K)))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)) )
        & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),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),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Na),K))) ) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),Na))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),M)) ),
    inference(fof_nnf,[status(thm)],[fact_39_le__diff__iff]) ).

fof(f_110_2,plain,
    ! [U_192,U_191,U_190] :
      ( ( ( 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_190),U_191)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_192),U_191)))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_190),U_192)) )
        & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_190),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_190),U_191)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_192),U_191))) ) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_191),U_192))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_191),U_190)) ),
    inference(variable_rename,[status(thm)],[f_110_1]) ).

fof(f_110_3,plain,
    ( ! [U_191,U_190,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_190),U_191)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_192),U_191)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_190),U_192))
        | ~ sP4(U_191,U_190,U_192) )
    & ! [U_191,U_190,U_192] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_190),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_190),U_191)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_192),U_191)))
        | ~ sP4(U_191,U_190,U_192) )
    & ! [U_191,U_190,U_192] :
        ( sP4(U_191,U_190,U_192)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_191),U_192))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_191),U_190)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP4])],[f_110_2]) ).

cnf(f_110_4,plain,
    ( sP4(U_191,U_190,U_192)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_191),U_192))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_191),U_190)) ),
    inference(clausify,[status(thm)],[f_110_3]) ).

cnf(f_110_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_190),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_190),U_191)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_192),U_191)))
    | ~ sP4(U_191,U_190,U_192) ),
    inference(clausify,[status(thm)],[f_110_3]) ).

cnf(f_110_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_190),U_191)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_192),U_191)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_190),U_192))
    | ~ sP4(U_191,U_190,U_192) ),
    inference(clausify,[status(thm)],[f_110_3]) ).

fof(f_111_1,plain,
    ! [N,K_1,M_1] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),K_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),M_1)) ),
    inference(fof_nnf,[status(thm)],[fact_40_Nat_Odiff__diff__eq]) ).

fof(f_111_2,plain,
    ! [U_195,U_194,U_193] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_193),U_194)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_195),U_194)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_193),U_195)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_194),U_195))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_194),U_193)) ),
    inference(variable_rename,[status(thm)],[f_111_1]) ).

fof(f_111_3,plain,
    ! [U_193,U_195,U_194] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_193),U_194)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_195),U_194)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_193),U_195)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_194),U_195))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_194),U_193)) ),
    inference(definitional_conversion,[status(esa)],[f_111_2]) ).

cnf(f_111_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_193),U_194)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_195),U_194)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_193),U_195)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_194),U_195))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_194),U_193)) ),
    inference(clausify,[status(thm)],[f_111_3]) ).

fof(f_112_1,plain,
    ! [Na,K,M] :
      ( ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Na),K)
          | M != Na )
        & ( M = Na
          | hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),K) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Na),K) ) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),Na))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),M)) ),
    inference(fof_nnf,[status(thm)],[fact_41_eq__diff__iff]) ).

fof(f_112_2,plain,
    ! [U_198,U_197,U_196] :
      ( ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_196),U_197) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_198),U_197)
          | U_196 != U_198 )
        & ( U_196 = U_198
          | hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_196),U_197) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_198),U_197) ) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_197),U_198))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_197),U_196)) ),
    inference(variable_rename,[status(thm)],[f_112_1]) ).

fof(f_112_3,plain,
    ( ! [U_196,U_197,U_198] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_196),U_197) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_198),U_197)
        | U_196 != U_198
        | ~ sP5(U_196,U_197,U_198) )
    & ! [U_196,U_197,U_198] :
        ( U_196 = U_198
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_196),U_197) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_198),U_197)
        | ~ sP5(U_196,U_197,U_198) )
    & ! [U_196,U_197,U_198] :
        ( sP5(U_196,U_197,U_198)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_197),U_198))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_197),U_196)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP5])],[f_112_2]) ).

cnf(f_112_4,plain,
    ( sP5(U_196,U_197,U_198)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_197),U_198))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_197),U_196)) ),
    inference(clausify,[status(thm)],[f_112_3]) ).

cnf(f_112_5,plain,
    ( U_196 = U_198
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_196),U_197) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_198),U_197)
    | ~ sP5(U_196,U_197,U_198) ),
    inference(clausify,[status(thm)],[f_112_3]) ).

cnf(f_112_6,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_196),U_197) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_198),U_197)
    | U_196 != U_198
    | ~ sP5(U_196,U_197,U_198) ),
    inference(clausify,[status(thm)],[f_112_3]) ).

fof(f_113_1,plain,
    ! [I_2,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_2)) = I_2
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),N)) ),
    inference(fof_nnf,[status(thm)],[fact_42_diff__diff__cancel]) ).

fof(f_113_2,plain,
    ! [U_200,U_199] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_199),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_199),U_200)) = U_200
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_200),U_199)) ),
    inference(variable_rename,[status(thm)],[f_113_1]) ).

fof(f_113_3,plain,
    ! [U_200,U_199] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_199),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_199),U_200)) = U_200
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_200),U_199)) ),
    inference(definitional_conversion,[status(esa)],[f_113_2]) ).

cnf(f_113_4,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_199),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_199),U_200)) = U_200
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_200),U_199)) ),
    inference(clausify,[status(thm)],[f_113_3]) ).

fof(f_114_1,plain,
    ! [L_1,M_1,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_1),L_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),L_1)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)) ),
    inference(fof_nnf,[status(thm)],[fact_43_diff__le__mono]) ).

fof(f_114_2,plain,
    ! [U_203,U_202,U_201] :
      ( 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_202),U_203)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_201),U_203)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_202),U_201)) ),
    inference(variable_rename,[status(thm)],[f_114_1]) ).

fof(f_114_3,plain,
    ! [U_201,U_202,U_203] :
      ( 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_202),U_203)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_201),U_203)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_202),U_201)) ),
    inference(definitional_conversion,[status(esa)],[f_114_2]) ).

cnf(f_114_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_202),U_203)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_201),U_203)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_202),U_201)) ),
    inference(clausify,[status(thm)],[f_114_3]) ).

fof(f_115_1,plain,
    ! [L_1,M_1,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_1),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L_1),M_1)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)) ),
    inference(fof_nnf,[status(thm)],[fact_44_diff__le__mono2]) ).

fof(f_115_2,plain,
    ! [U_206,U_205,U_204] :
      ( 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_206),U_204)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_206),U_205)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_205),U_204)) ),
    inference(variable_rename,[status(thm)],[f_115_1]) ).

fof(f_115_3,plain,
    ! [U_204,U_205,U_206] :
      ( 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_206),U_204)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_206),U_205)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_205),U_204)) ),
    inference(definitional_conversion,[status(esa)],[f_115_2]) ).

cnf(f_115_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_206),U_204)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_206),U_205)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_205),U_204)) ),
    inference(clausify,[status(thm)],[f_115_3]) ).

fof(f_116_1,plain,
    ! [M_1,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_1),N)),M_1)),
    inference(fof_nnf,[status(thm)],[fact_45_diff__le__self]) ).

fof(f_116_2,plain,
    ! [U_208,U_207] : 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_208),U_207)),U_208)),
    inference(variable_rename,[status(thm)],[f_116_1]) ).

fof(f_116_3,plain,
    ! [U_207,U_208] : 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_208),U_207)),U_208)),
    inference(definitional_conversion,[status(esa)],[f_116_2]) ).

cnf(f_116_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_208),U_207)),U_208)),
    inference(clausify,[status(thm)],[f_116_3]) ).

fof(f_117_1,plain,
    ! [X_c,X_b,B_1,F,A_3] :
      ( hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),B_1))
      | ~ 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_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,finite_finite(X_b),A_3)) ),
    inference(fof_nnf,[status(thm)],[fact_46_finite__surj]) ).

fof(f_117_2,plain,
    ! [U_213,U_212,U_211,U_210,U_209] :
      ( hBOOL(hAPP(fun(U_213,bool),bool,finite_finite(U_213),U_211))
      | ~ hBOOL(hAPP(fun(U_213,bool),bool,hAPP(fun(U_213,bool),fun(fun(U_213,bool),bool),ord_less_eq(fun(U_213,bool)),U_211),hAPP(fun(U_212,bool),fun(U_213,bool),hAPP(fun(U_212,U_213),fun(fun(U_212,bool),fun(U_213,bool)),image(U_212,U_213),U_210),U_209)))
      | ~ hBOOL(hAPP(fun(U_212,bool),bool,finite_finite(U_212),U_209)) ),
    inference(variable_rename,[status(thm)],[f_117_1]) ).

fof(f_117_3,plain,
    ! [U_212,U_209,U_211,U_210,U_213] :
      ( hBOOL(hAPP(fun(U_213,bool),bool,finite_finite(U_213),U_211))
      | ~ hBOOL(hAPP(fun(U_213,bool),bool,hAPP(fun(U_213,bool),fun(fun(U_213,bool),bool),ord_less_eq(fun(U_213,bool)),U_211),hAPP(fun(U_212,bool),fun(U_213,bool),hAPP(fun(U_212,U_213),fun(fun(U_212,bool),fun(U_213,bool)),image(U_212,U_213),U_210),U_209)))
      | ~ hBOOL(hAPP(fun(U_212,bool),bool,finite_finite(U_212),U_209)) ),
    inference(definitional_conversion,[status(esa)],[f_117_2]) ).

cnf(f_117_4,plain,
    ( hBOOL(hAPP(fun(U_213,bool),bool,finite_finite(U_213),U_211))
    | ~ hBOOL(hAPP(fun(U_213,bool),bool,hAPP(fun(U_213,bool),fun(fun(U_213,bool),bool),ord_less_eq(fun(U_213,bool)),U_211),hAPP(fun(U_212,bool),fun(U_213,bool),hAPP(fun(U_212,U_213),fun(fun(U_212,bool),fun(U_213,bool)),image(U_212,U_213),U_210),U_209)))
    | ~ hBOOL(hAPP(fun(U_212,bool),bool,finite_finite(U_212),U_209)) ),
    inference(clausify,[status(thm)],[f_117_3]) ).

fof(f_118_1,plain,
    ! [X_c,X_b,F,A_3,B_1] :
      ( ? [C_3] :
          ( ti(fun(X_b,bool),B_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),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_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)))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_1)) ),
    inference(fof_nnf,[status(thm)],[fact_47_finite__subset__image]) ).

fof(f_118_2,plain,
    ! [U_219,U_218,U_217,U_216,U_215] :
      ( ? [U_214] :
          ( ti(fun(U_218,bool),U_215) = hAPP(fun(U_219,bool),fun(U_218,bool),hAPP(fun(U_219,U_218),fun(fun(U_219,bool),fun(U_218,bool)),image(U_219,U_218),U_217),U_214)
          & hBOOL(hAPP(fun(U_219,bool),bool,finite_finite(U_219),U_214))
          & hBOOL(hAPP(fun(U_219,bool),bool,hAPP(fun(U_219,bool),fun(fun(U_219,bool),bool),ord_less_eq(fun(U_219,bool)),U_214),U_216)) )
      | ~ hBOOL(hAPP(fun(U_218,bool),bool,hAPP(fun(U_218,bool),fun(fun(U_218,bool),bool),ord_less_eq(fun(U_218,bool)),U_215),hAPP(fun(U_219,bool),fun(U_218,bool),hAPP(fun(U_219,U_218),fun(fun(U_219,bool),fun(U_218,bool)),image(U_219,U_218),U_217),U_216)))
      | ~ hBOOL(hAPP(fun(U_218,bool),bool,finite_finite(U_218),U_215)) ),
    inference(variable_rename,[status(thm)],[f_118_1]) ).

fof(f_118_3,plain,
    ! [U_219,U_218,U_217,U_216,U_215] :
      ( ( ti(fun(U_218,bool),U_215) = hAPP(fun(U_219,bool),fun(U_218,bool),hAPP(fun(U_219,U_218),fun(fun(U_219,bool),fun(U_218,bool)),image(U_219,U_218),U_217),sK1(U_219,U_218,U_217,U_216,U_215))
        & hBOOL(hAPP(fun(U_219,bool),bool,finite_finite(U_219),sK1(U_219,U_218,U_217,U_216,U_215)))
        & hBOOL(hAPP(fun(U_219,bool),bool,hAPP(fun(U_219,bool),fun(fun(U_219,bool),bool),ord_less_eq(fun(U_219,bool)),sK1(U_219,U_218,U_217,U_216,U_215)),U_216)) )
      | ~ hBOOL(hAPP(fun(U_218,bool),bool,hAPP(fun(U_218,bool),fun(fun(U_218,bool),bool),ord_less_eq(fun(U_218,bool)),U_215),hAPP(fun(U_219,bool),fun(U_218,bool),hAPP(fun(U_219,U_218),fun(fun(U_219,bool),fun(U_218,bool)),image(U_219,U_218),U_217),U_216)))
      | ~ hBOOL(hAPP(fun(U_218,bool),bool,finite_finite(U_218),U_215)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_214,sK1(U_219,U_218,U_217,U_216,U_215))],[f_118_2]) ).

fof(f_118_4,plain,
    ( ! [U_218,U_216,U_215,U_217,U_219] :
        ( ti(fun(U_218,bool),U_215) = hAPP(fun(U_219,bool),fun(U_218,bool),hAPP(fun(U_219,U_218),fun(fun(U_219,bool),fun(U_218,bool)),image(U_219,U_218),U_217),sK1(U_219,U_218,U_217,U_216,U_215))
        | ~ sP6(U_218,U_216,U_215,U_217,U_219) )
    & ! [U_218,U_216,U_215,U_217,U_219] :
        ( hBOOL(hAPP(fun(U_219,bool),bool,finite_finite(U_219),sK1(U_219,U_218,U_217,U_216,U_215)))
        | ~ sP6(U_218,U_216,U_215,U_217,U_219) )
    & ! [U_218,U_216,U_215,U_217,U_219] :
        ( hBOOL(hAPP(fun(U_219,bool),bool,hAPP(fun(U_219,bool),fun(fun(U_219,bool),bool),ord_less_eq(fun(U_219,bool)),sK1(U_219,U_218,U_217,U_216,U_215)),U_216))
        | ~ sP6(U_218,U_216,U_215,U_217,U_219) )
    & ! [U_218,U_216,U_215,U_217,U_219] :
        ( sP6(U_218,U_216,U_215,U_217,U_219)
        | ~ hBOOL(hAPP(fun(U_218,bool),bool,hAPP(fun(U_218,bool),fun(fun(U_218,bool),bool),ord_less_eq(fun(U_218,bool)),U_215),hAPP(fun(U_219,bool),fun(U_218,bool),hAPP(fun(U_219,U_218),fun(fun(U_219,bool),fun(U_218,bool)),image(U_219,U_218),U_217),U_216)))
        | ~ hBOOL(hAPP(fun(U_218,bool),bool,finite_finite(U_218),U_215)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP6])],[f_118_3]) ).

cnf(f_118_5,plain,
    ( sP6(U_218,U_216,U_215,U_217,U_219)
    | ~ hBOOL(hAPP(fun(U_218,bool),bool,hAPP(fun(U_218,bool),fun(fun(U_218,bool),bool),ord_less_eq(fun(U_218,bool)),U_215),hAPP(fun(U_219,bool),fun(U_218,bool),hAPP(fun(U_219,U_218),fun(fun(U_219,bool),fun(U_218,bool)),image(U_219,U_218),U_217),U_216)))
    | ~ hBOOL(hAPP(fun(U_218,bool),bool,finite_finite(U_218),U_215)) ),
    inference(clausify,[status(thm)],[f_118_4]) ).

cnf(f_118_6,plain,
    ( hBOOL(hAPP(fun(U_219,bool),bool,hAPP(fun(U_219,bool),fun(fun(U_219,bool),bool),ord_less_eq(fun(U_219,bool)),sK1(U_219,U_218,U_217,U_216,U_215)),U_216))
    | ~ sP6(U_218,U_216,U_215,U_217,U_219) ),
    inference(clausify,[status(thm)],[f_118_4]) ).

cnf(f_118_7,plain,
    ( hBOOL(hAPP(fun(U_219,bool),bool,finite_finite(U_219),sK1(U_219,U_218,U_217,U_216,U_215)))
    | ~ sP6(U_218,U_216,U_215,U_217,U_219) ),
    inference(clausify,[status(thm)],[f_118_4]) ).

cnf(f_118_8,plain,
    ( ti(fun(U_218,bool),U_215) = hAPP(fun(U_219,bool),fun(U_218,bool),hAPP(fun(U_219,U_218),fun(fun(U_219,bool),fun(U_218,bool)),image(U_219,U_218),U_217),sK1(U_219,U_218,U_217,U_216,U_215))
    | ~ sP6(U_218,U_216,U_215,U_217,U_219) ),
    inference(clausify,[status(thm)],[f_118_4]) ).

fof(f_119_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_1] : ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(nat,X_b,F,N_1)),hAPP(nat,X_b,F,hAPP(nat,nat,suc,N_1)))) )
      | ~ order(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_48_lift__Suc__mono__le]) ).

fof(f_119_2,plain,
    ! [U_224] :
      ( ! [U_223,U_222,U_221] :
          ( hBOOL(hAPP(U_224,bool,hAPP(U_224,fun(U_224,bool),ord_less_eq(U_224),hAPP(nat,U_224,U_221,U_223)),hAPP(nat,U_224,U_221,U_222)))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_223),U_222))
          | ? [U_220] : ~ hBOOL(hAPP(U_224,bool,hAPP(U_224,fun(U_224,bool),ord_less_eq(U_224),hAPP(nat,U_224,U_221,U_220)),hAPP(nat,U_224,U_221,hAPP(nat,nat,suc,U_220)))) )
      | ~ order(U_224) ),
    inference(variable_rename,[status(thm)],[f_119_1]) ).

fof(f_119_3,plain,
    ! [U_224] :
      ( ! [U_223,U_222,U_221] :
          ( hBOOL(hAPP(U_224,bool,hAPP(U_224,fun(U_224,bool),ord_less_eq(U_224),hAPP(nat,U_224,U_221,U_223)),hAPP(nat,U_224,U_221,U_222)))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_223),U_222))
          | ~ hBOOL(hAPP(U_224,bool,hAPP(U_224,fun(U_224,bool),ord_less_eq(U_224),hAPP(nat,U_224,U_221,sK2(U_224,U_223,U_222,U_221))),hAPP(nat,U_224,U_221,hAPP(nat,nat,suc,sK2(U_224,U_223,U_222,U_221))))) )
      | ~ order(U_224) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_220,sK2(U_224,U_223,U_222,U_221))],[f_119_2]) ).

fof(f_119_4,plain,
    ! [U_223,U_224,U_221,U_222] :
      ( hBOOL(hAPP(U_224,bool,hAPP(U_224,fun(U_224,bool),ord_less_eq(U_224),hAPP(nat,U_224,U_221,U_223)),hAPP(nat,U_224,U_221,U_222)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_223),U_222))
      | ~ hBOOL(hAPP(U_224,bool,hAPP(U_224,fun(U_224,bool),ord_less_eq(U_224),hAPP(nat,U_224,U_221,sK2(U_224,U_223,U_222,U_221))),hAPP(nat,U_224,U_221,hAPP(nat,nat,suc,sK2(U_224,U_223,U_222,U_221)))))
      | ~ order(U_224) ),
    inference(definitional_conversion,[status(esa)],[f_119_3]) ).

cnf(f_119_5,plain,
    ( hBOOL(hAPP(U_224,bool,hAPP(U_224,fun(U_224,bool),ord_less_eq(U_224),hAPP(nat,U_224,U_221,U_223)),hAPP(nat,U_224,U_221,U_222)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_223),U_222))
    | ~ hBOOL(hAPP(U_224,bool,hAPP(U_224,fun(U_224,bool),ord_less_eq(U_224),hAPP(nat,U_224,U_221,sK2(U_224,U_223,U_222,U_221))),hAPP(nat,U_224,U_221,hAPP(nat,nat,suc,sK2(U_224,U_223,U_222,U_221)))))
    | ~ order(U_224) ),
    inference(clausify,[status(thm)],[f_119_4]) ).

fof(f_120_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_120_2,plain,
    ! [U_229,U_228,U_227,U_226] :
      ( ? [U_225] :
          ( ~ hBOOL(hAPP(fun(U_228,bool),bool,finite_finite(U_228),hAPP(fun(U_228,bool),fun(U_228,bool),collect(U_228),hAPP(fun(U_228,bool),fun(U_228,bool),hAPP(fun(U_228,fun(bool,bool)),fun(fun(U_228,bool),fun(U_228,bool)),combs(U_228,bool,bool),hAPP(fun(U_228,bool),fun(U_228,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_228,bool),fun(U_228,fun(bool,bool))),combb(bool,fun(bool,bool),U_228),fconj),hAPP(fun(U_228,bool),fun(U_228,bool),hAPP(fun(U_228,fun(fun(U_228,bool),bool)),fun(fun(U_228,bool),fun(U_228,bool)),combc(U_228,fun(U_228,bool),bool),member(U_228)),U_226))),hAPP(U_229,fun(U_228,bool),hAPP(fun(U_228,fun(U_229,bool)),fun(U_229,fun(U_228,bool)),combc(U_228,U_229,bool),hAPP(fun(U_228,U_229),fun(U_228,fun(U_229,bool)),hAPP(fun(U_229,fun(U_229,bool)),fun(fun(U_228,U_229),fun(U_228,fun(U_229,bool))),combb(U_229,fun(U_229,bool),U_228),fequal(U_229)),U_227)),hAPP(U_228,U_229,U_227,U_225))))))
          & hBOOL(hAPP(fun(U_228,bool),bool,hAPP(U_228,fun(fun(U_228,bool),bool),member(U_228),U_225),U_226)) )
      | ~ hBOOL(hAPP(fun(U_229,bool),bool,finite_finite(U_229),hAPP(fun(U_228,bool),fun(U_229,bool),hAPP(fun(U_228,U_229),fun(fun(U_228,bool),fun(U_229,bool)),image(U_228,U_229),U_227),U_226)))
      | hBOOL(hAPP(fun(U_228,bool),bool,finite_finite(U_228),U_226)) ),
    inference(variable_rename,[status(thm)],[f_120_1]) ).

fof(f_120_3,plain,
    ! [U_229,U_228,U_227,U_226] :
      ( ( ~ hBOOL(hAPP(fun(U_228,bool),bool,finite_finite(U_228),hAPP(fun(U_228,bool),fun(U_228,bool),collect(U_228),hAPP(fun(U_228,bool),fun(U_228,bool),hAPP(fun(U_228,fun(bool,bool)),fun(fun(U_228,bool),fun(U_228,bool)),combs(U_228,bool,bool),hAPP(fun(U_228,bool),fun(U_228,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_228,bool),fun(U_228,fun(bool,bool))),combb(bool,fun(bool,bool),U_228),fconj),hAPP(fun(U_228,bool),fun(U_228,bool),hAPP(fun(U_228,fun(fun(U_228,bool),bool)),fun(fun(U_228,bool),fun(U_228,bool)),combc(U_228,fun(U_228,bool),bool),member(U_228)),U_226))),hAPP(U_229,fun(U_228,bool),hAPP(fun(U_228,fun(U_229,bool)),fun(U_229,fun(U_228,bool)),combc(U_228,U_229,bool),hAPP(fun(U_228,U_229),fun(U_228,fun(U_229,bool)),hAPP(fun(U_229,fun(U_229,bool)),fun(fun(U_228,U_229),fun(U_228,fun(U_229,bool))),combb(U_229,fun(U_229,bool),U_228),fequal(U_229)),U_227)),hAPP(U_228,U_229,U_227,sK3(U_229,U_228,U_227,U_226)))))))
        & hBOOL(hAPP(fun(U_228,bool),bool,hAPP(U_228,fun(fun(U_228,bool),bool),member(U_228),sK3(U_229,U_228,U_227,U_226)),U_226)) )
      | ~ hBOOL(hAPP(fun(U_229,bool),bool,finite_finite(U_229),hAPP(fun(U_228,bool),fun(U_229,bool),hAPP(fun(U_228,U_229),fun(fun(U_228,bool),fun(U_229,bool)),image(U_228,U_229),U_227),U_226)))
      | hBOOL(hAPP(fun(U_228,bool),bool,finite_finite(U_228),U_226)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_225,sK3(U_229,U_228,U_227,U_226))],[f_120_2]) ).

fof(f_120_4,plain,
    ( ! [U_228,U_226,U_227,U_229] :
        ( ~ hBOOL(hAPP(fun(U_228,bool),bool,finite_finite(U_228),hAPP(fun(U_228,bool),fun(U_228,bool),collect(U_228),hAPP(fun(U_228,bool),fun(U_228,bool),hAPP(fun(U_228,fun(bool,bool)),fun(fun(U_228,bool),fun(U_228,bool)),combs(U_228,bool,bool),hAPP(fun(U_228,bool),fun(U_228,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_228,bool),fun(U_228,fun(bool,bool))),combb(bool,fun(bool,bool),U_228),fconj),hAPP(fun(U_228,bool),fun(U_228,bool),hAPP(fun(U_228,fun(fun(U_228,bool),bool)),fun(fun(U_228,bool),fun(U_228,bool)),combc(U_228,fun(U_228,bool),bool),member(U_228)),U_226))),hAPP(U_229,fun(U_228,bool),hAPP(fun(U_228,fun(U_229,bool)),fun(U_229,fun(U_228,bool)),combc(U_228,U_229,bool),hAPP(fun(U_228,U_229),fun(U_228,fun(U_229,bool)),hAPP(fun(U_229,fun(U_229,bool)),fun(fun(U_228,U_229),fun(U_228,fun(U_229,bool))),combb(U_229,fun(U_229,bool),U_228),fequal(U_229)),U_227)),hAPP(U_228,U_229,U_227,sK3(U_229,U_228,U_227,U_226)))))))
        | ~ sP7(U_228,U_226,U_227,U_229) )
    & ! [U_228,U_226,U_227,U_229] :
        ( hBOOL(hAPP(fun(U_228,bool),bool,hAPP(U_228,fun(fun(U_228,bool),bool),member(U_228),sK3(U_229,U_228,U_227,U_226)),U_226))
        | ~ sP7(U_228,U_226,U_227,U_229) )
    & ! [U_228,U_226,U_227,U_229] :
        ( sP7(U_228,U_226,U_227,U_229)
        | ~ hBOOL(hAPP(fun(U_229,bool),bool,finite_finite(U_229),hAPP(fun(U_228,bool),fun(U_229,bool),hAPP(fun(U_228,U_229),fun(fun(U_228,bool),fun(U_229,bool)),image(U_228,U_229),U_227),U_226)))
        | hBOOL(hAPP(fun(U_228,bool),bool,finite_finite(U_228),U_226)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP7])],[f_120_3]) ).

cnf(f_120_5,plain,
    ( sP7(U_228,U_226,U_227,U_229)
    | ~ hBOOL(hAPP(fun(U_229,bool),bool,finite_finite(U_229),hAPP(fun(U_228,bool),fun(U_229,bool),hAPP(fun(U_228,U_229),fun(fun(U_228,bool),fun(U_229,bool)),image(U_228,U_229),U_227),U_226)))
    | hBOOL(hAPP(fun(U_228,bool),bool,finite_finite(U_228),U_226)) ),
    inference(clausify,[status(thm)],[f_120_4]) ).

cnf(f_120_6,plain,
    ( hBOOL(hAPP(fun(U_228,bool),bool,hAPP(U_228,fun(fun(U_228,bool),bool),member(U_228),sK3(U_229,U_228,U_227,U_226)),U_226))
    | ~ sP7(U_228,U_226,U_227,U_229) ),
    inference(clausify,[status(thm)],[f_120_4]) ).

cnf(f_120_7,plain,
    ( ~ hBOOL(hAPP(fun(U_228,bool),bool,finite_finite(U_228),hAPP(fun(U_228,bool),fun(U_228,bool),collect(U_228),hAPP(fun(U_228,bool),fun(U_228,bool),hAPP(fun(U_228,fun(bool,bool)),fun(fun(U_228,bool),fun(U_228,bool)),combs(U_228,bool,bool),hAPP(fun(U_228,bool),fun(U_228,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_228,bool),fun(U_228,fun(bool,bool))),combb(bool,fun(bool,bool),U_228),fconj),hAPP(fun(U_228,bool),fun(U_228,bool),hAPP(fun(U_228,fun(fun(U_228,bool),bool)),fun(fun(U_228,bool),fun(U_228,bool)),combc(U_228,fun(U_228,bool),bool),member(U_228)),U_226))),hAPP(U_229,fun(U_228,bool),hAPP(fun(U_228,fun(U_229,bool)),fun(U_229,fun(U_228,bool)),combc(U_228,U_229,bool),hAPP(fun(U_228,U_229),fun(U_228,fun(U_229,bool)),hAPP(fun(U_229,fun(U_229,bool)),fun(fun(U_228,U_229),fun(U_228,fun(U_229,bool))),combb(U_229,fun(U_229,bool),U_228),fequal(U_229)),U_227)),hAPP(U_228,U_229,U_227,sK3(U_229,U_228,U_227,U_226)))))))
    | ~ sP7(U_228,U_226,U_227,U_229) ),
    inference(clausify,[status(thm)],[f_120_4]) ).

fof(f_121_1,plain,
    ! [X_b,X_c,A_3,B_3,F,X_1] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_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)))
      | ~ 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_3) != hAPP(X_c,X_b,F,X_1) ),
    inference(fof_nnf,[status(thm)],[fact_50_image__eqI]) ).

fof(f_121_2,plain,
    ! [U_235,U_234,U_233,U_232,U_231,U_230] :
      ( hBOOL(hAPP(fun(U_235,bool),bool,hAPP(U_235,fun(fun(U_235,bool),bool),member(U_235),U_232),hAPP(fun(U_234,bool),fun(U_235,bool),hAPP(fun(U_234,U_235),fun(fun(U_234,bool),fun(U_235,bool)),image(U_234,U_235),U_231),U_233)))
      | ~ hBOOL(hAPP(fun(U_234,bool),bool,hAPP(U_234,fun(fun(U_234,bool),bool),member(U_234),U_230),U_233))
      | ti(U_235,U_232) != hAPP(U_234,U_235,U_231,U_230) ),
    inference(variable_rename,[status(thm)],[f_121_1]) ).

fof(f_121_3,plain,
    ! [U_235,U_232,U_230,U_231,U_234,U_233] :
      ( hBOOL(hAPP(fun(U_235,bool),bool,hAPP(U_235,fun(fun(U_235,bool),bool),member(U_235),U_232),hAPP(fun(U_234,bool),fun(U_235,bool),hAPP(fun(U_234,U_235),fun(fun(U_234,bool),fun(U_235,bool)),image(U_234,U_235),U_231),U_233)))
      | ~ hBOOL(hAPP(fun(U_234,bool),bool,hAPP(U_234,fun(fun(U_234,bool),bool),member(U_234),U_230),U_233))
      | ti(U_235,U_232) != hAPP(U_234,U_235,U_231,U_230) ),
    inference(definitional_conversion,[status(esa)],[f_121_2]) ).

cnf(f_121_4,plain,
    ( hBOOL(hAPP(fun(U_235,bool),bool,hAPP(U_235,fun(fun(U_235,bool),bool),member(U_235),U_232),hAPP(fun(U_234,bool),fun(U_235,bool),hAPP(fun(U_234,U_235),fun(fun(U_234,bool),fun(U_235,bool)),image(U_234,U_235),U_231),U_233)))
    | ~ hBOOL(hAPP(fun(U_234,bool),bool,hAPP(U_234,fun(fun(U_234,bool),bool),member(U_234),U_230),U_233))
    | ti(U_235,U_232) != hAPP(U_234,U_235,U_231,U_230) ),
    inference(clausify,[status(thm)],[f_121_3]) ).

fof(f_122_1,plain,
    ! [X_b,A_3,B_1] :
      ( ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_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)),B_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_1)) ),
    inference(fof_nnf,[status(thm)],[fact_51_equalityI]) ).

fof(f_122_2,plain,
    ! [U_238,U_237,U_236] :
      ( ti(fun(U_238,bool),U_237) = ti(fun(U_238,bool),U_236)
      | ~ hBOOL(hAPP(fun(U_238,bool),bool,hAPP(fun(U_238,bool),fun(fun(U_238,bool),bool),ord_less_eq(fun(U_238,bool)),U_236),U_237))
      | ~ hBOOL(hAPP(fun(U_238,bool),bool,hAPP(fun(U_238,bool),fun(fun(U_238,bool),bool),ord_less_eq(fun(U_238,bool)),U_237),U_236)) ),
    inference(variable_rename,[status(thm)],[f_122_1]) ).

fof(f_122_3,plain,
    ! [U_237,U_238,U_236] :
      ( ti(fun(U_238,bool),U_237) = ti(fun(U_238,bool),U_236)
      | ~ hBOOL(hAPP(fun(U_238,bool),bool,hAPP(fun(U_238,bool),fun(fun(U_238,bool),bool),ord_less_eq(fun(U_238,bool)),U_236),U_237))
      | ~ hBOOL(hAPP(fun(U_238,bool),bool,hAPP(fun(U_238,bool),fun(fun(U_238,bool),bool),ord_less_eq(fun(U_238,bool)),U_237),U_236)) ),
    inference(definitional_conversion,[status(esa)],[f_122_2]) ).

cnf(f_122_4,plain,
    ( ti(fun(U_238,bool),U_237) = ti(fun(U_238,bool),U_236)
    | ~ hBOOL(hAPP(fun(U_238,bool),bool,hAPP(fun(U_238,bool),fun(fun(U_238,bool),bool),ord_less_eq(fun(U_238,bool)),U_236),U_237))
    | ~ hBOOL(hAPP(fun(U_238,bool),bool,hAPP(fun(U_238,bool),fun(fun(U_238,bool),bool),ord_less_eq(fun(U_238,bool)),U_237),U_236)) ),
    inference(clausify,[status(thm)],[f_122_3]) ).

fof(f_123_1,plain,
    ! [X_b,C_1,A_3,B_1] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_1))
      | ~ 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_1)) ),
    inference(fof_nnf,[status(thm)],[fact_52_subsetD]) ).

fof(f_123_2,plain,
    ! [U_242,U_241,U_240,U_239] :
      ( hBOOL(hAPP(fun(U_242,bool),bool,hAPP(U_242,fun(fun(U_242,bool),bool),member(U_242),U_241),U_239))
      | ~ hBOOL(hAPP(fun(U_242,bool),bool,hAPP(U_242,fun(fun(U_242,bool),bool),member(U_242),U_241),U_240))
      | ~ hBOOL(hAPP(fun(U_242,bool),bool,hAPP(fun(U_242,bool),fun(fun(U_242,bool),bool),ord_less_eq(fun(U_242,bool)),U_240),U_239)) ),
    inference(variable_rename,[status(thm)],[f_123_1]) ).

fof(f_123_3,plain,
    ! [U_242,U_240,U_239,U_241] :
      ( hBOOL(hAPP(fun(U_242,bool),bool,hAPP(U_242,fun(fun(U_242,bool),bool),member(U_242),U_241),U_239))
      | ~ hBOOL(hAPP(fun(U_242,bool),bool,hAPP(U_242,fun(fun(U_242,bool),bool),member(U_242),U_241),U_240))
      | ~ hBOOL(hAPP(fun(U_242,bool),bool,hAPP(fun(U_242,bool),fun(fun(U_242,bool),bool),ord_less_eq(fun(U_242,bool)),U_240),U_239)) ),
    inference(definitional_conversion,[status(esa)],[f_123_2]) ).

cnf(f_123_4,plain,
    ( hBOOL(hAPP(fun(U_242,bool),bool,hAPP(U_242,fun(fun(U_242,bool),bool),member(U_242),U_241),U_239))
    | ~ hBOOL(hAPP(fun(U_242,bool),bool,hAPP(U_242,fun(fun(U_242,bool),bool),member(U_242),U_241),U_240))
    | ~ hBOOL(hAPP(fun(U_242,bool),bool,hAPP(fun(U_242,bool),fun(fun(U_242,bool),bool),ord_less_eq(fun(U_242,bool)),U_240),U_239)) ),
    inference(clausify,[status(thm)],[f_123_3]) ).

fof(f_124_1,plain,
    ! [X_b,B_3,A_2,B_1] :
      ( 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_3),B_1)))
      | ( ti(X_b,A_2) != ti(X_b,B_3)
        & ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),B_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_53_insertCI]) ).

fof(f_124_2,plain,
    ! [U_246,U_245,U_244,U_243] :
      ( hBOOL(hAPP(fun(U_246,bool),bool,hAPP(U_246,fun(fun(U_246,bool),bool),member(U_246),U_244),hAPP(fun(U_246,bool),fun(U_246,bool),hAPP(U_246,fun(fun(U_246,bool),fun(U_246,bool)),insert(U_246),U_245),U_243)))
      | ( ti(U_246,U_244) != ti(U_246,U_245)
        & ~ hBOOL(hAPP(fun(U_246,bool),bool,hAPP(U_246,fun(fun(U_246,bool),bool),member(U_246),U_244),U_243)) ) ),
    inference(variable_rename,[status(thm)],[f_124_1]) ).

fof(f_124_3,plain,
    ( ! [U_244,U_243,U_245,U_246] :
        ( ti(U_246,U_244) != ti(U_246,U_245)
        | ~ sP8(U_244,U_243,U_245,U_246) )
    & ! [U_244,U_243,U_245,U_246] :
        ( ~ hBOOL(hAPP(fun(U_246,bool),bool,hAPP(U_246,fun(fun(U_246,bool),bool),member(U_246),U_244),U_243))
        | ~ sP8(U_244,U_243,U_245,U_246) )
    & ! [U_244,U_243,U_245,U_246] :
        ( hBOOL(hAPP(fun(U_246,bool),bool,hAPP(U_246,fun(fun(U_246,bool),bool),member(U_246),U_244),hAPP(fun(U_246,bool),fun(U_246,bool),hAPP(U_246,fun(fun(U_246,bool),fun(U_246,bool)),insert(U_246),U_245),U_243)))
        | sP8(U_244,U_243,U_245,U_246) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP8])],[f_124_2]) ).

cnf(f_124_4,plain,
    ( hBOOL(hAPP(fun(U_246,bool),bool,hAPP(U_246,fun(fun(U_246,bool),bool),member(U_246),U_244),hAPP(fun(U_246,bool),fun(U_246,bool),hAPP(U_246,fun(fun(U_246,bool),fun(U_246,bool)),insert(U_246),U_245),U_243)))
    | sP8(U_244,U_243,U_245,U_246) ),
    inference(clausify,[status(thm)],[f_124_3]) ).

cnf(f_124_5,plain,
    ( ~ hBOOL(hAPP(fun(U_246,bool),bool,hAPP(U_246,fun(fun(U_246,bool),bool),member(U_246),U_244),U_243))
    | ~ sP8(U_244,U_243,U_245,U_246) ),
    inference(clausify,[status(thm)],[f_124_3]) ).

cnf(f_124_6,plain,
    ( ti(U_246,U_244) != ti(U_246,U_245)
    | ~ sP8(U_244,U_243,U_245,U_246) ),
    inference(clausify,[status(thm)],[f_124_3]) ).

fof(f_125_1,plain,
    ! [X_b,A_2,B_3,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_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_3),A_3))) ),
    inference(fof_nnf,[status(thm)],[fact_54_insertE]) ).

fof(f_125_2,plain,
    ! [U_250,U_249,U_248,U_247] :
      ( hBOOL(hAPP(fun(U_250,bool),bool,hAPP(U_250,fun(fun(U_250,bool),bool),member(U_250),U_249),U_247))
      | ti(U_250,U_249) = ti(U_250,U_248)
      | ~ hBOOL(hAPP(fun(U_250,bool),bool,hAPP(U_250,fun(fun(U_250,bool),bool),member(U_250),U_249),hAPP(fun(U_250,bool),fun(U_250,bool),hAPP(U_250,fun(fun(U_250,bool),fun(U_250,bool)),insert(U_250),U_248),U_247))) ),
    inference(variable_rename,[status(thm)],[f_125_1]) ).

fof(f_125_3,plain,
    ! [U_249,U_248,U_247,U_250] :
      ( hBOOL(hAPP(fun(U_250,bool),bool,hAPP(U_250,fun(fun(U_250,bool),bool),member(U_250),U_249),U_247))
      | ti(U_250,U_249) = ti(U_250,U_248)
      | ~ hBOOL(hAPP(fun(U_250,bool),bool,hAPP(U_250,fun(fun(U_250,bool),bool),member(U_250),U_249),hAPP(fun(U_250,bool),fun(U_250,bool),hAPP(U_250,fun(fun(U_250,bool),fun(U_250,bool)),insert(U_250),U_248),U_247))) ),
    inference(definitional_conversion,[status(esa)],[f_125_2]) ).

cnf(f_125_4,plain,
    ( hBOOL(hAPP(fun(U_250,bool),bool,hAPP(U_250,fun(fun(U_250,bool),bool),member(U_250),U_249),U_247))
    | ti(U_250,U_249) = ti(U_250,U_248)
    | ~ hBOOL(hAPP(fun(U_250,bool),bool,hAPP(U_250,fun(fun(U_250,bool),bool),member(U_250),U_249),hAPP(fun(U_250,bool),fun(U_250,bool),hAPP(U_250,fun(fun(U_250,bool),fun(U_250,bool)),insert(U_250),U_248),U_247))) ),
    inference(clausify,[status(thm)],[f_125_3]) ).

fof(f_126_1,plain,
    ! [I_1,Pa,K] :
      ( hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),K),I_1)))
      | ? [N_1] :
          ( ~ hBOOL(hAPP(nat,bool,Pa,N_1))
          & hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,N_1))) )
      | ~ hBOOL(hAPP(nat,bool,Pa,K)) ),
    inference(fof_nnf,[status(thm)],[fact_55_zero__induct__lemma]) ).

fof(f_126_2,plain,
    ! [U_254,U_253,U_252] :
      ( hBOOL(hAPP(nat,bool,U_253,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_252),U_254)))
      | ? [U_251] :
          ( ~ hBOOL(hAPP(nat,bool,U_253,U_251))
          & hBOOL(hAPP(nat,bool,U_253,hAPP(nat,nat,suc,U_251))) )
      | ~ hBOOL(hAPP(nat,bool,U_253,U_252)) ),
    inference(variable_rename,[status(thm)],[f_126_1]) ).

fof(f_126_3,plain,
    ! [U_254,U_253,U_252] :
      ( hBOOL(hAPP(nat,bool,U_253,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_252),U_254)))
      | ( ~ hBOOL(hAPP(nat,bool,U_253,sK4(U_254,U_253,U_252)))
        & hBOOL(hAPP(nat,bool,U_253,hAPP(nat,nat,suc,sK4(U_254,U_253,U_252)))) )
      | ~ hBOOL(hAPP(nat,bool,U_253,U_252)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_251,sK4(U_254,U_253,U_252))],[f_126_2]) ).

fof(f_126_4,plain,
    ( ! [U_252,U_253,U_254] :
        ( ~ hBOOL(hAPP(nat,bool,U_253,sK4(U_254,U_253,U_252)))
        | ~ sP9(U_252,U_253,U_254) )
    & ! [U_252,U_253,U_254] :
        ( hBOOL(hAPP(nat,bool,U_253,hAPP(nat,nat,suc,sK4(U_254,U_253,U_252))))
        | ~ sP9(U_252,U_253,U_254) )
    & ! [U_252,U_253,U_254] :
        ( hBOOL(hAPP(nat,bool,U_253,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_252),U_254)))
        | sP9(U_252,U_253,U_254)
        | ~ hBOOL(hAPP(nat,bool,U_253,U_252)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP9])],[f_126_3]) ).

cnf(f_126_5,plain,
    ( hBOOL(hAPP(nat,bool,U_253,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_252),U_254)))
    | sP9(U_252,U_253,U_254)
    | ~ hBOOL(hAPP(nat,bool,U_253,U_252)) ),
    inference(clausify,[status(thm)],[f_126_4]) ).

cnf(f_126_6,plain,
    ( hBOOL(hAPP(nat,bool,U_253,hAPP(nat,nat,suc,sK4(U_254,U_253,U_252))))
    | ~ sP9(U_252,U_253,U_254) ),
    inference(clausify,[status(thm)],[f_126_4]) ).

cnf(f_126_7,plain,
    ( ~ hBOOL(hAPP(nat,bool,U_253,sK4(U_254,U_253,U_252)))
    | ~ sP9(U_252,U_253,U_254) ),
    inference(clausify,[status(thm)],[f_126_4]) ).

fof(f_127_1,plain,
    ! [N,M_4] :
      ( ? [M_2] : M_4 = 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_4)) ),
    inference(fof_nnf,[status(thm)],[fact_56_Suc__le__D]) ).

fof(f_127_2,plain,
    ! [U_257,U_256] :
      ( ? [U_255] : U_256 = hAPP(nat,nat,suc,U_255)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_257)),U_256)) ),
    inference(variable_rename,[status(thm)],[f_127_1]) ).

fof(f_127_3,plain,
    ! [U_257,U_256] :
      ( U_256 = hAPP(nat,nat,suc,sK5(U_257,U_256))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_257)),U_256)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_255,sK5(U_257,U_256))],[f_127_2]) ).

fof(f_127_4,plain,
    ! [U_257,U_256] :
      ( U_256 = hAPP(nat,nat,suc,sK5(U_257,U_256))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_257)),U_256)) ),
    inference(definitional_conversion,[status(esa)],[f_127_3]) ).

cnf(f_127_5,plain,
    ( U_256 = hAPP(nat,nat,suc,sK5(U_257,U_256))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_257)),U_256)) ),
    inference(clausify,[status(thm)],[f_127_4]) ).

fof(f_128_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_57_order__refl]) ).

fof(f_128_2,plain,
    ! [U_259] :
      ( ! [U_258] : hBOOL(hAPP(U_259,bool,hAPP(U_259,fun(U_259,bool),ord_less_eq(U_259),U_258),U_258))
      | ~ preorder(U_259) ),
    inference(variable_rename,[status(thm)],[f_128_1]) ).

fof(f_128_3,plain,
    ! [U_259,U_258] :
      ( hBOOL(hAPP(U_259,bool,hAPP(U_259,fun(U_259,bool),ord_less_eq(U_259),U_258),U_258))
      | ~ preorder(U_259) ),
    inference(definitional_conversion,[status(esa)],[f_128_2]) ).

cnf(f_128_4,plain,
    ( hBOOL(hAPP(U_259,bool,hAPP(U_259,fun(U_259,bool),ord_less_eq(U_259),U_258),U_258))
    | ~ preorder(U_259) ),
    inference(clausify,[status(thm)],[f_128_3]) ).

fof(f_129_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_58_linorder__linear]) ).

fof(f_129_2,plain,
    ! [U_262] :
      ( ! [U_261,U_260] :
          ( hBOOL(hAPP(U_262,bool,hAPP(U_262,fun(U_262,bool),ord_less_eq(U_262),U_260),U_261))
          | hBOOL(hAPP(U_262,bool,hAPP(U_262,fun(U_262,bool),ord_less_eq(U_262),U_261),U_260)) )
      | ~ linorder(U_262) ),
    inference(variable_rename,[status(thm)],[f_129_1]) ).

fof(f_129_3,plain,
    ! [U_262,U_261,U_260] :
      ( hBOOL(hAPP(U_262,bool,hAPP(U_262,fun(U_262,bool),ord_less_eq(U_262),U_260),U_261))
      | hBOOL(hAPP(U_262,bool,hAPP(U_262,fun(U_262,bool),ord_less_eq(U_262),U_261),U_260))
      | ~ linorder(U_262) ),
    inference(definitional_conversion,[status(esa)],[f_129_2]) ).

cnf(f_129_4,plain,
    ( hBOOL(hAPP(U_262,bool,hAPP(U_262,fun(U_262,bool),ord_less_eq(U_262),U_260),U_261))
    | hBOOL(hAPP(U_262,bool,hAPP(U_262,fun(U_262,bool),ord_less_eq(U_262),U_261),U_260))
    | ~ linorder(U_262) ),
    inference(clausify,[status(thm)],[f_129_3]) ).

fof(f_130_1,plain,
    ! [X_b] :
      ( ! [X_1,Y_2] :
          ( ( ti(X_b,X_1) = ti(X_b,Y_2)
            | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_2),X_1))
            | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2)) )
          & ( ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_2),X_1))
              & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2)) )
            | ti(X_b,X_1) != ti(X_b,Y_2) ) )
      | ~ order(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_59_order__eq__iff]) ).

fof(f_130_2,plain,
    ! [U_265] :
      ( ! [U_264,U_263] :
          ( ( ti(U_265,U_264) = ti(U_265,U_263)
            | ~ hBOOL(hAPP(U_265,bool,hAPP(U_265,fun(U_265,bool),ord_less_eq(U_265),U_263),U_264))
            | ~ hBOOL(hAPP(U_265,bool,hAPP(U_265,fun(U_265,bool),ord_less_eq(U_265),U_264),U_263)) )
          & ( ( hBOOL(hAPP(U_265,bool,hAPP(U_265,fun(U_265,bool),ord_less_eq(U_265),U_263),U_264))
              & hBOOL(hAPP(U_265,bool,hAPP(U_265,fun(U_265,bool),ord_less_eq(U_265),U_264),U_263)) )
            | ti(U_265,U_264) != ti(U_265,U_263) ) )
      | ~ order(U_265) ),
    inference(variable_rename,[status(thm)],[f_130_1]) ).

fof(f_130_3,plain,
    ! [U_265] :
      ( ( ! [U_269,U_267] :
            ( ti(U_265,U_269) = ti(U_265,U_267)
            | ~ hBOOL(hAPP(U_265,bool,hAPP(U_265,fun(U_265,bool),ord_less_eq(U_265),U_267),U_269))
            | ~ hBOOL(hAPP(U_265,bool,hAPP(U_265,fun(U_265,bool),ord_less_eq(U_265),U_269),U_267)) )
        & ! [U_268,U_266] :
            ( ( hBOOL(hAPP(U_265,bool,hAPP(U_265,fun(U_265,bool),ord_less_eq(U_265),U_266),U_268))
              & hBOOL(hAPP(U_265,bool,hAPP(U_265,fun(U_265,bool),ord_less_eq(U_265),U_268),U_266)) )
            | ti(U_265,U_268) != ti(U_265,U_266) ) )
      | ~ order(U_265) ),
    inference(miniscope,[status(thm)],[f_130_2]) ).

fof(f_130_4,plain,
    ( ! [U_265,U_268,U_266] :
        ( hBOOL(hAPP(U_265,bool,hAPP(U_265,fun(U_265,bool),ord_less_eq(U_265),U_266),U_268))
        | ~ sP10(U_265,U_268,U_266) )
    & ! [U_265,U_268,U_266] :
        ( hBOOL(hAPP(U_265,bool,hAPP(U_265,fun(U_265,bool),ord_less_eq(U_265),U_268),U_266))
        | ~ sP10(U_265,U_268,U_266) )
    & ! [U_265,U_268,U_266,U_267,U_269] :
        ( ti(U_265,U_269) = ti(U_265,U_267)
        | ~ hBOOL(hAPP(U_265,bool,hAPP(U_265,fun(U_265,bool),ord_less_eq(U_265),U_267),U_269))
        | ~ hBOOL(hAPP(U_265,bool,hAPP(U_265,fun(U_265,bool),ord_less_eq(U_265),U_269),U_267))
        | ~ sP11(U_265,U_268,U_266,U_267,U_269) )
    & ! [U_265,U_268,U_266,U_267,U_269] :
        ( sP10(U_265,U_268,U_266)
        | ti(U_265,U_268) != ti(U_265,U_266)
        | ~ sP11(U_265,U_268,U_266,U_267,U_269) )
    & ! [U_265,U_268,U_266,U_267,U_269] :
        ( sP11(U_265,U_268,U_266,U_267,U_269)
        | ~ order(U_265) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP10,sP11])],[f_130_3]) ).

cnf(f_130_5,plain,
    ( sP11(U_265,U_268,U_266,U_267,U_269)
    | ~ order(U_265) ),
    inference(clausify,[status(thm)],[f_130_4]) ).

cnf(f_130_6,plain,
    ( sP10(U_265,U_268,U_266)
    | ti(U_265,U_268) != ti(U_265,U_266)
    | ~ sP11(U_265,U_268,U_266,U_267,U_269) ),
    inference(clausify,[status(thm)],[f_130_4]) ).

cnf(f_130_7,plain,
    ( ti(U_265,U_269) = ti(U_265,U_267)
    | ~ hBOOL(hAPP(U_265,bool,hAPP(U_265,fun(U_265,bool),ord_less_eq(U_265),U_267),U_269))
    | ~ hBOOL(hAPP(U_265,bool,hAPP(U_265,fun(U_265,bool),ord_less_eq(U_265),U_269),U_267))
    | ~ sP11(U_265,U_268,U_266,U_267,U_269) ),
    inference(clausify,[status(thm)],[f_130_4]) ).

cnf(f_130_8,plain,
    ( hBOOL(hAPP(U_265,bool,hAPP(U_265,fun(U_265,bool),ord_less_eq(U_265),U_268),U_266))
    | ~ sP10(U_265,U_268,U_266) ),
    inference(clausify,[status(thm)],[f_130_4]) ).

cnf(f_130_9,plain,
    ( hBOOL(hAPP(U_265,bool,hAPP(U_265,fun(U_265,bool),ord_less_eq(U_265),U_266),U_268))
    | ~ sP10(U_265,U_268,U_266) ),
    inference(clausify,[status(thm)],[f_130_4]) ).

fof(f_131_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_60_order__eq__refl]) ).

fof(f_131_2,plain,
    ! [U_272] :
      ( ! [U_271,U_270] :
          ( hBOOL(hAPP(U_272,bool,hAPP(U_272,fun(U_272,bool),ord_less_eq(U_272),U_271),U_270))
          | U_271 != U_270 )
      | ~ preorder(U_272) ),
    inference(variable_rename,[status(thm)],[f_131_1]) ).

fof(f_131_3,plain,
    ! [U_271,U_270,U_272] :
      ( hBOOL(hAPP(U_272,bool,hAPP(U_272,fun(U_272,bool),ord_less_eq(U_272),U_271),U_270))
      | U_271 != U_270
      | ~ preorder(U_272) ),
    inference(definitional_conversion,[status(esa)],[f_131_2]) ).

cnf(f_131_4,plain,
    ( hBOOL(hAPP(U_272,bool,hAPP(U_272,fun(U_272,bool),ord_less_eq(U_272),U_271),U_270))
    | U_271 != U_270
    | ~ preorder(U_272) ),
    inference(clausify,[status(thm)],[f_131_3]) ).

fof(f_132_1,plain,
    ! [X_b] :
      ( ! [Y_2,X_1] :
          ( ( ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2))
              | ti(X_b,X_1) != ti(X_b,Y_2) )
            & ( ti(X_b,X_1) = ti(X_b,Y_2)
              | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2)) ) )
          | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_2),X_1)) )
      | ~ order(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_61_order__antisym__conv]) ).

fof(f_132_2,plain,
    ! [U_275] :
      ( ! [U_274,U_273] :
          ( ( ( hBOOL(hAPP(U_275,bool,hAPP(U_275,fun(U_275,bool),ord_less_eq(U_275),U_273),U_274))
              | ti(U_275,U_273) != ti(U_275,U_274) )
            & ( ti(U_275,U_273) = ti(U_275,U_274)
              | ~ hBOOL(hAPP(U_275,bool,hAPP(U_275,fun(U_275,bool),ord_less_eq(U_275),U_273),U_274)) ) )
          | ~ hBOOL(hAPP(U_275,bool,hAPP(U_275,fun(U_275,bool),ord_less_eq(U_275),U_274),U_273)) )
      | ~ order(U_275) ),
    inference(variable_rename,[status(thm)],[f_132_1]) ).

fof(f_132_3,plain,
    ( ! [U_273,U_274,U_275] :
        ( hBOOL(hAPP(U_275,bool,hAPP(U_275,fun(U_275,bool),ord_less_eq(U_275),U_273),U_274))
        | ti(U_275,U_273) != ti(U_275,U_274)
        | ~ sP12(U_273,U_274,U_275) )
    & ! [U_273,U_274,U_275] :
        ( ti(U_275,U_273) = ti(U_275,U_274)
        | ~ hBOOL(hAPP(U_275,bool,hAPP(U_275,fun(U_275,bool),ord_less_eq(U_275),U_273),U_274))
        | ~ sP12(U_273,U_274,U_275) )
    & ! [U_273,U_274,U_275] :
        ( sP12(U_273,U_274,U_275)
        | ~ hBOOL(hAPP(U_275,bool,hAPP(U_275,fun(U_275,bool),ord_less_eq(U_275),U_274),U_273))
        | ~ order(U_275) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP12])],[f_132_2]) ).

cnf(f_132_4,plain,
    ( sP12(U_273,U_274,U_275)
    | ~ hBOOL(hAPP(U_275,bool,hAPP(U_275,fun(U_275,bool),ord_less_eq(U_275),U_274),U_273))
    | ~ order(U_275) ),
    inference(clausify,[status(thm)],[f_132_3]) ).

cnf(f_132_5,plain,
    ( ti(U_275,U_273) = ti(U_275,U_274)
    | ~ hBOOL(hAPP(U_275,bool,hAPP(U_275,fun(U_275,bool),ord_less_eq(U_275),U_273),U_274))
    | ~ sP12(U_273,U_274,U_275) ),
    inference(clausify,[status(thm)],[f_132_3]) ).

cnf(f_132_6,plain,
    ( hBOOL(hAPP(U_275,bool,hAPP(U_275,fun(U_275,bool),ord_less_eq(U_275),U_273),U_274))
    | ti(U_275,U_273) != ti(U_275,U_274)
    | ~ sP12(U_273,U_274,U_275) ),
    inference(clausify,[status(thm)],[f_132_3]) ).

fof(f_133_1,plain,
    ! [X_a] :
      ( ! [C,A_1,B] :
          ( 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),C))
          | A_1 != B )
      | ~ ord(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_62_ord__eq__le__trans]) ).

fof(f_133_2,plain,
    ! [U_279] :
      ( ! [U_278,U_277,U_276] :
          ( hBOOL(hAPP(U_279,bool,hAPP(U_279,fun(U_279,bool),ord_less_eq(U_279),U_277),U_278))
          | ~ hBOOL(hAPP(U_279,bool,hAPP(U_279,fun(U_279,bool),ord_less_eq(U_279),U_276),U_278))
          | U_277 != U_276 )
      | ~ ord(U_279) ),
    inference(variable_rename,[status(thm)],[f_133_1]) ).

fof(f_133_3,plain,
    ! [U_277,U_276,U_278,U_279] :
      ( hBOOL(hAPP(U_279,bool,hAPP(U_279,fun(U_279,bool),ord_less_eq(U_279),U_277),U_278))
      | ~ hBOOL(hAPP(U_279,bool,hAPP(U_279,fun(U_279,bool),ord_less_eq(U_279),U_276),U_278))
      | U_277 != U_276
      | ~ ord(U_279) ),
    inference(definitional_conversion,[status(esa)],[f_133_2]) ).

cnf(f_133_4,plain,
    ( hBOOL(hAPP(U_279,bool,hAPP(U_279,fun(U_279,bool),ord_less_eq(U_279),U_277),U_278))
    | ~ hBOOL(hAPP(U_279,bool,hAPP(U_279,fun(U_279,bool),ord_less_eq(U_279),U_276),U_278))
    | U_277 != U_276
    | ~ ord(U_279) ),
    inference(clausify,[status(thm)],[f_133_3]) ).

fof(f_134_1,plain,
    ! [X_a] :
      ( ! [C,A_1,B] :
          ( 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))
          | ti(X_a,A_1) != ti(X_a,B) )
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_63_xt1_I3_J]) ).

fof(f_134_2,plain,
    ! [U_283] :
      ( ! [U_282,U_281,U_280] :
          ( hBOOL(hAPP(U_283,bool,hAPP(U_283,fun(U_283,bool),ord_less_eq(U_283),U_282),U_281))
          | ~ hBOOL(hAPP(U_283,bool,hAPP(U_283,fun(U_283,bool),ord_less_eq(U_283),U_282),U_280))
          | ti(U_283,U_281) != ti(U_283,U_280) )
      | ~ order(U_283) ),
    inference(variable_rename,[status(thm)],[f_134_1]) ).

fof(f_134_3,plain,
    ! [U_281,U_283,U_282,U_280] :
      ( hBOOL(hAPP(U_283,bool,hAPP(U_283,fun(U_283,bool),ord_less_eq(U_283),U_282),U_281))
      | ~ hBOOL(hAPP(U_283,bool,hAPP(U_283,fun(U_283,bool),ord_less_eq(U_283),U_282),U_280))
      | ti(U_283,U_281) != ti(U_283,U_280)
      | ~ order(U_283) ),
    inference(definitional_conversion,[status(esa)],[f_134_2]) ).

cnf(f_134_4,plain,
    ( hBOOL(hAPP(U_283,bool,hAPP(U_283,fun(U_283,bool),ord_less_eq(U_283),U_282),U_281))
    | ~ hBOOL(hAPP(U_283,bool,hAPP(U_283,fun(U_283,bool),ord_less_eq(U_283),U_282),U_280))
    | ti(U_283,U_281) != ti(U_283,U_280)
    | ~ order(U_283) ),
    inference(clausify,[status(thm)],[f_134_3]) ).

fof(f_135_1,plain,
    ! [X_a] :
      ( ! [C,A_1,B] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),C))
          | B != C
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) )
      | ~ ord(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_64_ord__le__eq__trans]) ).

fof(f_135_2,plain,
    ! [U_287] :
      ( ! [U_286,U_285,U_284] :
          ( hBOOL(hAPP(U_287,bool,hAPP(U_287,fun(U_287,bool),ord_less_eq(U_287),U_285),U_286))
          | U_284 != U_286
          | ~ hBOOL(hAPP(U_287,bool,hAPP(U_287,fun(U_287,bool),ord_less_eq(U_287),U_285),U_284)) )
      | ~ ord(U_287) ),
    inference(variable_rename,[status(thm)],[f_135_1]) ).

fof(f_135_3,plain,
    ! [U_286,U_285,U_284,U_287] :
      ( hBOOL(hAPP(U_287,bool,hAPP(U_287,fun(U_287,bool),ord_less_eq(U_287),U_285),U_286))
      | U_284 != U_286
      | ~ hBOOL(hAPP(U_287,bool,hAPP(U_287,fun(U_287,bool),ord_less_eq(U_287),U_285),U_284))
      | ~ ord(U_287) ),
    inference(definitional_conversion,[status(esa)],[f_135_2]) ).

cnf(f_135_4,plain,
    ( hBOOL(hAPP(U_287,bool,hAPP(U_287,fun(U_287,bool),ord_less_eq(U_287),U_285),U_286))
    | U_284 != U_286
    | ~ hBOOL(hAPP(U_287,bool,hAPP(U_287,fun(U_287,bool),ord_less_eq(U_287),U_285),U_284))
    | ~ ord(U_287) ),
    inference(clausify,[status(thm)],[f_135_3]) ).

fof(f_136_1,plain,
    ! [X_a] :
      ( ! [C,B,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) != ti(X_a,C)
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1)) )
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_65_xt1_I4_J]) ).

fof(f_136_2,plain,
    ! [U_291] :
      ( ! [U_290,U_289,U_288] :
          ( hBOOL(hAPP(U_291,bool,hAPP(U_291,fun(U_291,bool),ord_less_eq(U_291),U_290),U_288))
          | ti(U_291,U_289) != ti(U_291,U_290)
          | ~ hBOOL(hAPP(U_291,bool,hAPP(U_291,fun(U_291,bool),ord_less_eq(U_291),U_289),U_288)) )
      | ~ order(U_291) ),
    inference(variable_rename,[status(thm)],[f_136_1]) ).

fof(f_136_3,plain,
    ! [U_289,U_290,U_288,U_291] :
      ( hBOOL(hAPP(U_291,bool,hAPP(U_291,fun(U_291,bool),ord_less_eq(U_291),U_290),U_288))
      | ti(U_291,U_289) != ti(U_291,U_290)
      | ~ hBOOL(hAPP(U_291,bool,hAPP(U_291,fun(U_291,bool),ord_less_eq(U_291),U_289),U_288))
      | ~ order(U_291) ),
    inference(definitional_conversion,[status(esa)],[f_136_2]) ).

cnf(f_136_4,plain,
    ( hBOOL(hAPP(U_291,bool,hAPP(U_291,fun(U_291,bool),ord_less_eq(U_291),U_290),U_288))
    | ti(U_291,U_289) != ti(U_291,U_290)
    | ~ hBOOL(hAPP(U_291,bool,hAPP(U_291,fun(U_291,bool),ord_less_eq(U_291),U_289),U_288))
    | ~ order(U_291) ),
    inference(clausify,[status(thm)],[f_136_3]) ).

fof(f_137_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_66_order__antisym]) ).

fof(f_137_2,plain,
    ! [U_294] :
      ( ! [U_293,U_292] :
          ( ti(U_294,U_293) = ti(U_294,U_292)
          | ~ hBOOL(hAPP(U_294,bool,hAPP(U_294,fun(U_294,bool),ord_less_eq(U_294),U_292),U_293))
          | ~ hBOOL(hAPP(U_294,bool,hAPP(U_294,fun(U_294,bool),ord_less_eq(U_294),U_293),U_292)) )
      | ~ order(U_294) ),
    inference(variable_rename,[status(thm)],[f_137_1]) ).

fof(f_137_3,plain,
    ! [U_294,U_292,U_293] :
      ( ti(U_294,U_293) = ti(U_294,U_292)
      | ~ hBOOL(hAPP(U_294,bool,hAPP(U_294,fun(U_294,bool),ord_less_eq(U_294),U_292),U_293))
      | ~ hBOOL(hAPP(U_294,bool,hAPP(U_294,fun(U_294,bool),ord_less_eq(U_294),U_293),U_292))
      | ~ order(U_294) ),
    inference(definitional_conversion,[status(esa)],[f_137_2]) ).

cnf(f_137_4,plain,
    ( ti(U_294,U_293) = ti(U_294,U_292)
    | ~ hBOOL(hAPP(U_294,bool,hAPP(U_294,fun(U_294,bool),ord_less_eq(U_294),U_292),U_293))
    | ~ hBOOL(hAPP(U_294,bool,hAPP(U_294,fun(U_294,bool),ord_less_eq(U_294),U_293),U_292))
    | ~ order(U_294) ),
    inference(clausify,[status(thm)],[f_137_3]) ).

fof(f_138_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_67_order__trans]) ).

fof(f_138_2,plain,
    ! [U_298] :
      ( ! [U_297,U_296,U_295] :
          ( hBOOL(hAPP(U_298,bool,hAPP(U_298,fun(U_298,bool),ord_less_eq(U_298),U_296),U_297))
          | ~ hBOOL(hAPP(U_298,bool,hAPP(U_298,fun(U_298,bool),ord_less_eq(U_298),U_295),U_297))
          | ~ hBOOL(hAPP(U_298,bool,hAPP(U_298,fun(U_298,bool),ord_less_eq(U_298),U_296),U_295)) )
      | ~ preorder(U_298) ),
    inference(variable_rename,[status(thm)],[f_138_1]) ).

fof(f_138_3,plain,
    ! [U_296,U_297,U_295,U_298] :
      ( hBOOL(hAPP(U_298,bool,hAPP(U_298,fun(U_298,bool),ord_less_eq(U_298),U_296),U_297))
      | ~ hBOOL(hAPP(U_298,bool,hAPP(U_298,fun(U_298,bool),ord_less_eq(U_298),U_295),U_297))
      | ~ hBOOL(hAPP(U_298,bool,hAPP(U_298,fun(U_298,bool),ord_less_eq(U_298),U_296),U_295))
      | ~ preorder(U_298) ),
    inference(definitional_conversion,[status(esa)],[f_138_2]) ).

cnf(f_138_4,plain,
    ( hBOOL(hAPP(U_298,bool,hAPP(U_298,fun(U_298,bool),ord_less_eq(U_298),U_296),U_297))
    | ~ hBOOL(hAPP(U_298,bool,hAPP(U_298,fun(U_298,bool),ord_less_eq(U_298),U_295),U_297))
    | ~ hBOOL(hAPP(U_298,bool,hAPP(U_298,fun(U_298,bool),ord_less_eq(U_298),U_296),U_295))
    | ~ preorder(U_298) ),
    inference(clausify,[status(thm)],[f_138_3]) ).

fof(f_139_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_68_xt1_I5_J]) ).

fof(f_139_2,plain,
    ! [U_301] :
      ( ! [U_300,U_299] :
          ( ti(U_301,U_299) = ti(U_301,U_300)
          | ~ hBOOL(hAPP(U_301,bool,hAPP(U_301,fun(U_301,bool),ord_less_eq(U_301),U_299),U_300))
          | ~ hBOOL(hAPP(U_301,bool,hAPP(U_301,fun(U_301,bool),ord_less_eq(U_301),U_300),U_299)) )
      | ~ order(U_301) ),
    inference(variable_rename,[status(thm)],[f_139_1]) ).

fof(f_139_3,plain,
    ! [U_301,U_299,U_300] :
      ( ti(U_301,U_299) = ti(U_301,U_300)
      | ~ hBOOL(hAPP(U_301,bool,hAPP(U_301,fun(U_301,bool),ord_less_eq(U_301),U_299),U_300))
      | ~ hBOOL(hAPP(U_301,bool,hAPP(U_301,fun(U_301,bool),ord_less_eq(U_301),U_300),U_299))
      | ~ order(U_301) ),
    inference(definitional_conversion,[status(esa)],[f_139_2]) ).

cnf(f_139_4,plain,
    ( ti(U_301,U_299) = ti(U_301,U_300)
    | ~ hBOOL(hAPP(U_301,bool,hAPP(U_301,fun(U_301,bool),ord_less_eq(U_301),U_299),U_300))
    | ~ hBOOL(hAPP(U_301,bool,hAPP(U_301,fun(U_301,bool),ord_less_eq(U_301),U_300),U_299))
    | ~ order(U_301) ),
    inference(clausify,[status(thm)],[f_139_3]) ).

fof(f_140_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_69_xt1_I6_J]) ).

fof(f_140_2,plain,
    ! [U_305] :
      ( ! [U_304,U_303,U_302] :
          ( hBOOL(hAPP(U_305,bool,hAPP(U_305,fun(U_305,bool),ord_less_eq(U_305),U_304),U_302))
          | ~ hBOOL(hAPP(U_305,bool,hAPP(U_305,fun(U_305,bool),ord_less_eq(U_305),U_304),U_303))
          | ~ hBOOL(hAPP(U_305,bool,hAPP(U_305,fun(U_305,bool),ord_less_eq(U_305),U_303),U_302)) )
      | ~ order(U_305) ),
    inference(variable_rename,[status(thm)],[f_140_1]) ).

fof(f_140_3,plain,
    ! [U_304,U_303,U_305,U_302] :
      ( hBOOL(hAPP(U_305,bool,hAPP(U_305,fun(U_305,bool),ord_less_eq(U_305),U_304),U_302))
      | ~ hBOOL(hAPP(U_305,bool,hAPP(U_305,fun(U_305,bool),ord_less_eq(U_305),U_304),U_303))
      | ~ hBOOL(hAPP(U_305,bool,hAPP(U_305,fun(U_305,bool),ord_less_eq(U_305),U_303),U_302))
      | ~ order(U_305) ),
    inference(definitional_conversion,[status(esa)],[f_140_2]) ).

cnf(f_140_4,plain,
    ( hBOOL(hAPP(U_305,bool,hAPP(U_305,fun(U_305,bool),ord_less_eq(U_305),U_304),U_302))
    | ~ hBOOL(hAPP(U_305,bool,hAPP(U_305,fun(U_305,bool),ord_less_eq(U_305),U_304),U_303))
    | ~ hBOOL(hAPP(U_305,bool,hAPP(U_305,fun(U_305,bool),ord_less_eq(U_305),U_303),U_302))
    | ~ order(U_305) ),
    inference(clausify,[status(thm)],[f_140_3]) ).

fof(f_141_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_70_linorder__le__cases]) ).

fof(f_141_2,plain,
    ! [U_308] :
      ( ! [U_307,U_306] :
          ( hBOOL(hAPP(U_308,bool,hAPP(U_308,fun(U_308,bool),ord_less_eq(U_308),U_306),U_307))
          | hBOOL(hAPP(U_308,bool,hAPP(U_308,fun(U_308,bool),ord_less_eq(U_308),U_307),U_306)) )
      | ~ linorder(U_308) ),
    inference(variable_rename,[status(thm)],[f_141_1]) ).

fof(f_141_3,plain,
    ! [U_308,U_307,U_306] :
      ( hBOOL(hAPP(U_308,bool,hAPP(U_308,fun(U_308,bool),ord_less_eq(U_308),U_306),U_307))
      | hBOOL(hAPP(U_308,bool,hAPP(U_308,fun(U_308,bool),ord_less_eq(U_308),U_307),U_306))
      | ~ linorder(U_308) ),
    inference(definitional_conversion,[status(esa)],[f_141_2]) ).

cnf(f_141_4,plain,
    ( hBOOL(hAPP(U_308,bool,hAPP(U_308,fun(U_308,bool),ord_less_eq(U_308),U_306),U_307))
    | hBOOL(hAPP(U_308,bool,hAPP(U_308,fun(U_308,bool),ord_less_eq(U_308),U_307),U_306))
    | ~ linorder(U_308) ),
    inference(clausify,[status(thm)],[f_141_3]) ).

fof(f_142_1,plain,
    ! [X_b,A_2,B_1] : 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_1))),
    inference(fof_nnf,[status(thm)],[fact_71_insertI1]) ).

fof(f_142_2,plain,
    ! [U_311,U_310,U_309] : hBOOL(hAPP(fun(U_311,bool),bool,hAPP(U_311,fun(fun(U_311,bool),bool),member(U_311),U_310),hAPP(fun(U_311,bool),fun(U_311,bool),hAPP(U_311,fun(fun(U_311,bool),fun(U_311,bool)),insert(U_311),U_310),U_309))),
    inference(variable_rename,[status(thm)],[f_142_1]) ).

fof(f_142_3,plain,
    ! [U_309,U_310,U_311] : hBOOL(hAPP(fun(U_311,bool),bool,hAPP(U_311,fun(fun(U_311,bool),bool),member(U_311),U_310),hAPP(fun(U_311,bool),fun(U_311,bool),hAPP(U_311,fun(fun(U_311,bool),fun(U_311,bool)),insert(U_311),U_310),U_309))),
    inference(definitional_conversion,[status(esa)],[f_142_2]) ).

cnf(f_142_4,plain,
    hBOOL(hAPP(fun(U_311,bool),bool,hAPP(U_311,fun(fun(U_311,bool),bool),member(U_311),U_310),hAPP(fun(U_311,bool),fun(U_311,bool),hAPP(U_311,fun(fun(U_311,bool),fun(U_311,bool)),insert(U_311),U_310),U_309))),
    inference(clausify,[status(thm)],[f_142_3]) ).

fof(f_143_1,plain,
    ! [X_b,A_2,B_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),B_1) = 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_1))),
    inference(fof_nnf,[status(thm)],[fact_72_insert__compr]) ).

fof(f_143_2,plain,
    ! [U_314,U_313,U_312] : hAPP(fun(U_314,bool),fun(U_314,bool),hAPP(U_314,fun(fun(U_314,bool),fun(U_314,bool)),insert(U_314),U_313),U_312) = hAPP(fun(U_314,bool),fun(U_314,bool),collect(U_314),hAPP(fun(U_314,bool),fun(U_314,bool),hAPP(fun(U_314,fun(bool,bool)),fun(fun(U_314,bool),fun(U_314,bool)),combs(U_314,bool,bool),hAPP(fun(U_314,bool),fun(U_314,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_314,bool),fun(U_314,fun(bool,bool))),combb(bool,fun(bool,bool),U_314),fdisj),hAPP(U_314,fun(U_314,bool),hAPP(fun(U_314,fun(U_314,bool)),fun(U_314,fun(U_314,bool)),combc(U_314,U_314,bool),fequal(U_314)),U_313))),hAPP(fun(U_314,bool),fun(U_314,bool),hAPP(fun(U_314,fun(fun(U_314,bool),bool)),fun(fun(U_314,bool),fun(U_314,bool)),combc(U_314,fun(U_314,bool),bool),member(U_314)),U_312))),
    inference(variable_rename,[status(thm)],[f_143_1]) ).

fof(f_143_3,plain,
    ! [U_313,U_314,U_312] : hAPP(fun(U_314,bool),fun(U_314,bool),hAPP(U_314,fun(fun(U_314,bool),fun(U_314,bool)),insert(U_314),U_313),U_312) = hAPP(fun(U_314,bool),fun(U_314,bool),collect(U_314),hAPP(fun(U_314,bool),fun(U_314,bool),hAPP(fun(U_314,fun(bool,bool)),fun(fun(U_314,bool),fun(U_314,bool)),combs(U_314,bool,bool),hAPP(fun(U_314,bool),fun(U_314,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_314,bool),fun(U_314,fun(bool,bool))),combb(bool,fun(bool,bool),U_314),fdisj),hAPP(U_314,fun(U_314,bool),hAPP(fun(U_314,fun(U_314,bool)),fun(U_314,fun(U_314,bool)),combc(U_314,U_314,bool),fequal(U_314)),U_313))),hAPP(fun(U_314,bool),fun(U_314,bool),hAPP(fun(U_314,fun(fun(U_314,bool),bool)),fun(fun(U_314,bool),fun(U_314,bool)),combc(U_314,fun(U_314,bool),bool),member(U_314)),U_312))),
    inference(definitional_conversion,[status(esa)],[f_143_2]) ).

cnf(f_143_4,plain,
    hAPP(fun(U_314,bool),fun(U_314,bool),hAPP(U_314,fun(fun(U_314,bool),fun(U_314,bool)),insert(U_314),U_313),U_312) = hAPP(fun(U_314,bool),fun(U_314,bool),collect(U_314),hAPP(fun(U_314,bool),fun(U_314,bool),hAPP(fun(U_314,fun(bool,bool)),fun(fun(U_314,bool),fun(U_314,bool)),combs(U_314,bool,bool),hAPP(fun(U_314,bool),fun(U_314,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_314,bool),fun(U_314,fun(bool,bool))),combb(bool,fun(bool,bool),U_314),fdisj),hAPP(U_314,fun(U_314,bool),hAPP(fun(U_314,fun(U_314,bool)),fun(U_314,fun(U_314,bool)),combc(U_314,U_314,bool),fequal(U_314)),U_313))),hAPP(fun(U_314,bool),fun(U_314,bool),hAPP(fun(U_314,fun(fun(U_314,bool),bool)),fun(fun(U_314,bool),fun(U_314,bool)),combc(U_314,fun(U_314,bool),bool),member(U_314)),U_312))),
    inference(clausify,[status(thm)],[f_143_3]) ).

fof(f_144_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_73_insert__Collect]) ).

fof(f_144_2,plain,
    ! [U_317,U_316,U_315] : hAPP(fun(U_317,bool),fun(U_317,bool),hAPP(U_317,fun(fun(U_317,bool),fun(U_317,bool)),insert(U_317),U_316),hAPP(fun(U_317,bool),fun(U_317,bool),collect(U_317),U_315)) = hAPP(fun(U_317,bool),fun(U_317,bool),collect(U_317),hAPP(fun(U_317,bool),fun(U_317,bool),hAPP(fun(U_317,fun(bool,bool)),fun(fun(U_317,bool),fun(U_317,bool)),combs(U_317,bool,bool),hAPP(fun(U_317,bool),fun(U_317,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_317,bool),fun(U_317,fun(bool,bool))),combb(bool,fun(bool,bool),U_317),fimplies),hAPP(fun(U_317,bool),fun(U_317,bool),hAPP(fun(bool,bool),fun(fun(U_317,bool),fun(U_317,bool)),combb(bool,bool,U_317),fNot),hAPP(U_317,fun(U_317,bool),hAPP(fun(U_317,fun(U_317,bool)),fun(U_317,fun(U_317,bool)),combc(U_317,U_317,bool),fequal(U_317)),U_316)))),U_315)),
    inference(variable_rename,[status(thm)],[f_144_1]) ).

fof(f_144_3,plain,
    ! [U_315,U_317,U_316] : hAPP(fun(U_317,bool),fun(U_317,bool),hAPP(U_317,fun(fun(U_317,bool),fun(U_317,bool)),insert(U_317),U_316),hAPP(fun(U_317,bool),fun(U_317,bool),collect(U_317),U_315)) = hAPP(fun(U_317,bool),fun(U_317,bool),collect(U_317),hAPP(fun(U_317,bool),fun(U_317,bool),hAPP(fun(U_317,fun(bool,bool)),fun(fun(U_317,bool),fun(U_317,bool)),combs(U_317,bool,bool),hAPP(fun(U_317,bool),fun(U_317,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_317,bool),fun(U_317,fun(bool,bool))),combb(bool,fun(bool,bool),U_317),fimplies),hAPP(fun(U_317,bool),fun(U_317,bool),hAPP(fun(bool,bool),fun(fun(U_317,bool),fun(U_317,bool)),combb(bool,bool,U_317),fNot),hAPP(U_317,fun(U_317,bool),hAPP(fun(U_317,fun(U_317,bool)),fun(U_317,fun(U_317,bool)),combc(U_317,U_317,bool),fequal(U_317)),U_316)))),U_315)),
    inference(definitional_conversion,[status(esa)],[f_144_2]) ).

cnf(f_144_4,plain,
    hAPP(fun(U_317,bool),fun(U_317,bool),hAPP(U_317,fun(fun(U_317,bool),fun(U_317,bool)),insert(U_317),U_316),hAPP(fun(U_317,bool),fun(U_317,bool),collect(U_317),U_315)) = hAPP(fun(U_317,bool),fun(U_317,bool),collect(U_317),hAPP(fun(U_317,bool),fun(U_317,bool),hAPP(fun(U_317,fun(bool,bool)),fun(fun(U_317,bool),fun(U_317,bool)),combs(U_317,bool,bool),hAPP(fun(U_317,bool),fun(U_317,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_317,bool),fun(U_317,fun(bool,bool))),combb(bool,fun(bool,bool),U_317),fimplies),hAPP(fun(U_317,bool),fun(U_317,bool),hAPP(fun(bool,bool),fun(fun(U_317,bool),fun(U_317,bool)),combb(bool,bool,U_317),fNot),hAPP(U_317,fun(U_317,bool),hAPP(fun(U_317,fun(U_317,bool)),fun(U_317,fun(U_317,bool)),combc(U_317,U_317,bool),fequal(U_317)),U_316)))),U_315)),
    inference(clausify,[status(thm)],[f_144_3]) ).

fof(f_145_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_145_2,plain,
    ! [U_322,U_321,U_320,U_319] :
      ( ti(fun(U_322,U_321),U_320) = ti(fun(U_322,U_321),U_319)
      | ? [U_318] : hAPP(U_322,U_321,U_320,U_318) != hAPP(U_322,U_321,U_319,U_318) ),
    inference(variable_rename,[status(thm)],[f_145_1]) ).

fof(f_145_3,plain,
    ! [U_322,U_321,U_320,U_319] :
      ( ti(fun(U_322,U_321),U_320) = ti(fun(U_322,U_321),U_319)
      | hAPP(U_322,U_321,U_320,sK6(U_322,U_321,U_320,U_319)) != hAPP(U_322,U_321,U_319,sK6(U_322,U_321,U_320,U_319)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_318,sK6(U_322,U_321,U_320,U_319))],[f_145_2]) ).

fof(f_145_4,plain,
    ! [U_319,U_320,U_321,U_322] :
      ( ti(fun(U_322,U_321),U_320) = ti(fun(U_322,U_321),U_319)
      | hAPP(U_322,U_321,U_320,sK6(U_322,U_321,U_320,U_319)) != hAPP(U_322,U_321,U_319,sK6(U_322,U_321,U_320,U_319)) ),
    inference(definitional_conversion,[status(esa)],[f_145_3]) ).

cnf(f_145_5,plain,
    ( ti(fun(U_322,U_321),U_320) = ti(fun(U_322,U_321),U_319)
    | hAPP(U_322,U_321,U_320,sK6(U_322,U_321,U_320,U_319)) != hAPP(U_322,U_321,U_319,sK6(U_322,U_321,U_320,U_319)) ),
    inference(clausify,[status(thm)],[f_145_4]) ).

fof(f_146_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_146_2,plain,
    ! [U_325,U_324,U_323] :
      ( ( hBOOL(hAPP(fun(U_325,bool),bool,hAPP(U_325,fun(fun(U_325,bool),bool),member(U_325),U_324),U_323))
        | ~ hBOOL(hAPP(U_325,bool,U_323,U_324)) )
      & ( hBOOL(hAPP(U_325,bool,U_323,U_324))
        | ~ hBOOL(hAPP(fun(U_325,bool),bool,hAPP(U_325,fun(fun(U_325,bool),bool),member(U_325),U_324),U_323)) ) ),
    inference(variable_rename,[status(thm)],[f_146_1]) ).

fof(f_146_3,plain,
    ( ! [U_331,U_329,U_327] :
        ( hBOOL(hAPP(fun(U_331,bool),bool,hAPP(U_331,fun(fun(U_331,bool),bool),member(U_331),U_329),U_327))
        | ~ hBOOL(hAPP(U_331,bool,U_327,U_329)) )
    & ! [U_330,U_328,U_326] :
        ( hBOOL(hAPP(U_330,bool,U_326,U_328))
        | ~ hBOOL(hAPP(fun(U_330,bool),bool,hAPP(U_330,fun(fun(U_330,bool),bool),member(U_330),U_328),U_326)) ) ),
    inference(miniscope,[status(thm)],[f_146_2]) ).

fof(f_146_4,plain,
    ( ! [U_327,U_331,U_329] :
        ( hBOOL(hAPP(fun(U_331,bool),bool,hAPP(U_331,fun(fun(U_331,bool),bool),member(U_331),U_329),U_327))
        | ~ hBOOL(hAPP(U_331,bool,U_327,U_329)) )
    & ! [U_330,U_326,U_328] :
        ( hBOOL(hAPP(U_330,bool,U_326,U_328))
        | ~ hBOOL(hAPP(fun(U_330,bool),bool,hAPP(U_330,fun(fun(U_330,bool),bool),member(U_330),U_328),U_326)) ) ),
    inference(definitional_conversion,[status(esa)],[f_146_3]) ).

cnf(f_146_5,plain,
    ( hBOOL(hAPP(U_330,bool,U_326,U_328))
    | ~ hBOOL(hAPP(fun(U_330,bool),bool,hAPP(U_330,fun(fun(U_330,bool),bool),member(U_330),U_328),U_326)) ),
    inference(clausify,[status(thm)],[f_146_4]) ).

cnf(f_146_6,plain,
    ( hBOOL(hAPP(fun(U_331,bool),bool,hAPP(U_331,fun(fun(U_331,bool),bool),member(U_331),U_329),U_327))
    | ~ hBOOL(hAPP(U_331,bool,U_327,U_329)) ),
    inference(clausify,[status(thm)],[f_146_4]) ).

fof(f_147_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_147_2,plain,
    ! [U_333,U_332] : hAPP(fun(U_333,bool),fun(U_333,bool),collect(U_333),U_332) = ti(fun(U_333,bool),U_332),
    inference(variable_rename,[status(thm)],[f_147_1]) ).

fof(f_147_3,plain,
    ! [U_333,U_332] : hAPP(fun(U_333,bool),fun(U_333,bool),collect(U_333),U_332) = ti(fun(U_333,bool),U_332),
    inference(definitional_conversion,[status(esa)],[f_147_2]) ).

cnf(f_147_4,plain,
    hAPP(fun(U_333,bool),fun(U_333,bool),collect(U_333),U_332) = ti(fun(U_333,bool),U_332),
    inference(clausify,[status(thm)],[f_147_3]) ).

fof(f_148_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_77_insert__absorb2]) ).

fof(f_148_2,plain,
    ! [U_336,U_335,U_334] : hAPP(fun(U_336,bool),fun(U_336,bool),hAPP(U_336,fun(fun(U_336,bool),fun(U_336,bool)),insert(U_336),U_335),hAPP(fun(U_336,bool),fun(U_336,bool),hAPP(U_336,fun(fun(U_336,bool),fun(U_336,bool)),insert(U_336),U_335),U_334)) = hAPP(fun(U_336,bool),fun(U_336,bool),hAPP(U_336,fun(fun(U_336,bool),fun(U_336,bool)),insert(U_336),U_335),U_334),
    inference(variable_rename,[status(thm)],[f_148_1]) ).

fof(f_148_3,plain,
    ! [U_336,U_335,U_334] : hAPP(fun(U_336,bool),fun(U_336,bool),hAPP(U_336,fun(fun(U_336,bool),fun(U_336,bool)),insert(U_336),U_335),hAPP(fun(U_336,bool),fun(U_336,bool),hAPP(U_336,fun(fun(U_336,bool),fun(U_336,bool)),insert(U_336),U_335),U_334)) = hAPP(fun(U_336,bool),fun(U_336,bool),hAPP(U_336,fun(fun(U_336,bool),fun(U_336,bool)),insert(U_336),U_335),U_334),
    inference(definitional_conversion,[status(esa)],[f_148_2]) ).

cnf(f_148_4,plain,
    hAPP(fun(U_336,bool),fun(U_336,bool),hAPP(U_336,fun(fun(U_336,bool),fun(U_336,bool)),insert(U_336),U_335),hAPP(fun(U_336,bool),fun(U_336,bool),hAPP(U_336,fun(fun(U_336,bool),fun(U_336,bool)),insert(U_336),U_335),U_334)) = hAPP(fun(U_336,bool),fun(U_336,bool),hAPP(U_336,fun(fun(U_336,bool),fun(U_336,bool)),insert(U_336),U_335),U_334),
    inference(clausify,[status(thm)],[f_148_3]) ).

fof(f_149_1,plain,
    ! [X_b,X_1,Y_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),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_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),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_1),A_3)),
    inference(fof_nnf,[status(thm)],[fact_78_insert__commute]) ).

fof(f_149_2,plain,
    ! [U_340,U_339,U_338,U_337] : hAPP(fun(U_340,bool),fun(U_340,bool),hAPP(U_340,fun(fun(U_340,bool),fun(U_340,bool)),insert(U_340),U_339),hAPP(fun(U_340,bool),fun(U_340,bool),hAPP(U_340,fun(fun(U_340,bool),fun(U_340,bool)),insert(U_340),U_338),U_337)) = hAPP(fun(U_340,bool),fun(U_340,bool),hAPP(U_340,fun(fun(U_340,bool),fun(U_340,bool)),insert(U_340),U_338),hAPP(fun(U_340,bool),fun(U_340,bool),hAPP(U_340,fun(fun(U_340,bool),fun(U_340,bool)),insert(U_340),U_339),U_337)),
    inference(variable_rename,[status(thm)],[f_149_1]) ).

fof(f_149_3,plain,
    ! [U_339,U_337,U_340,U_338] : hAPP(fun(U_340,bool),fun(U_340,bool),hAPP(U_340,fun(fun(U_340,bool),fun(U_340,bool)),insert(U_340),U_339),hAPP(fun(U_340,bool),fun(U_340,bool),hAPP(U_340,fun(fun(U_340,bool),fun(U_340,bool)),insert(U_340),U_338),U_337)) = hAPP(fun(U_340,bool),fun(U_340,bool),hAPP(U_340,fun(fun(U_340,bool),fun(U_340,bool)),insert(U_340),U_338),hAPP(fun(U_340,bool),fun(U_340,bool),hAPP(U_340,fun(fun(U_340,bool),fun(U_340,bool)),insert(U_340),U_339),U_337)),
    inference(definitional_conversion,[status(esa)],[f_149_2]) ).

cnf(f_149_4,plain,
    hAPP(fun(U_340,bool),fun(U_340,bool),hAPP(U_340,fun(fun(U_340,bool),fun(U_340,bool)),insert(U_340),U_339),hAPP(fun(U_340,bool),fun(U_340,bool),hAPP(U_340,fun(fun(U_340,bool),fun(U_340,bool)),insert(U_340),U_338),U_337)) = hAPP(fun(U_340,bool),fun(U_340,bool),hAPP(U_340,fun(fun(U_340,bool),fun(U_340,bool)),insert(U_340),U_338),hAPP(fun(U_340,bool),fun(U_340,bool),hAPP(U_340,fun(fun(U_340,bool),fun(U_340,bool)),insert(U_340),U_339),U_337)),
    inference(clausify,[status(thm)],[f_149_3]) ).

fof(f_150_1,plain,
    ! [X_b,A_2,B_3,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_3),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_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_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_3),A_3))) ) ),
    inference(fof_nnf,[status(thm)],[fact_79_insert__iff]) ).

fof(f_150_2,plain,
    ! [U_344,U_343,U_342,U_341] :
      ( ( hBOOL(hAPP(fun(U_344,bool),bool,hAPP(U_344,fun(fun(U_344,bool),bool),member(U_344),U_343),hAPP(fun(U_344,bool),fun(U_344,bool),hAPP(U_344,fun(fun(U_344,bool),fun(U_344,bool)),insert(U_344),U_342),U_341)))
        | ( ~ hBOOL(hAPP(fun(U_344,bool),bool,hAPP(U_344,fun(fun(U_344,bool),bool),member(U_344),U_343),U_341))
          & ti(U_344,U_343) != ti(U_344,U_342) ) )
      & ( hBOOL(hAPP(fun(U_344,bool),bool,hAPP(U_344,fun(fun(U_344,bool),bool),member(U_344),U_343),U_341))
        | ti(U_344,U_343) = ti(U_344,U_342)
        | ~ hBOOL(hAPP(fun(U_344,bool),bool,hAPP(U_344,fun(fun(U_344,bool),bool),member(U_344),U_343),hAPP(fun(U_344,bool),fun(U_344,bool),hAPP(U_344,fun(fun(U_344,bool),fun(U_344,bool)),insert(U_344),U_342),U_341))) ) ),
    inference(variable_rename,[status(thm)],[f_150_1]) ).

fof(f_150_3,plain,
    ( ! [U_352,U_350,U_348,U_346] :
        ( hBOOL(hAPP(fun(U_352,bool),bool,hAPP(U_352,fun(fun(U_352,bool),bool),member(U_352),U_350),hAPP(fun(U_352,bool),fun(U_352,bool),hAPP(U_352,fun(fun(U_352,bool),fun(U_352,bool)),insert(U_352),U_348),U_346)))
        | ( ~ hBOOL(hAPP(fun(U_352,bool),bool,hAPP(U_352,fun(fun(U_352,bool),bool),member(U_352),U_350),U_346))
          & ti(U_352,U_350) != ti(U_352,U_348) ) )
    & ! [U_351,U_349,U_347,U_345] :
        ( hBOOL(hAPP(fun(U_351,bool),bool,hAPP(U_351,fun(fun(U_351,bool),bool),member(U_351),U_349),U_345))
        | ti(U_351,U_349) = ti(U_351,U_347)
        | ~ hBOOL(hAPP(fun(U_351,bool),bool,hAPP(U_351,fun(fun(U_351,bool),bool),member(U_351),U_349),hAPP(fun(U_351,bool),fun(U_351,bool),hAPP(U_351,fun(fun(U_351,bool),fun(U_351,bool)),insert(U_351),U_347),U_345))) ) ),
    inference(miniscope,[status(thm)],[f_150_2]) ).

fof(f_150_4,plain,
    ( ! [U_350,U_346,U_348,U_352] :
        ( ~ hBOOL(hAPP(fun(U_352,bool),bool,hAPP(U_352,fun(fun(U_352,bool),bool),member(U_352),U_350),U_346))
        | ~ sP13(U_350,U_346,U_348,U_352) )
    & ! [U_350,U_346,U_348,U_352] :
        ( ti(U_352,U_350) != ti(U_352,U_348)
        | ~ sP13(U_350,U_346,U_348,U_352) )
    & ! [U_350,U_346,U_348,U_352] :
        ( hBOOL(hAPP(fun(U_352,bool),bool,hAPP(U_352,fun(fun(U_352,bool),bool),member(U_352),U_350),hAPP(fun(U_352,bool),fun(U_352,bool),hAPP(U_352,fun(fun(U_352,bool),fun(U_352,bool)),insert(U_352),U_348),U_346)))
        | sP13(U_350,U_346,U_348,U_352) )
    & ! [U_345,U_347,U_349,U_351] :
        ( hBOOL(hAPP(fun(U_351,bool),bool,hAPP(U_351,fun(fun(U_351,bool),bool),member(U_351),U_349),U_345))
        | ti(U_351,U_349) = ti(U_351,U_347)
        | ~ hBOOL(hAPP(fun(U_351,bool),bool,hAPP(U_351,fun(fun(U_351,bool),bool),member(U_351),U_349),hAPP(fun(U_351,bool),fun(U_351,bool),hAPP(U_351,fun(fun(U_351,bool),fun(U_351,bool)),insert(U_351),U_347),U_345))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP13])],[f_150_3]) ).

cnf(f_150_5,plain,
    ( hBOOL(hAPP(fun(U_351,bool),bool,hAPP(U_351,fun(fun(U_351,bool),bool),member(U_351),U_349),U_345))
    | ti(U_351,U_349) = ti(U_351,U_347)
    | ~ hBOOL(hAPP(fun(U_351,bool),bool,hAPP(U_351,fun(fun(U_351,bool),bool),member(U_351),U_349),hAPP(fun(U_351,bool),fun(U_351,bool),hAPP(U_351,fun(fun(U_351,bool),fun(U_351,bool)),insert(U_351),U_347),U_345))) ),
    inference(clausify,[status(thm)],[f_150_4]) ).

cnf(f_150_6,plain,
    ( hBOOL(hAPP(fun(U_352,bool),bool,hAPP(U_352,fun(fun(U_352,bool),bool),member(U_352),U_350),hAPP(fun(U_352,bool),fun(U_352,bool),hAPP(U_352,fun(fun(U_352,bool),fun(U_352,bool)),insert(U_352),U_348),U_346)))
    | sP13(U_350,U_346,U_348,U_352) ),
    inference(clausify,[status(thm)],[f_150_4]) ).

cnf(f_150_7,plain,
    ( ti(U_352,U_350) != ti(U_352,U_348)
    | ~ sP13(U_350,U_346,U_348,U_352) ),
    inference(clausify,[status(thm)],[f_150_4]) ).

cnf(f_150_8,plain,
    ( ~ hBOOL(hAPP(fun(U_352,bool),bool,hAPP(U_352,fun(fun(U_352,bool),bool),member(U_352),U_350),U_346))
    | ~ sP13(U_350,U_346,U_348,U_352) ),
    inference(clausify,[status(thm)],[f_150_4]) ).

fof(f_151_1,plain,
    ! [X_b,Y_2,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_2),A_3),X_1))
        | ( ~ hBOOL(hAPP(X_b,bool,A_3,X_1))
          & ti(X_b,Y_2) != ti(X_b,X_1) ) )
      & ( hBOOL(hAPP(X_b,bool,A_3,X_1))
        | ti(X_b,Y_2) = 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_2),A_3),X_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_80_insert__code]) ).

fof(f_151_2,plain,
    ! [U_356,U_355,U_354,U_353] :
      ( ( hBOOL(hAPP(U_356,bool,hAPP(fun(U_356,bool),fun(U_356,bool),hAPP(U_356,fun(fun(U_356,bool),fun(U_356,bool)),insert(U_356),U_355),U_354),U_353))
        | ( ~ hBOOL(hAPP(U_356,bool,U_354,U_353))
          & ti(U_356,U_355) != ti(U_356,U_353) ) )
      & ( hBOOL(hAPP(U_356,bool,U_354,U_353))
        | ti(U_356,U_355) = ti(U_356,U_353)
        | ~ hBOOL(hAPP(U_356,bool,hAPP(fun(U_356,bool),fun(U_356,bool),hAPP(U_356,fun(fun(U_356,bool),fun(U_356,bool)),insert(U_356),U_355),U_354),U_353)) ) ),
    inference(variable_rename,[status(thm)],[f_151_1]) ).

fof(f_151_3,plain,
    ( ! [U_364,U_362,U_360,U_358] :
        ( hBOOL(hAPP(U_364,bool,hAPP(fun(U_364,bool),fun(U_364,bool),hAPP(U_364,fun(fun(U_364,bool),fun(U_364,bool)),insert(U_364),U_362),U_360),U_358))
        | ( ~ hBOOL(hAPP(U_364,bool,U_360,U_358))
          & ti(U_364,U_362) != ti(U_364,U_358) ) )
    & ! [U_363,U_361,U_359,U_357] :
        ( hBOOL(hAPP(U_363,bool,U_359,U_357))
        | ti(U_363,U_361) = ti(U_363,U_357)
        | ~ hBOOL(hAPP(U_363,bool,hAPP(fun(U_363,bool),fun(U_363,bool),hAPP(U_363,fun(fun(U_363,bool),fun(U_363,bool)),insert(U_363),U_361),U_359),U_357)) ) ),
    inference(miniscope,[status(thm)],[f_151_2]) ).

fof(f_151_4,plain,
    ( ! [U_358,U_362,U_360,U_364] :
        ( ~ hBOOL(hAPP(U_364,bool,U_360,U_358))
        | ~ sP14(U_358,U_362,U_360,U_364) )
    & ! [U_358,U_362,U_360,U_364] :
        ( ti(U_364,U_362) != ti(U_364,U_358)
        | ~ sP14(U_358,U_362,U_360,U_364) )
    & ! [U_358,U_362,U_360,U_364] :
        ( hBOOL(hAPP(U_364,bool,hAPP(fun(U_364,bool),fun(U_364,bool),hAPP(U_364,fun(fun(U_364,bool),fun(U_364,bool)),insert(U_364),U_362),U_360),U_358))
        | sP14(U_358,U_362,U_360,U_364) )
    & ! [U_357,U_361,U_359,U_363] :
        ( hBOOL(hAPP(U_363,bool,U_359,U_357))
        | ti(U_363,U_361) = ti(U_363,U_357)
        | ~ hBOOL(hAPP(U_363,bool,hAPP(fun(U_363,bool),fun(U_363,bool),hAPP(U_363,fun(fun(U_363,bool),fun(U_363,bool)),insert(U_363),U_361),U_359),U_357)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP14])],[f_151_3]) ).

cnf(f_151_5,plain,
    ( hBOOL(hAPP(U_363,bool,U_359,U_357))
    | ti(U_363,U_361) = ti(U_363,U_357)
    | ~ hBOOL(hAPP(U_363,bool,hAPP(fun(U_363,bool),fun(U_363,bool),hAPP(U_363,fun(fun(U_363,bool),fun(U_363,bool)),insert(U_363),U_361),U_359),U_357)) ),
    inference(clausify,[status(thm)],[f_151_4]) ).

cnf(f_151_6,plain,
    ( hBOOL(hAPP(U_364,bool,hAPP(fun(U_364,bool),fun(U_364,bool),hAPP(U_364,fun(fun(U_364,bool),fun(U_364,bool)),insert(U_364),U_362),U_360),U_358))
    | sP14(U_358,U_362,U_360,U_364) ),
    inference(clausify,[status(thm)],[f_151_4]) ).

cnf(f_151_7,plain,
    ( ti(U_364,U_362) != ti(U_364,U_358)
    | ~ sP14(U_358,U_362,U_360,U_364) ),
    inference(clausify,[status(thm)],[f_151_4]) ).

cnf(f_151_8,plain,
    ( ~ hBOOL(hAPP(U_364,bool,U_360,U_358))
    | ~ sP14(U_358,U_362,U_360,U_364) ),
    inference(clausify,[status(thm)],[f_151_4]) ).

fof(f_152_1,plain,
    ! [X_b,B_1,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_1)
          | ti(fun(X_b,bool),A_3) != ti(fun(X_b,bool),B_1) )
        & ( ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_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),B_1) ) )
      | hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_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_insert__ident]) ).

fof(f_152_2,plain,
    ! [U_368,U_367,U_366,U_365] :
      ( ( ( hAPP(fun(U_368,bool),fun(U_368,bool),hAPP(U_368,fun(fun(U_368,bool),fun(U_368,bool)),insert(U_368),U_366),U_365) = hAPP(fun(U_368,bool),fun(U_368,bool),hAPP(U_368,fun(fun(U_368,bool),fun(U_368,bool)),insert(U_368),U_366),U_367)
          | ti(fun(U_368,bool),U_365) != ti(fun(U_368,bool),U_367) )
        & ( ti(fun(U_368,bool),U_365) = ti(fun(U_368,bool),U_367)
          | hAPP(fun(U_368,bool),fun(U_368,bool),hAPP(U_368,fun(fun(U_368,bool),fun(U_368,bool)),insert(U_368),U_366),U_365) != hAPP(fun(U_368,bool),fun(U_368,bool),hAPP(U_368,fun(fun(U_368,bool),fun(U_368,bool)),insert(U_368),U_366),U_367) ) )
      | hBOOL(hAPP(fun(U_368,bool),bool,hAPP(U_368,fun(fun(U_368,bool),bool),member(U_368),U_366),U_367))
      | hBOOL(hAPP(fun(U_368,bool),bool,hAPP(U_368,fun(fun(U_368,bool),bool),member(U_368),U_366),U_365)) ),
    inference(variable_rename,[status(thm)],[f_152_1]) ).

fof(f_152_3,plain,
    ( ! [U_366,U_367,U_365,U_368] :
        ( hAPP(fun(U_368,bool),fun(U_368,bool),hAPP(U_368,fun(fun(U_368,bool),fun(U_368,bool)),insert(U_368),U_366),U_365) = hAPP(fun(U_368,bool),fun(U_368,bool),hAPP(U_368,fun(fun(U_368,bool),fun(U_368,bool)),insert(U_368),U_366),U_367)
        | ti(fun(U_368,bool),U_365) != ti(fun(U_368,bool),U_367)
        | ~ sP15(U_366,U_367,U_365,U_368) )
    & ! [U_366,U_367,U_365,U_368] :
        ( ti(fun(U_368,bool),U_365) = ti(fun(U_368,bool),U_367)
        | hAPP(fun(U_368,bool),fun(U_368,bool),hAPP(U_368,fun(fun(U_368,bool),fun(U_368,bool)),insert(U_368),U_366),U_365) != hAPP(fun(U_368,bool),fun(U_368,bool),hAPP(U_368,fun(fun(U_368,bool),fun(U_368,bool)),insert(U_368),U_366),U_367)
        | ~ sP15(U_366,U_367,U_365,U_368) )
    & ! [U_366,U_367,U_365,U_368] :
        ( sP15(U_366,U_367,U_365,U_368)
        | hBOOL(hAPP(fun(U_368,bool),bool,hAPP(U_368,fun(fun(U_368,bool),bool),member(U_368),U_366),U_367))
        | hBOOL(hAPP(fun(U_368,bool),bool,hAPP(U_368,fun(fun(U_368,bool),bool),member(U_368),U_366),U_365)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP15])],[f_152_2]) ).

cnf(f_152_4,plain,
    ( sP15(U_366,U_367,U_365,U_368)
    | hBOOL(hAPP(fun(U_368,bool),bool,hAPP(U_368,fun(fun(U_368,bool),bool),member(U_368),U_366),U_367))
    | hBOOL(hAPP(fun(U_368,bool),bool,hAPP(U_368,fun(fun(U_368,bool),bool),member(U_368),U_366),U_365)) ),
    inference(clausify,[status(thm)],[f_152_3]) ).

cnf(f_152_5,plain,
    ( ti(fun(U_368,bool),U_365) = ti(fun(U_368,bool),U_367)
    | hAPP(fun(U_368,bool),fun(U_368,bool),hAPP(U_368,fun(fun(U_368,bool),fun(U_368,bool)),insert(U_368),U_366),U_365) != hAPP(fun(U_368,bool),fun(U_368,bool),hAPP(U_368,fun(fun(U_368,bool),fun(U_368,bool)),insert(U_368),U_366),U_367)
    | ~ sP15(U_366,U_367,U_365,U_368) ),
    inference(clausify,[status(thm)],[f_152_3]) ).

cnf(f_152_6,plain,
    ( hAPP(fun(U_368,bool),fun(U_368,bool),hAPP(U_368,fun(fun(U_368,bool),fun(U_368,bool)),insert(U_368),U_366),U_365) = hAPP(fun(U_368,bool),fun(U_368,bool),hAPP(U_368,fun(fun(U_368,bool),fun(U_368,bool)),insert(U_368),U_366),U_367)
    | ti(fun(U_368,bool),U_365) != ti(fun(U_368,bool),U_367)
    | ~ sP15(U_366,U_367,U_365,U_368) ),
    inference(clausify,[status(thm)],[f_152_3]) ).

fof(f_153_1,plain,
    ! [X_b,B_3,A_2,B_1] :
      ( 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_3),B_1)))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),B_1)) ),
    inference(fof_nnf,[status(thm)],[fact_82_insertI2]) ).

fof(f_153_2,plain,
    ! [U_372,U_371,U_370,U_369] :
      ( hBOOL(hAPP(fun(U_372,bool),bool,hAPP(U_372,fun(fun(U_372,bool),bool),member(U_372),U_370),hAPP(fun(U_372,bool),fun(U_372,bool),hAPP(U_372,fun(fun(U_372,bool),fun(U_372,bool)),insert(U_372),U_371),U_369)))
      | ~ hBOOL(hAPP(fun(U_372,bool),bool,hAPP(U_372,fun(fun(U_372,bool),bool),member(U_372),U_370),U_369)) ),
    inference(variable_rename,[status(thm)],[f_153_1]) ).

fof(f_153_3,plain,
    ! [U_372,U_369,U_371,U_370] :
      ( hBOOL(hAPP(fun(U_372,bool),bool,hAPP(U_372,fun(fun(U_372,bool),bool),member(U_372),U_370),hAPP(fun(U_372,bool),fun(U_372,bool),hAPP(U_372,fun(fun(U_372,bool),fun(U_372,bool)),insert(U_372),U_371),U_369)))
      | ~ hBOOL(hAPP(fun(U_372,bool),bool,hAPP(U_372,fun(fun(U_372,bool),bool),member(U_372),U_370),U_369)) ),
    inference(definitional_conversion,[status(esa)],[f_153_2]) ).

cnf(f_153_4,plain,
    ( hBOOL(hAPP(fun(U_372,bool),bool,hAPP(U_372,fun(fun(U_372,bool),bool),member(U_372),U_370),hAPP(fun(U_372,bool),fun(U_372,bool),hAPP(U_372,fun(fun(U_372,bool),fun(U_372,bool)),insert(U_372),U_371),U_369)))
    | ~ hBOOL(hAPP(fun(U_372,bool),bool,hAPP(U_372,fun(fun(U_372,bool),bool),member(U_372),U_370),U_369)) ),
    inference(clausify,[status(thm)],[f_153_3]) ).

fof(f_154_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_83_insert__absorb]) ).

fof(f_154_2,plain,
    ! [U_375,U_374,U_373] :
      ( hAPP(fun(U_375,bool),fun(U_375,bool),hAPP(U_375,fun(fun(U_375,bool),fun(U_375,bool)),insert(U_375),U_374),U_373) = ti(fun(U_375,bool),U_373)
      | ~ hBOOL(hAPP(fun(U_375,bool),bool,hAPP(U_375,fun(fun(U_375,bool),bool),member(U_375),U_374),U_373)) ),
    inference(variable_rename,[status(thm)],[f_154_1]) ).

fof(f_154_3,plain,
    ! [U_375,U_373,U_374] :
      ( hAPP(fun(U_375,bool),fun(U_375,bool),hAPP(U_375,fun(fun(U_375,bool),fun(U_375,bool)),insert(U_375),U_374),U_373) = ti(fun(U_375,bool),U_373)
      | ~ hBOOL(hAPP(fun(U_375,bool),bool,hAPP(U_375,fun(fun(U_375,bool),bool),member(U_375),U_374),U_373)) ),
    inference(definitional_conversion,[status(esa)],[f_154_2]) ).

cnf(f_154_4,plain,
    ( hAPP(fun(U_375,bool),fun(U_375,bool),hAPP(U_375,fun(fun(U_375,bool),fun(U_375,bool)),insert(U_375),U_374),U_373) = ti(fun(U_375,bool),U_373)
    | ~ hBOOL(hAPP(fun(U_375,bool),bool,hAPP(U_375,fun(fun(U_375,bool),bool),member(U_375),U_374),U_373)) ),
    inference(clausify,[status(thm)],[f_154_3]) ).

fof(f_155_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_84_subset__refl]) ).

fof(f_155_2,plain,
    ! [U_377,U_376] : hBOOL(hAPP(fun(U_377,bool),bool,hAPP(fun(U_377,bool),fun(fun(U_377,bool),bool),ord_less_eq(fun(U_377,bool)),U_376),U_376)),
    inference(variable_rename,[status(thm)],[f_155_1]) ).

fof(f_155_3,plain,
    ! [U_376,U_377] : hBOOL(hAPP(fun(U_377,bool),bool,hAPP(fun(U_377,bool),fun(fun(U_377,bool),bool),ord_less_eq(fun(U_377,bool)),U_376),U_376)),
    inference(definitional_conversion,[status(esa)],[f_155_2]) ).

cnf(f_155_4,plain,
    hBOOL(hAPP(fun(U_377,bool),bool,hAPP(fun(U_377,bool),fun(fun(U_377,bool),bool),ord_less_eq(fun(U_377,bool)),U_376),U_376)),
    inference(clausify,[status(thm)],[f_155_3]) ).

fof(f_156_1,plain,
    ! [X_b,A_3,B_1] :
      ( ( ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_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)),B_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_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)),B_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_1)) )
        | ti(fun(X_b,bool),A_3) != ti(fun(X_b,bool),B_1) ) ),
    inference(fof_nnf,[status(thm)],[fact_85_set__eq__subset]) ).

fof(f_156_2,plain,
    ! [U_380,U_379,U_378] :
      ( ( ti(fun(U_380,bool),U_379) = ti(fun(U_380,bool),U_378)
        | ~ hBOOL(hAPP(fun(U_380,bool),bool,hAPP(fun(U_380,bool),fun(fun(U_380,bool),bool),ord_less_eq(fun(U_380,bool)),U_378),U_379))
        | ~ hBOOL(hAPP(fun(U_380,bool),bool,hAPP(fun(U_380,bool),fun(fun(U_380,bool),bool),ord_less_eq(fun(U_380,bool)),U_379),U_378)) )
      & ( ( hBOOL(hAPP(fun(U_380,bool),bool,hAPP(fun(U_380,bool),fun(fun(U_380,bool),bool),ord_less_eq(fun(U_380,bool)),U_378),U_379))
          & hBOOL(hAPP(fun(U_380,bool),bool,hAPP(fun(U_380,bool),fun(fun(U_380,bool),bool),ord_less_eq(fun(U_380,bool)),U_379),U_378)) )
        | ti(fun(U_380,bool),U_379) != ti(fun(U_380,bool),U_378) ) ),
    inference(variable_rename,[status(thm)],[f_156_1]) ).

fof(f_156_3,plain,
    ( ! [U_386,U_384,U_382] :
        ( ti(fun(U_386,bool),U_384) = ti(fun(U_386,bool),U_382)
        | ~ hBOOL(hAPP(fun(U_386,bool),bool,hAPP(fun(U_386,bool),fun(fun(U_386,bool),bool),ord_less_eq(fun(U_386,bool)),U_382),U_384))
        | ~ hBOOL(hAPP(fun(U_386,bool),bool,hAPP(fun(U_386,bool),fun(fun(U_386,bool),bool),ord_less_eq(fun(U_386,bool)),U_384),U_382)) )
    & ! [U_385,U_383,U_381] :
        ( ( hBOOL(hAPP(fun(U_385,bool),bool,hAPP(fun(U_385,bool),fun(fun(U_385,bool),bool),ord_less_eq(fun(U_385,bool)),U_381),U_383))
          & hBOOL(hAPP(fun(U_385,bool),bool,hAPP(fun(U_385,bool),fun(fun(U_385,bool),bool),ord_less_eq(fun(U_385,bool)),U_383),U_381)) )
        | ti(fun(U_385,bool),U_383) != ti(fun(U_385,bool),U_381) ) ),
    inference(miniscope,[status(thm)],[f_156_2]) ).

fof(f_156_4,plain,
    ( ! [U_381,U_385,U_383] :
        ( hBOOL(hAPP(fun(U_385,bool),bool,hAPP(fun(U_385,bool),fun(fun(U_385,bool),bool),ord_less_eq(fun(U_385,bool)),U_381),U_383))
        | ~ sP16(U_381,U_385,U_383) )
    & ! [U_381,U_385,U_383] :
        ( hBOOL(hAPP(fun(U_385,bool),bool,hAPP(fun(U_385,bool),fun(fun(U_385,bool),bool),ord_less_eq(fun(U_385,bool)),U_383),U_381))
        | ~ sP16(U_381,U_385,U_383) )
    & ! [U_386,U_384,U_382] :
        ( ti(fun(U_386,bool),U_384) = ti(fun(U_386,bool),U_382)
        | ~ hBOOL(hAPP(fun(U_386,bool),bool,hAPP(fun(U_386,bool),fun(fun(U_386,bool),bool),ord_less_eq(fun(U_386,bool)),U_382),U_384))
        | ~ hBOOL(hAPP(fun(U_386,bool),bool,hAPP(fun(U_386,bool),fun(fun(U_386,bool),bool),ord_less_eq(fun(U_386,bool)),U_384),U_382)) )
    & ! [U_381,U_385,U_383] :
        ( sP16(U_381,U_385,U_383)
        | ti(fun(U_385,bool),U_383) != ti(fun(U_385,bool),U_381) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP16])],[f_156_3]) ).

cnf(f_156_5,plain,
    ( sP16(U_381,U_385,U_383)
    | ti(fun(U_385,bool),U_383) != ti(fun(U_385,bool),U_381) ),
    inference(clausify,[status(thm)],[f_156_4]) ).

cnf(f_156_6,plain,
    ( ti(fun(U_386,bool),U_384) = ti(fun(U_386,bool),U_382)
    | ~ hBOOL(hAPP(fun(U_386,bool),bool,hAPP(fun(U_386,bool),fun(fun(U_386,bool),bool),ord_less_eq(fun(U_386,bool)),U_382),U_384))
    | ~ hBOOL(hAPP(fun(U_386,bool),bool,hAPP(fun(U_386,bool),fun(fun(U_386,bool),bool),ord_less_eq(fun(U_386,bool)),U_384),U_382)) ),
    inference(clausify,[status(thm)],[f_156_4]) ).

cnf(f_156_7,plain,
    ( hBOOL(hAPP(fun(U_385,bool),bool,hAPP(fun(U_385,bool),fun(fun(U_385,bool),bool),ord_less_eq(fun(U_385,bool)),U_383),U_381))
    | ~ sP16(U_381,U_385,U_383) ),
    inference(clausify,[status(thm)],[f_156_4]) ).

cnf(f_156_8,plain,
    ( hBOOL(hAPP(fun(U_385,bool),bool,hAPP(fun(U_385,bool),fun(fun(U_385,bool),bool),ord_less_eq(fun(U_385,bool)),U_381),U_383))
    | ~ sP16(U_381,U_385,U_383) ),
    inference(clausify,[status(thm)],[f_156_4]) ).

fof(f_157_1,plain,
    ! [X_b,A_3,B_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),B_1))
      | ti(fun(X_b,bool),A_3) != ti(fun(X_b,bool),B_1) ),
    inference(fof_nnf,[status(thm)],[fact_86_equalityD1]) ).

fof(f_157_2,plain,
    ! [U_389,U_388,U_387] :
      ( hBOOL(hAPP(fun(U_389,bool),bool,hAPP(fun(U_389,bool),fun(fun(U_389,bool),bool),ord_less_eq(fun(U_389,bool)),U_388),U_387))
      | ti(fun(U_389,bool),U_388) != ti(fun(U_389,bool),U_387) ),
    inference(variable_rename,[status(thm)],[f_157_1]) ).

fof(f_157_3,plain,
    ! [U_388,U_387,U_389] :
      ( hBOOL(hAPP(fun(U_389,bool),bool,hAPP(fun(U_389,bool),fun(fun(U_389,bool),bool),ord_less_eq(fun(U_389,bool)),U_388),U_387))
      | ti(fun(U_389,bool),U_388) != ti(fun(U_389,bool),U_387) ),
    inference(definitional_conversion,[status(esa)],[f_157_2]) ).

cnf(f_157_4,plain,
    ( hBOOL(hAPP(fun(U_389,bool),bool,hAPP(fun(U_389,bool),fun(fun(U_389,bool),bool),ord_less_eq(fun(U_389,bool)),U_388),U_387))
    | ti(fun(U_389,bool),U_388) != ti(fun(U_389,bool),U_387) ),
    inference(clausify,[status(thm)],[f_157_3]) ).

fof(f_158_1,plain,
    ! [X_b,A_3,B_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)),B_1),A_3))
      | ti(fun(X_b,bool),A_3) != ti(fun(X_b,bool),B_1) ),
    inference(fof_nnf,[status(thm)],[fact_87_equalityD2]) ).

fof(f_158_2,plain,
    ! [U_392,U_391,U_390] :
      ( hBOOL(hAPP(fun(U_392,bool),bool,hAPP(fun(U_392,bool),fun(fun(U_392,bool),bool),ord_less_eq(fun(U_392,bool)),U_390),U_391))
      | ti(fun(U_392,bool),U_391) != ti(fun(U_392,bool),U_390) ),
    inference(variable_rename,[status(thm)],[f_158_1]) ).

fof(f_158_3,plain,
    ! [U_391,U_390,U_392] :
      ( hBOOL(hAPP(fun(U_392,bool),bool,hAPP(fun(U_392,bool),fun(fun(U_392,bool),bool),ord_less_eq(fun(U_392,bool)),U_390),U_391))
      | ti(fun(U_392,bool),U_391) != ti(fun(U_392,bool),U_390) ),
    inference(definitional_conversion,[status(esa)],[f_158_2]) ).

cnf(f_158_4,plain,
    ( hBOOL(hAPP(fun(U_392,bool),bool,hAPP(fun(U_392,bool),fun(fun(U_392,bool),bool),ord_less_eq(fun(U_392,bool)),U_390),U_391))
    | ti(fun(U_392,bool),U_391) != ti(fun(U_392,bool),U_390) ),
    inference(clausify,[status(thm)],[f_158_3]) ).

fof(f_159_1,plain,
    ! [X_b,X_1,A_3,B_1] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_1))
      | ~ 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_1)) ),
    inference(fof_nnf,[status(thm)],[fact_88_in__mono]) ).

fof(f_159_2,plain,
    ! [U_396,U_395,U_394,U_393] :
      ( hBOOL(hAPP(fun(U_396,bool),bool,hAPP(U_396,fun(fun(U_396,bool),bool),member(U_396),U_395),U_393))
      | ~ hBOOL(hAPP(fun(U_396,bool),bool,hAPP(U_396,fun(fun(U_396,bool),bool),member(U_396),U_395),U_394))
      | ~ hBOOL(hAPP(fun(U_396,bool),bool,hAPP(fun(U_396,bool),fun(fun(U_396,bool),bool),ord_less_eq(fun(U_396,bool)),U_394),U_393)) ),
    inference(variable_rename,[status(thm)],[f_159_1]) ).

fof(f_159_3,plain,
    ! [U_393,U_396,U_394,U_395] :
      ( hBOOL(hAPP(fun(U_396,bool),bool,hAPP(U_396,fun(fun(U_396,bool),bool),member(U_396),U_395),U_393))
      | ~ hBOOL(hAPP(fun(U_396,bool),bool,hAPP(U_396,fun(fun(U_396,bool),bool),member(U_396),U_395),U_394))
      | ~ hBOOL(hAPP(fun(U_396,bool),bool,hAPP(fun(U_396,bool),fun(fun(U_396,bool),bool),ord_less_eq(fun(U_396,bool)),U_394),U_393)) ),
    inference(definitional_conversion,[status(esa)],[f_159_2]) ).

cnf(f_159_4,plain,
    ( hBOOL(hAPP(fun(U_396,bool),bool,hAPP(U_396,fun(fun(U_396,bool),bool),member(U_396),U_395),U_393))
    | ~ hBOOL(hAPP(fun(U_396,bool),bool,hAPP(U_396,fun(fun(U_396,bool),bool),member(U_396),U_395),U_394))
    | ~ hBOOL(hAPP(fun(U_396,bool),bool,hAPP(fun(U_396,bool),fun(fun(U_396,bool),bool),ord_less_eq(fun(U_396,bool)),U_394),U_393)) ),
    inference(clausify,[status(thm)],[f_159_3]) ).

fof(f_160_1,plain,
    ! [X_b,B_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),B_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),B_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_89_set__rev__mp]) ).

fof(f_160_2,plain,
    ! [U_400,U_399,U_398,U_397] :
      ( hBOOL(hAPP(fun(U_400,bool),bool,hAPP(U_400,fun(fun(U_400,bool),bool),member(U_400),U_398),U_399))
      | ~ hBOOL(hAPP(fun(U_400,bool),bool,hAPP(fun(U_400,bool),fun(fun(U_400,bool),bool),ord_less_eq(fun(U_400,bool)),U_397),U_399))
      | ~ hBOOL(hAPP(fun(U_400,bool),bool,hAPP(U_400,fun(fun(U_400,bool),bool),member(U_400),U_398),U_397)) ),
    inference(variable_rename,[status(thm)],[f_160_1]) ).

fof(f_160_3,plain,
    ! [U_398,U_397,U_400,U_399] :
      ( hBOOL(hAPP(fun(U_400,bool),bool,hAPP(U_400,fun(fun(U_400,bool),bool),member(U_400),U_398),U_399))
      | ~ hBOOL(hAPP(fun(U_400,bool),bool,hAPP(fun(U_400,bool),fun(fun(U_400,bool),bool),ord_less_eq(fun(U_400,bool)),U_397),U_399))
      | ~ hBOOL(hAPP(fun(U_400,bool),bool,hAPP(U_400,fun(fun(U_400,bool),bool),member(U_400),U_398),U_397)) ),
    inference(definitional_conversion,[status(esa)],[f_160_2]) ).

cnf(f_160_4,plain,
    ( hBOOL(hAPP(fun(U_400,bool),bool,hAPP(U_400,fun(fun(U_400,bool),bool),member(U_400),U_398),U_399))
    | ~ hBOOL(hAPP(fun(U_400,bool),bool,hAPP(fun(U_400,bool),fun(fun(U_400,bool),bool),ord_less_eq(fun(U_400,bool)),U_397),U_399))
    | ~ hBOOL(hAPP(fun(U_400,bool),bool,hAPP(U_400,fun(fun(U_400,bool),bool),member(U_400),U_398),U_397)) ),
    inference(clausify,[status(thm)],[f_160_3]) ).

fof(f_161_1,plain,
    ! [X_b,X_1,A_3,B_1] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_1))
      | ~ 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_1)) ),
    inference(fof_nnf,[status(thm)],[fact_90_set__mp]) ).

fof(f_161_2,plain,
    ! [U_404,U_403,U_402,U_401] :
      ( hBOOL(hAPP(fun(U_404,bool),bool,hAPP(U_404,fun(fun(U_404,bool),bool),member(U_404),U_403),U_401))
      | ~ hBOOL(hAPP(fun(U_404,bool),bool,hAPP(U_404,fun(fun(U_404,bool),bool),member(U_404),U_403),U_402))
      | ~ hBOOL(hAPP(fun(U_404,bool),bool,hAPP(fun(U_404,bool),fun(fun(U_404,bool),bool),ord_less_eq(fun(U_404,bool)),U_402),U_401)) ),
    inference(variable_rename,[status(thm)],[f_161_1]) ).

fof(f_161_3,plain,
    ! [U_403,U_402,U_404,U_401] :
      ( hBOOL(hAPP(fun(U_404,bool),bool,hAPP(U_404,fun(fun(U_404,bool),bool),member(U_404),U_403),U_401))
      | ~ hBOOL(hAPP(fun(U_404,bool),bool,hAPP(U_404,fun(fun(U_404,bool),bool),member(U_404),U_403),U_402))
      | ~ hBOOL(hAPP(fun(U_404,bool),bool,hAPP(fun(U_404,bool),fun(fun(U_404,bool),bool),ord_less_eq(fun(U_404,bool)),U_402),U_401)) ),
    inference(definitional_conversion,[status(esa)],[f_161_2]) ).

cnf(f_161_4,plain,
    ( hBOOL(hAPP(fun(U_404,bool),bool,hAPP(U_404,fun(fun(U_404,bool),bool),member(U_404),U_403),U_401))
    | ~ hBOOL(hAPP(fun(U_404,bool),bool,hAPP(U_404,fun(fun(U_404,bool),bool),member(U_404),U_403),U_402))
    | ~ hBOOL(hAPP(fun(U_404,bool),bool,hAPP(fun(U_404,bool),fun(fun(U_404,bool),bool),ord_less_eq(fun(U_404,bool)),U_402),U_401)) ),
    inference(clausify,[status(thm)],[f_161_3]) ).

fof(f_162_1,plain,
    ! [X_b,C_2,A_3,B_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),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_1),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_1)) ),
    inference(fof_nnf,[status(thm)],[fact_91_subset__trans]) ).

fof(f_162_2,plain,
    ! [U_408,U_407,U_406,U_405] :
      ( hBOOL(hAPP(fun(U_408,bool),bool,hAPP(fun(U_408,bool),fun(fun(U_408,bool),bool),ord_less_eq(fun(U_408,bool)),U_406),U_407))
      | ~ hBOOL(hAPP(fun(U_408,bool),bool,hAPP(fun(U_408,bool),fun(fun(U_408,bool),bool),ord_less_eq(fun(U_408,bool)),U_405),U_407))
      | ~ hBOOL(hAPP(fun(U_408,bool),bool,hAPP(fun(U_408,bool),fun(fun(U_408,bool),bool),ord_less_eq(fun(U_408,bool)),U_406),U_405)) ),
    inference(variable_rename,[status(thm)],[f_162_1]) ).

fof(f_162_3,plain,
    ! [U_408,U_406,U_405,U_407] :
      ( hBOOL(hAPP(fun(U_408,bool),bool,hAPP(fun(U_408,bool),fun(fun(U_408,bool),bool),ord_less_eq(fun(U_408,bool)),U_406),U_407))
      | ~ hBOOL(hAPP(fun(U_408,bool),bool,hAPP(fun(U_408,bool),fun(fun(U_408,bool),bool),ord_less_eq(fun(U_408,bool)),U_405),U_407))
      | ~ hBOOL(hAPP(fun(U_408,bool),bool,hAPP(fun(U_408,bool),fun(fun(U_408,bool),bool),ord_less_eq(fun(U_408,bool)),U_406),U_405)) ),
    inference(definitional_conversion,[status(esa)],[f_162_2]) ).

cnf(f_162_4,plain,
    ( hBOOL(hAPP(fun(U_408,bool),bool,hAPP(fun(U_408,bool),fun(fun(U_408,bool),bool),ord_less_eq(fun(U_408,bool)),U_406),U_407))
    | ~ hBOOL(hAPP(fun(U_408,bool),bool,hAPP(fun(U_408,bool),fun(fun(U_408,bool),bool),ord_less_eq(fun(U_408,bool)),U_405),U_407))
    | ~ hBOOL(hAPP(fun(U_408,bool),bool,hAPP(fun(U_408,bool),fun(fun(U_408,bool),bool),ord_less_eq(fun(U_408,bool)),U_406),U_405)) ),
    inference(clausify,[status(thm)],[f_162_3]) ).

fof(f_163_1,plain,
    ! [X_b,A_3,B_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)),B_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_1)) )
      | ti(fun(X_b,bool),A_3) != ti(fun(X_b,bool),B_1) ),
    inference(fof_nnf,[status(thm)],[fact_92_equalityE]) ).

fof(f_163_2,plain,
    ! [U_411,U_410,U_409] :
      ( ( 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_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)),U_410),U_409)) )
      | ti(fun(U_411,bool),U_410) != ti(fun(U_411,bool),U_409) ),
    inference(variable_rename,[status(thm)],[f_163_1]) ).

fof(f_163_3,plain,
    ( ! [U_410,U_409,U_411] :
        ( 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_410))
        | ~ sP17(U_410,U_409,U_411) )
    & ! [U_410,U_409,U_411] :
        ( 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_410),U_409))
        | ~ sP17(U_410,U_409,U_411) )
    & ! [U_410,U_409,U_411] :
        ( sP17(U_410,U_409,U_411)
        | ti(fun(U_411,bool),U_410) != ti(fun(U_411,bool),U_409) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP17])],[f_163_2]) ).

cnf(f_163_4,plain,
    ( sP17(U_410,U_409,U_411)
    | ti(fun(U_411,bool),U_410) != ti(fun(U_411,bool),U_409) ),
    inference(clausify,[status(thm)],[f_163_3]) ).

cnf(f_163_5,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)),U_410),U_409))
    | ~ sP17(U_410,U_409,U_411) ),
    inference(clausify,[status(thm)],[f_163_3]) ).

cnf(f_163_6,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)),U_409),U_410))
    | ~ sP17(U_410,U_409,U_411) ),
    inference(clausify,[status(thm)],[f_163_3]) ).

fof(f_164_1,plain,
    ! [X_b,X_c,Z_2,F,A_3] :
      ( ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Z_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)))
        | ! [X_2] :
            ( ti(X_b,Z_2) != 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_2) = 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_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_93_image__iff]) ).

fof(f_164_2,plain,
    ! [U_418,U_417,U_416,U_415,U_414] :
      ( ( hBOOL(hAPP(fun(U_418,bool),bool,hAPP(U_418,fun(fun(U_418,bool),bool),member(U_418),U_416),hAPP(fun(U_417,bool),fun(U_418,bool),hAPP(fun(U_417,U_418),fun(fun(U_417,bool),fun(U_418,bool)),image(U_417,U_418),U_415),U_414)))
        | ! [U_413] :
            ( ti(U_418,U_416) != hAPP(U_417,U_418,U_415,U_413)
            | ~ hBOOL(hAPP(fun(U_417,bool),bool,hAPP(U_417,fun(fun(U_417,bool),bool),member(U_417),U_413),U_414)) ) )
      & ( ? [U_412] :
            ( ti(U_418,U_416) = hAPP(U_417,U_418,U_415,U_412)
            & hBOOL(hAPP(fun(U_417,bool),bool,hAPP(U_417,fun(fun(U_417,bool),bool),member(U_417),U_412),U_414)) )
        | ~ hBOOL(hAPP(fun(U_418,bool),bool,hAPP(U_418,fun(fun(U_418,bool),bool),member(U_418),U_416),hAPP(fun(U_417,bool),fun(U_418,bool),hAPP(fun(U_417,U_418),fun(fun(U_417,bool),fun(U_418,bool)),image(U_417,U_418),U_415),U_414))) ) ),
    inference(variable_rename,[status(thm)],[f_164_1]) ).

fof(f_164_3,plain,
    ( ! [U_428,U_426,U_424,U_422,U_420] :
        ( hBOOL(hAPP(fun(U_428,bool),bool,hAPP(U_428,fun(fun(U_428,bool),bool),member(U_428),U_424),hAPP(fun(U_426,bool),fun(U_428,bool),hAPP(fun(U_426,U_428),fun(fun(U_426,bool),fun(U_428,bool)),image(U_426,U_428),U_422),U_420)))
        | ! [U_413] :
            ( ti(U_428,U_424) != hAPP(U_426,U_428,U_422,U_413)
            | ~ hBOOL(hAPP(fun(U_426,bool),bool,hAPP(U_426,fun(fun(U_426,bool),bool),member(U_426),U_413),U_420)) ) )
    & ! [U_427,U_425,U_423,U_421,U_419] :
        ( ? [U_412] :
            ( ti(U_427,U_423) = hAPP(U_425,U_427,U_421,U_412)
            & hBOOL(hAPP(fun(U_425,bool),bool,hAPP(U_425,fun(fun(U_425,bool),bool),member(U_425),U_412),U_419)) )
        | ~ hBOOL(hAPP(fun(U_427,bool),bool,hAPP(U_427,fun(fun(U_427,bool),bool),member(U_427),U_423),hAPP(fun(U_425,bool),fun(U_427,bool),hAPP(fun(U_425,U_427),fun(fun(U_425,bool),fun(U_427,bool)),image(U_425,U_427),U_421),U_419))) ) ),
    inference(miniscope,[status(thm)],[f_164_2]) ).

fof(f_164_4,plain,
    ( ! [U_428,U_426,U_424,U_422,U_420] :
        ( hBOOL(hAPP(fun(U_428,bool),bool,hAPP(U_428,fun(fun(U_428,bool),bool),member(U_428),U_424),hAPP(fun(U_426,bool),fun(U_428,bool),hAPP(fun(U_426,U_428),fun(fun(U_426,bool),fun(U_428,bool)),image(U_426,U_428),U_422),U_420)))
        | ! [U_413] :
            ( ti(U_428,U_424) != hAPP(U_426,U_428,U_422,U_413)
            | ~ hBOOL(hAPP(fun(U_426,bool),bool,hAPP(U_426,fun(fun(U_426,bool),bool),member(U_426),U_413),U_420)) ) )
    & ! [U_427,U_425,U_423,U_421,U_419] :
        ( ( ti(U_427,U_423) = hAPP(U_425,U_427,U_421,sK7(U_427,U_425,U_423,U_421,U_419))
          & hBOOL(hAPP(fun(U_425,bool),bool,hAPP(U_425,fun(fun(U_425,bool),bool),member(U_425),sK7(U_427,U_425,U_423,U_421,U_419)),U_419)) )
        | ~ hBOOL(hAPP(fun(U_427,bool),bool,hAPP(U_427,fun(fun(U_427,bool),bool),member(U_427),U_423),hAPP(fun(U_425,bool),fun(U_427,bool),hAPP(fun(U_425,U_427),fun(fun(U_425,bool),fun(U_427,bool)),image(U_425,U_427),U_421),U_419))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_412,sK7(U_427,U_425,U_423,U_421,U_419))],[f_164_3]) ).

fof(f_164_5,plain,
    ( ! [U_419,U_421,U_423,U_425,U_427] :
        ( ti(U_427,U_423) = hAPP(U_425,U_427,U_421,sK7(U_427,U_425,U_423,U_421,U_419))
        | ~ sP18(U_419,U_421,U_423,U_425,U_427) )
    & ! [U_419,U_421,U_423,U_425,U_427] :
        ( hBOOL(hAPP(fun(U_425,bool),bool,hAPP(U_425,fun(fun(U_425,bool),bool),member(U_425),sK7(U_427,U_425,U_423,U_421,U_419)),U_419))
        | ~ sP18(U_419,U_421,U_423,U_425,U_427) )
    & ! [U_422,U_420,U_413,U_424,U_426,U_428] :
        ( hBOOL(hAPP(fun(U_428,bool),bool,hAPP(U_428,fun(fun(U_428,bool),bool),member(U_428),U_424),hAPP(fun(U_426,bool),fun(U_428,bool),hAPP(fun(U_426,U_428),fun(fun(U_426,bool),fun(U_428,bool)),image(U_426,U_428),U_422),U_420)))
        | ti(U_428,U_424) != hAPP(U_426,U_428,U_422,U_413)
        | ~ hBOOL(hAPP(fun(U_426,bool),bool,hAPP(U_426,fun(fun(U_426,bool),bool),member(U_426),U_413),U_420)) )
    & ! [U_419,U_421,U_423,U_425,U_427] :
        ( sP18(U_419,U_421,U_423,U_425,U_427)
        | ~ hBOOL(hAPP(fun(U_427,bool),bool,hAPP(U_427,fun(fun(U_427,bool),bool),member(U_427),U_423),hAPP(fun(U_425,bool),fun(U_427,bool),hAPP(fun(U_425,U_427),fun(fun(U_425,bool),fun(U_427,bool)),image(U_425,U_427),U_421),U_419))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP18])],[f_164_4]) ).

cnf(f_164_6,plain,
    ( sP18(U_419,U_421,U_423,U_425,U_427)
    | ~ hBOOL(hAPP(fun(U_427,bool),bool,hAPP(U_427,fun(fun(U_427,bool),bool),member(U_427),U_423),hAPP(fun(U_425,bool),fun(U_427,bool),hAPP(fun(U_425,U_427),fun(fun(U_425,bool),fun(U_427,bool)),image(U_425,U_427),U_421),U_419))) ),
    inference(clausify,[status(thm)],[f_164_5]) ).

cnf(f_164_7,plain,
    ( hBOOL(hAPP(fun(U_428,bool),bool,hAPP(U_428,fun(fun(U_428,bool),bool),member(U_428),U_424),hAPP(fun(U_426,bool),fun(U_428,bool),hAPP(fun(U_426,U_428),fun(fun(U_426,bool),fun(U_428,bool)),image(U_426,U_428),U_422),U_420)))
    | ti(U_428,U_424) != hAPP(U_426,U_428,U_422,U_413)
    | ~ hBOOL(hAPP(fun(U_426,bool),bool,hAPP(U_426,fun(fun(U_426,bool),bool),member(U_426),U_413),U_420)) ),
    inference(clausify,[status(thm)],[f_164_5]) ).

cnf(f_164_8,plain,
    ( hBOOL(hAPP(fun(U_425,bool),bool,hAPP(U_425,fun(fun(U_425,bool),bool),member(U_425),sK7(U_427,U_425,U_423,U_421,U_419)),U_419))
    | ~ sP18(U_419,U_421,U_423,U_425,U_427) ),
    inference(clausify,[status(thm)],[f_164_5]) ).

cnf(f_164_9,plain,
    ( ti(U_427,U_423) = hAPP(U_425,U_427,U_421,sK7(U_427,U_425,U_423,U_421,U_419))
    | ~ sP18(U_419,U_421,U_423,U_425,U_427) ),
    inference(clausify,[status(thm)],[f_164_5]) ).

fof(f_165_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_94_imageI]) ).

fof(f_165_2,plain,
    ! [U_433,U_432,U_431,U_430,U_429] :
      ( hBOOL(hAPP(fun(U_433,bool),bool,hAPP(U_433,fun(fun(U_433,bool),bool),member(U_433),hAPP(U_432,U_433,U_431,U_430)),hAPP(fun(U_432,bool),fun(U_433,bool),hAPP(fun(U_432,U_433),fun(fun(U_432,bool),fun(U_433,bool)),image(U_432,U_433),U_431),U_429)))
      | ~ hBOOL(hAPP(fun(U_432,bool),bool,hAPP(U_432,fun(fun(U_432,bool),bool),member(U_432),U_430),U_429)) ),
    inference(variable_rename,[status(thm)],[f_165_1]) ).

fof(f_165_3,plain,
    ! [U_429,U_432,U_430,U_431,U_433] :
      ( hBOOL(hAPP(fun(U_433,bool),bool,hAPP(U_433,fun(fun(U_433,bool),bool),member(U_433),hAPP(U_432,U_433,U_431,U_430)),hAPP(fun(U_432,bool),fun(U_433,bool),hAPP(fun(U_432,U_433),fun(fun(U_432,bool),fun(U_433,bool)),image(U_432,U_433),U_431),U_429)))
      | ~ hBOOL(hAPP(fun(U_432,bool),bool,hAPP(U_432,fun(fun(U_432,bool),bool),member(U_432),U_430),U_429)) ),
    inference(definitional_conversion,[status(esa)],[f_165_2]) ).

cnf(f_165_4,plain,
    ( hBOOL(hAPP(fun(U_433,bool),bool,hAPP(U_433,fun(fun(U_433,bool),bool),member(U_433),hAPP(U_432,U_433,U_431,U_430)),hAPP(fun(U_432,bool),fun(U_433,bool),hAPP(fun(U_432,U_433),fun(fun(U_432,bool),fun(U_433,bool)),image(U_432,U_433),U_431),U_429)))
    | ~ hBOOL(hAPP(fun(U_432,bool),bool,hAPP(U_432,fun(fun(U_432,bool),bool),member(U_432),U_430),U_429)) ),
    inference(clausify,[status(thm)],[f_165_3]) ).

fof(f_166_1,plain,
    ! [X_c,X_b,B_3,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_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)))
      | ti(X_c,B_3) != 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_95_rev__image__eqI]) ).

fof(f_166_2,plain,
    ! [U_439,U_438,U_437,U_436,U_435,U_434] :
      ( hBOOL(hAPP(fun(U_439,bool),bool,hAPP(U_439,fun(fun(U_439,bool),bool),member(U_439),U_437),hAPP(fun(U_438,bool),fun(U_439,bool),hAPP(fun(U_438,U_439),fun(fun(U_438,bool),fun(U_439,bool)),image(U_438,U_439),U_436),U_434)))
      | ti(U_439,U_437) != hAPP(U_438,U_439,U_436,U_435)
      | ~ hBOOL(hAPP(fun(U_438,bool),bool,hAPP(U_438,fun(fun(U_438,bool),bool),member(U_438),U_435),U_434)) ),
    inference(variable_rename,[status(thm)],[f_166_1]) ).

fof(f_166_3,plain,
    ! [U_435,U_434,U_436,U_437,U_438,U_439] :
      ( hBOOL(hAPP(fun(U_439,bool),bool,hAPP(U_439,fun(fun(U_439,bool),bool),member(U_439),U_437),hAPP(fun(U_438,bool),fun(U_439,bool),hAPP(fun(U_438,U_439),fun(fun(U_438,bool),fun(U_439,bool)),image(U_438,U_439),U_436),U_434)))
      | ti(U_439,U_437) != hAPP(U_438,U_439,U_436,U_435)
      | ~ hBOOL(hAPP(fun(U_438,bool),bool,hAPP(U_438,fun(fun(U_438,bool),bool),member(U_438),U_435),U_434)) ),
    inference(definitional_conversion,[status(esa)],[f_166_2]) ).

cnf(f_166_4,plain,
    ( hBOOL(hAPP(fun(U_439,bool),bool,hAPP(U_439,fun(fun(U_439,bool),bool),member(U_439),U_437),hAPP(fun(U_438,bool),fun(U_439,bool),hAPP(fun(U_438,U_439),fun(fun(U_438,bool),fun(U_439,bool)),image(U_438,U_439),U_436),U_434)))
    | ti(U_439,U_437) != hAPP(U_438,U_439,U_436,U_435)
    | ~ hBOOL(hAPP(fun(U_438,bool),bool,hAPP(U_438,fun(fun(U_438,bool),bool),member(U_438),U_435),U_434)) ),
    inference(clausify,[status(thm)],[f_166_3]) ).

fof(f_167_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_96_insert__compr__raw]) ).

fof(f_167_2,plain,
    ! [U_442,U_441,U_440] : hAPP(fun(U_442,bool),fun(U_442,bool),hAPP(U_442,fun(fun(U_442,bool),fun(U_442,bool)),insert(U_442),U_441),U_440) = hAPP(fun(U_442,bool),fun(U_442,bool),collect(U_442),hAPP(fun(U_442,bool),fun(U_442,bool),hAPP(fun(U_442,fun(bool,bool)),fun(fun(U_442,bool),fun(U_442,bool)),combs(U_442,bool,bool),hAPP(fun(U_442,bool),fun(U_442,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_442,bool),fun(U_442,fun(bool,bool))),combb(bool,fun(bool,bool),U_442),fdisj),hAPP(U_442,fun(U_442,bool),hAPP(fun(U_442,fun(U_442,bool)),fun(U_442,fun(U_442,bool)),combc(U_442,U_442,bool),fequal(U_442)),U_441))),hAPP(fun(U_442,bool),fun(U_442,bool),hAPP(fun(U_442,fun(fun(U_442,bool),bool)),fun(fun(U_442,bool),fun(U_442,bool)),combc(U_442,fun(U_442,bool),bool),member(U_442)),U_440))),
    inference(variable_rename,[status(thm)],[f_167_1]) ).

fof(f_167_3,plain,
    ! [U_441,U_440,U_442] : hAPP(fun(U_442,bool),fun(U_442,bool),hAPP(U_442,fun(fun(U_442,bool),fun(U_442,bool)),insert(U_442),U_441),U_440) = hAPP(fun(U_442,bool),fun(U_442,bool),collect(U_442),hAPP(fun(U_442,bool),fun(U_442,bool),hAPP(fun(U_442,fun(bool,bool)),fun(fun(U_442,bool),fun(U_442,bool)),combs(U_442,bool,bool),hAPP(fun(U_442,bool),fun(U_442,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_442,bool),fun(U_442,fun(bool,bool))),combb(bool,fun(bool,bool),U_442),fdisj),hAPP(U_442,fun(U_442,bool),hAPP(fun(U_442,fun(U_442,bool)),fun(U_442,fun(U_442,bool)),combc(U_442,U_442,bool),fequal(U_442)),U_441))),hAPP(fun(U_442,bool),fun(U_442,bool),hAPP(fun(U_442,fun(fun(U_442,bool),bool)),fun(fun(U_442,bool),fun(U_442,bool)),combc(U_442,fun(U_442,bool),bool),member(U_442)),U_440))),
    inference(definitional_conversion,[status(esa)],[f_167_2]) ).

cnf(f_167_4,plain,
    hAPP(fun(U_442,bool),fun(U_442,bool),hAPP(U_442,fun(fun(U_442,bool),fun(U_442,bool)),insert(U_442),U_441),U_440) = hAPP(fun(U_442,bool),fun(U_442,bool),collect(U_442),hAPP(fun(U_442,bool),fun(U_442,bool),hAPP(fun(U_442,fun(bool,bool)),fun(fun(U_442,bool),fun(U_442,bool)),combs(U_442,bool,bool),hAPP(fun(U_442,bool),fun(U_442,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_442,bool),fun(U_442,fun(bool,bool))),combb(bool,fun(bool,bool),U_442),fdisj),hAPP(U_442,fun(U_442,bool),hAPP(fun(U_442,fun(U_442,bool)),fun(U_442,fun(U_442,bool)),combc(U_442,U_442,bool),fequal(U_442)),U_441))),hAPP(fun(U_442,bool),fun(U_442,bool),hAPP(fun(U_442,fun(fun(U_442,bool),bool)),fun(fun(U_442,bool),fun(U_442,bool)),combc(U_442,fun(U_442,bool),bool),member(U_442)),U_440))),
    inference(clausify,[status(thm)],[f_167_3]) ).

fof(f_168_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_97_image__image]) ).

fof(f_168_2,plain,
    ! [U_448,U_447,U_446,U_445,U_444,U_443] : hAPP(fun(U_448,bool),fun(U_447,bool),hAPP(fun(U_448,U_447),fun(fun(U_448,bool),fun(U_447,bool)),image(U_448,U_447),U_445),hAPP(fun(U_446,bool),fun(U_448,bool),hAPP(fun(U_446,U_448),fun(fun(U_446,bool),fun(U_448,bool)),image(U_446,U_448),U_444),U_443)) = hAPP(fun(U_446,bool),fun(U_447,bool),hAPP(fun(U_446,U_447),fun(fun(U_446,bool),fun(U_447,bool)),image(U_446,U_447),hAPP(fun(U_446,U_448),fun(U_446,U_447),hAPP(fun(U_448,U_447),fun(fun(U_446,U_448),fun(U_446,U_447)),combb(U_448,U_447,U_446),U_445),U_444)),U_443),
    inference(variable_rename,[status(thm)],[f_168_1]) ).

fof(f_168_3,plain,
    ! [U_445,U_443,U_444,U_446,U_447,U_448] : hAPP(fun(U_448,bool),fun(U_447,bool),hAPP(fun(U_448,U_447),fun(fun(U_448,bool),fun(U_447,bool)),image(U_448,U_447),U_445),hAPP(fun(U_446,bool),fun(U_448,bool),hAPP(fun(U_446,U_448),fun(fun(U_446,bool),fun(U_448,bool)),image(U_446,U_448),U_444),U_443)) = hAPP(fun(U_446,bool),fun(U_447,bool),hAPP(fun(U_446,U_447),fun(fun(U_446,bool),fun(U_447,bool)),image(U_446,U_447),hAPP(fun(U_446,U_448),fun(U_446,U_447),hAPP(fun(U_448,U_447),fun(fun(U_446,U_448),fun(U_446,U_447)),combb(U_448,U_447,U_446),U_445),U_444)),U_443),
    inference(definitional_conversion,[status(esa)],[f_168_2]) ).

cnf(f_168_4,plain,
    hAPP(fun(U_448,bool),fun(U_447,bool),hAPP(fun(U_448,U_447),fun(fun(U_448,bool),fun(U_447,bool)),image(U_448,U_447),U_445),hAPP(fun(U_446,bool),fun(U_448,bool),hAPP(fun(U_446,U_448),fun(fun(U_446,bool),fun(U_448,bool)),image(U_446,U_448),U_444),U_443)) = hAPP(fun(U_446,bool),fun(U_447,bool),hAPP(fun(U_446,U_447),fun(fun(U_446,bool),fun(U_447,bool)),image(U_446,U_447),hAPP(fun(U_446,U_448),fun(U_446,U_447),hAPP(fun(U_448,U_447),fun(fun(U_446,U_448),fun(U_446,U_447)),combb(U_448,U_447,U_446),U_445),U_444)),U_443),
    inference(clausify,[status(thm)],[f_168_3]) ).

fof(f_169_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_98_image__ident]) ).

fof(f_169_2,plain,
    ! [U_450,U_449] : hAPP(fun(U_450,bool),fun(U_450,bool),hAPP(fun(U_450,U_450),fun(fun(U_450,bool),fun(U_450,bool)),image(U_450,U_450),combi(U_450)),U_449) = ti(fun(U_450,bool),U_449),
    inference(variable_rename,[status(thm)],[f_169_1]) ).

fof(f_169_3,plain,
    ! [U_449,U_450] : hAPP(fun(U_450,bool),fun(U_450,bool),hAPP(fun(U_450,U_450),fun(fun(U_450,bool),fun(U_450,bool)),image(U_450,U_450),combi(U_450)),U_449) = ti(fun(U_450,bool),U_449),
    inference(definitional_conversion,[status(esa)],[f_169_2]) ).

cnf(f_169_4,plain,
    hAPP(fun(U_450,bool),fun(U_450,bool),hAPP(fun(U_450,U_450),fun(fun(U_450,bool),fun(U_450,bool)),image(U_450,U_450),combi(U_450)),U_449) = ti(fun(U_450,bool),U_449),
    inference(clausify,[status(thm)],[f_169_3]) ).

fof(f_170_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_99_le__fun__def]) ).

fof(f_170_2,plain,
    ! [U_456,U_455] :
      ( ! [U_454,U_453] :
          ( ( hBOOL(hAPP(fun(U_456,U_455),bool,hAPP(fun(U_456,U_455),fun(fun(U_456,U_455),bool),ord_less_eq(fun(U_456,U_455)),U_454),U_453))
            | ? [U_452] : ~ hBOOL(hAPP(U_455,bool,hAPP(U_455,fun(U_455,bool),ord_less_eq(U_455),hAPP(U_456,U_455,U_454,U_452)),hAPP(U_456,U_455,U_453,U_452))) )
          & ( ! [U_451] : hBOOL(hAPP(U_455,bool,hAPP(U_455,fun(U_455,bool),ord_less_eq(U_455),hAPP(U_456,U_455,U_454,U_451)),hAPP(U_456,U_455,U_453,U_451)))
            | ~ hBOOL(hAPP(fun(U_456,U_455),bool,hAPP(fun(U_456,U_455),fun(fun(U_456,U_455),bool),ord_less_eq(fun(U_456,U_455)),U_454),U_453)) ) )
      | ~ ord(U_455) ),
    inference(variable_rename,[status(thm)],[f_170_1]) ).

fof(f_170_3,plain,
    ! [U_456,U_455] :
      ( ( ! [U_460,U_458] :
            ( hBOOL(hAPP(fun(U_456,U_455),bool,hAPP(fun(U_456,U_455),fun(fun(U_456,U_455),bool),ord_less_eq(fun(U_456,U_455)),U_460),U_458))
            | ? [U_452] : ~ hBOOL(hAPP(U_455,bool,hAPP(U_455,fun(U_455,bool),ord_less_eq(U_455),hAPP(U_456,U_455,U_460,U_452)),hAPP(U_456,U_455,U_458,U_452))) )
        & ! [U_459,U_457] :
            ( ! [U_451] : hBOOL(hAPP(U_455,bool,hAPP(U_455,fun(U_455,bool),ord_less_eq(U_455),hAPP(U_456,U_455,U_459,U_451)),hAPP(U_456,U_455,U_457,U_451)))
            | ~ hBOOL(hAPP(fun(U_456,U_455),bool,hAPP(fun(U_456,U_455),fun(fun(U_456,U_455),bool),ord_less_eq(fun(U_456,U_455)),U_459),U_457)) ) )
      | ~ ord(U_455) ),
    inference(miniscope,[status(thm)],[f_170_2]) ).

fof(f_170_4,plain,
    ! [U_456,U_455] :
      ( ( ! [U_460,U_458] :
            ( hBOOL(hAPP(fun(U_456,U_455),bool,hAPP(fun(U_456,U_455),fun(fun(U_456,U_455),bool),ord_less_eq(fun(U_456,U_455)),U_460),U_458))
            | ~ hBOOL(hAPP(U_455,bool,hAPP(U_455,fun(U_455,bool),ord_less_eq(U_455),hAPP(U_456,U_455,U_460,sK8(U_456,U_455,U_460,U_458))),hAPP(U_456,U_455,U_458,sK8(U_456,U_455,U_460,U_458)))) )
        & ! [U_459,U_457] :
            ( ! [U_451] : hBOOL(hAPP(U_455,bool,hAPP(U_455,fun(U_455,bool),ord_less_eq(U_455),hAPP(U_456,U_455,U_459,U_451)),hAPP(U_456,U_455,U_457,U_451)))
            | ~ hBOOL(hAPP(fun(U_456,U_455),bool,hAPP(fun(U_456,U_455),fun(fun(U_456,U_455),bool),ord_less_eq(fun(U_456,U_455)),U_459),U_457)) ) )
      | ~ ord(U_455) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_452,sK8(U_456,U_455,U_460,U_458))],[f_170_3]) ).

fof(f_170_5,plain,
    ( ! [U_460,U_455,U_451,U_456,U_458,U_457,U_459] :
        ( hBOOL(hAPP(fun(U_456,U_455),bool,hAPP(fun(U_456,U_455),fun(fun(U_456,U_455),bool),ord_less_eq(fun(U_456,U_455)),U_460),U_458))
        | ~ hBOOL(hAPP(U_455,bool,hAPP(U_455,fun(U_455,bool),ord_less_eq(U_455),hAPP(U_456,U_455,U_460,sK8(U_456,U_455,U_460,U_458))),hAPP(U_456,U_455,U_458,sK8(U_456,U_455,U_460,U_458))))
        | ~ sP19(U_460,U_455,U_451,U_456,U_458,U_457,U_459) )
    & ! [U_460,U_455,U_451,U_456,U_458,U_457,U_459] :
        ( hBOOL(hAPP(U_455,bool,hAPP(U_455,fun(U_455,bool),ord_less_eq(U_455),hAPP(U_456,U_455,U_459,U_451)),hAPP(U_456,U_455,U_457,U_451)))
        | ~ hBOOL(hAPP(fun(U_456,U_455),bool,hAPP(fun(U_456,U_455),fun(fun(U_456,U_455),bool),ord_less_eq(fun(U_456,U_455)),U_459),U_457))
        | ~ sP19(U_460,U_455,U_451,U_456,U_458,U_457,U_459) )
    & ! [U_460,U_455,U_451,U_456,U_458,U_457,U_459] :
        ( sP19(U_460,U_455,U_451,U_456,U_458,U_457,U_459)
        | ~ ord(U_455) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP19])],[f_170_4]) ).

cnf(f_170_6,plain,
    ( sP19(U_460,U_455,U_451,U_456,U_458,U_457,U_459)
    | ~ ord(U_455) ),
    inference(clausify,[status(thm)],[f_170_5]) ).

cnf(f_170_7,plain,
    ( hBOOL(hAPP(U_455,bool,hAPP(U_455,fun(U_455,bool),ord_less_eq(U_455),hAPP(U_456,U_455,U_459,U_451)),hAPP(U_456,U_455,U_457,U_451)))
    | ~ hBOOL(hAPP(fun(U_456,U_455),bool,hAPP(fun(U_456,U_455),fun(fun(U_456,U_455),bool),ord_less_eq(fun(U_456,U_455)),U_459),U_457))
    | ~ sP19(U_460,U_455,U_451,U_456,U_458,U_457,U_459) ),
    inference(clausify,[status(thm)],[f_170_5]) ).

cnf(f_170_8,plain,
    ( hBOOL(hAPP(fun(U_456,U_455),bool,hAPP(fun(U_456,U_455),fun(fun(U_456,U_455),bool),ord_less_eq(fun(U_456,U_455)),U_460),U_458))
    | ~ hBOOL(hAPP(U_455,bool,hAPP(U_455,fun(U_455,bool),ord_less_eq(U_455),hAPP(U_456,U_455,U_460,sK8(U_456,U_455,U_460,U_458))),hAPP(U_456,U_455,U_458,sK8(U_456,U_455,U_460,U_458))))
    | ~ sP19(U_460,U_455,U_451,U_456,U_458,U_457,U_459) ),
    inference(clausify,[status(thm)],[f_170_5]) ).

fof(f_171_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_100_le__funD]) ).

fof(f_171_2,plain,
    ! [U_465,U_464] :
      ( ! [U_463,U_462,U_461] :
          ( hBOOL(hAPP(U_464,bool,hAPP(U_464,fun(U_464,bool),ord_less_eq(U_464),hAPP(U_465,U_464,U_462,U_463)),hAPP(U_465,U_464,U_461,U_463)))
          | ~ hBOOL(hAPP(fun(U_465,U_464),bool,hAPP(fun(U_465,U_464),fun(fun(U_465,U_464),bool),ord_less_eq(fun(U_465,U_464)),U_462),U_461)) )
      | ~ ord(U_464) ),
    inference(variable_rename,[status(thm)],[f_171_1]) ).

fof(f_171_3,plain,
    ! [U_461,U_462,U_464,U_463,U_465] :
      ( hBOOL(hAPP(U_464,bool,hAPP(U_464,fun(U_464,bool),ord_less_eq(U_464),hAPP(U_465,U_464,U_462,U_463)),hAPP(U_465,U_464,U_461,U_463)))
      | ~ hBOOL(hAPP(fun(U_465,U_464),bool,hAPP(fun(U_465,U_464),fun(fun(U_465,U_464),bool),ord_less_eq(fun(U_465,U_464)),U_462),U_461))
      | ~ ord(U_464) ),
    inference(definitional_conversion,[status(esa)],[f_171_2]) ).

cnf(f_171_4,plain,
    ( hBOOL(hAPP(U_464,bool,hAPP(U_464,fun(U_464,bool),ord_less_eq(U_464),hAPP(U_465,U_464,U_462,U_463)),hAPP(U_465,U_464,U_461,U_463)))
    | ~ hBOOL(hAPP(fun(U_465,U_464),bool,hAPP(fun(U_465,U_464),fun(fun(U_465,U_464),bool),ord_less_eq(fun(U_465,U_464)),U_462),U_461))
    | ~ ord(U_464) ),
    inference(clausify,[status(thm)],[f_171_3]) ).

fof(f_172_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__funE]) ).

fof(f_172_2,plain,
    ! [U_470,U_469] :
      ( ! [U_468,U_467,U_466] :
          ( hBOOL(hAPP(U_469,bool,hAPP(U_469,fun(U_469,bool),ord_less_eq(U_469),hAPP(U_470,U_469,U_467,U_468)),hAPP(U_470,U_469,U_466,U_468)))
          | ~ hBOOL(hAPP(fun(U_470,U_469),bool,hAPP(fun(U_470,U_469),fun(fun(U_470,U_469),bool),ord_less_eq(fun(U_470,U_469)),U_467),U_466)) )
      | ~ ord(U_469) ),
    inference(variable_rename,[status(thm)],[f_172_1]) ).

fof(f_172_3,plain,
    ! [U_466,U_469,U_467,U_468,U_470] :
      ( hBOOL(hAPP(U_469,bool,hAPP(U_469,fun(U_469,bool),ord_less_eq(U_469),hAPP(U_470,U_469,U_467,U_468)),hAPP(U_470,U_469,U_466,U_468)))
      | ~ hBOOL(hAPP(fun(U_470,U_469),bool,hAPP(fun(U_470,U_469),fun(fun(U_470,U_469),bool),ord_less_eq(fun(U_470,U_469)),U_467),U_466))
      | ~ ord(U_469) ),
    inference(definitional_conversion,[status(esa)],[f_172_2]) ).

cnf(f_172_4,plain,
    ( hBOOL(hAPP(U_469,bool,hAPP(U_469,fun(U_469,bool),ord_less_eq(U_469),hAPP(U_470,U_469,U_467,U_468)),hAPP(U_470,U_469,U_466,U_468)))
    | ~ hBOOL(hAPP(fun(U_470,U_469),bool,hAPP(fun(U_470,U_469),fun(fun(U_470,U_469),bool),ord_less_eq(fun(U_470,U_469)),U_467),U_466))
    | ~ ord(U_469) ),
    inference(clausify,[status(thm)],[f_172_3]) ).

fof(f_173_1,plain,
    ! [X_b,B_1,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_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),B_1))),
    inference(fof_nnf,[status(thm)],[fact_102_subset__insertI]) ).

fof(f_173_2,plain,
    ! [U_473,U_472,U_471] : hBOOL(hAPP(fun(U_473,bool),bool,hAPP(fun(U_473,bool),fun(fun(U_473,bool),bool),ord_less_eq(fun(U_473,bool)),U_472),hAPP(fun(U_473,bool),fun(U_473,bool),hAPP(U_473,fun(fun(U_473,bool),fun(U_473,bool)),insert(U_473),U_471),U_472))),
    inference(variable_rename,[status(thm)],[f_173_1]) ).

fof(f_173_3,plain,
    ! [U_472,U_471,U_473] : hBOOL(hAPP(fun(U_473,bool),bool,hAPP(fun(U_473,bool),fun(fun(U_473,bool),bool),ord_less_eq(fun(U_473,bool)),U_472),hAPP(fun(U_473,bool),fun(U_473,bool),hAPP(U_473,fun(fun(U_473,bool),fun(U_473,bool)),insert(U_473),U_471),U_472))),
    inference(definitional_conversion,[status(esa)],[f_173_2]) ).

cnf(f_173_4,plain,
    hBOOL(hAPP(fun(U_473,bool),bool,hAPP(fun(U_473,bool),fun(fun(U_473,bool),bool),ord_less_eq(fun(U_473,bool)),U_472),hAPP(fun(U_473,bool),fun(U_473,bool),hAPP(U_473,fun(fun(U_473,bool),fun(U_473,bool)),insert(U_473),U_471),U_472))),
    inference(clausify,[status(thm)],[f_173_3]) ).

fof(f_174_1,plain,
    ! [X_b,X_1,A_3,B_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)),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_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),B_1))
        | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_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),B_1))
          & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_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)),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_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_103_insert__subset]) ).

fof(f_174_2,plain,
    ! [U_477,U_476,U_475,U_474] :
      ( ( hBOOL(hAPP(fun(U_477,bool),bool,hAPP(fun(U_477,bool),fun(fun(U_477,bool),bool),ord_less_eq(fun(U_477,bool)),hAPP(fun(U_477,bool),fun(U_477,bool),hAPP(U_477,fun(fun(U_477,bool),fun(U_477,bool)),insert(U_477),U_476),U_475)),U_474))
        | ~ hBOOL(hAPP(fun(U_477,bool),bool,hAPP(fun(U_477,bool),fun(fun(U_477,bool),bool),ord_less_eq(fun(U_477,bool)),U_475),U_474))
        | ~ hBOOL(hAPP(fun(U_477,bool),bool,hAPP(U_477,fun(fun(U_477,bool),bool),member(U_477),U_476),U_474)) )
      & ( ( hBOOL(hAPP(fun(U_477,bool),bool,hAPP(fun(U_477,bool),fun(fun(U_477,bool),bool),ord_less_eq(fun(U_477,bool)),U_475),U_474))
          & hBOOL(hAPP(fun(U_477,bool),bool,hAPP(U_477,fun(fun(U_477,bool),bool),member(U_477),U_476),U_474)) )
        | ~ hBOOL(hAPP(fun(U_477,bool),bool,hAPP(fun(U_477,bool),fun(fun(U_477,bool),bool),ord_less_eq(fun(U_477,bool)),hAPP(fun(U_477,bool),fun(U_477,bool),hAPP(U_477,fun(fun(U_477,bool),fun(U_477,bool)),insert(U_477),U_476),U_475)),U_474)) ) ),
    inference(variable_rename,[status(thm)],[f_174_1]) ).

fof(f_174_3,plain,
    ( ! [U_485,U_483,U_481,U_479] :
        ( hBOOL(hAPP(fun(U_485,bool),bool,hAPP(fun(U_485,bool),fun(fun(U_485,bool),bool),ord_less_eq(fun(U_485,bool)),hAPP(fun(U_485,bool),fun(U_485,bool),hAPP(U_485,fun(fun(U_485,bool),fun(U_485,bool)),insert(U_485),U_483),U_481)),U_479))
        | ~ hBOOL(hAPP(fun(U_485,bool),bool,hAPP(fun(U_485,bool),fun(fun(U_485,bool),bool),ord_less_eq(fun(U_485,bool)),U_481),U_479))
        | ~ hBOOL(hAPP(fun(U_485,bool),bool,hAPP(U_485,fun(fun(U_485,bool),bool),member(U_485),U_483),U_479)) )
    & ! [U_484,U_482,U_480,U_478] :
        ( ( hBOOL(hAPP(fun(U_484,bool),bool,hAPP(fun(U_484,bool),fun(fun(U_484,bool),bool),ord_less_eq(fun(U_484,bool)),U_480),U_478))
          & hBOOL(hAPP(fun(U_484,bool),bool,hAPP(U_484,fun(fun(U_484,bool),bool),member(U_484),U_482),U_478)) )
        | ~ hBOOL(hAPP(fun(U_484,bool),bool,hAPP(fun(U_484,bool),fun(fun(U_484,bool),bool),ord_less_eq(fun(U_484,bool)),hAPP(fun(U_484,bool),fun(U_484,bool),hAPP(U_484,fun(fun(U_484,bool),fun(U_484,bool)),insert(U_484),U_482),U_480)),U_478)) ) ),
    inference(miniscope,[status(thm)],[f_174_2]) ).

fof(f_174_4,plain,
    ( ! [U_480,U_484,U_478,U_482] :
        ( hBOOL(hAPP(fun(U_484,bool),bool,hAPP(fun(U_484,bool),fun(fun(U_484,bool),bool),ord_less_eq(fun(U_484,bool)),U_480),U_478))
        | ~ sP20(U_480,U_484,U_478,U_482) )
    & ! [U_480,U_484,U_478,U_482] :
        ( hBOOL(hAPP(fun(U_484,bool),bool,hAPP(U_484,fun(fun(U_484,bool),bool),member(U_484),U_482),U_478))
        | ~ sP20(U_480,U_484,U_478,U_482) )
    & ! [U_479,U_481,U_483,U_485] :
        ( hBOOL(hAPP(fun(U_485,bool),bool,hAPP(fun(U_485,bool),fun(fun(U_485,bool),bool),ord_less_eq(fun(U_485,bool)),hAPP(fun(U_485,bool),fun(U_485,bool),hAPP(U_485,fun(fun(U_485,bool),fun(U_485,bool)),insert(U_485),U_483),U_481)),U_479))
        | ~ hBOOL(hAPP(fun(U_485,bool),bool,hAPP(fun(U_485,bool),fun(fun(U_485,bool),bool),ord_less_eq(fun(U_485,bool)),U_481),U_479))
        | ~ hBOOL(hAPP(fun(U_485,bool),bool,hAPP(U_485,fun(fun(U_485,bool),bool),member(U_485),U_483),U_479)) )
    & ! [U_480,U_484,U_478,U_482] :
        ( sP20(U_480,U_484,U_478,U_482)
        | ~ hBOOL(hAPP(fun(U_484,bool),bool,hAPP(fun(U_484,bool),fun(fun(U_484,bool),bool),ord_less_eq(fun(U_484,bool)),hAPP(fun(U_484,bool),fun(U_484,bool),hAPP(U_484,fun(fun(U_484,bool),fun(U_484,bool)),insert(U_484),U_482),U_480)),U_478)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP20])],[f_174_3]) ).

cnf(f_174_5,plain,
    ( sP20(U_480,U_484,U_478,U_482)
    | ~ hBOOL(hAPP(fun(U_484,bool),bool,hAPP(fun(U_484,bool),fun(fun(U_484,bool),bool),ord_less_eq(fun(U_484,bool)),hAPP(fun(U_484,bool),fun(U_484,bool),hAPP(U_484,fun(fun(U_484,bool),fun(U_484,bool)),insert(U_484),U_482),U_480)),U_478)) ),
    inference(clausify,[status(thm)],[f_174_4]) ).

cnf(f_174_6,plain,
    ( hBOOL(hAPP(fun(U_485,bool),bool,hAPP(fun(U_485,bool),fun(fun(U_485,bool),bool),ord_less_eq(fun(U_485,bool)),hAPP(fun(U_485,bool),fun(U_485,bool),hAPP(U_485,fun(fun(U_485,bool),fun(U_485,bool)),insert(U_485),U_483),U_481)),U_479))
    | ~ hBOOL(hAPP(fun(U_485,bool),bool,hAPP(fun(U_485,bool),fun(fun(U_485,bool),bool),ord_less_eq(fun(U_485,bool)),U_481),U_479))
    | ~ hBOOL(hAPP(fun(U_485,bool),bool,hAPP(U_485,fun(fun(U_485,bool),bool),member(U_485),U_483),U_479)) ),
    inference(clausify,[status(thm)],[f_174_4]) ).

cnf(f_174_7,plain,
    ( hBOOL(hAPP(fun(U_484,bool),bool,hAPP(U_484,fun(fun(U_484,bool),bool),member(U_484),U_482),U_478))
    | ~ sP20(U_480,U_484,U_478,U_482) ),
    inference(clausify,[status(thm)],[f_174_4]) ).

cnf(f_174_8,plain,
    ( hBOOL(hAPP(fun(U_484,bool),bool,hAPP(fun(U_484,bool),fun(fun(U_484,bool),bool),ord_less_eq(fun(U_484,bool)),U_480),U_478))
    | ~ sP20(U_480,U_484,U_478,U_482) ),
    inference(clausify,[status(thm)],[f_174_4]) ).

fof(f_175_1,plain,
    ! [X_b,B_1,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_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),B_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),B_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),B_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_104_subset__insert]) ).

fof(f_175_2,plain,
    ! [U_489,U_488,U_487,U_486] :
      ( ( ( hBOOL(hAPP(fun(U_489,bool),bool,hAPP(fun(U_489,bool),fun(fun(U_489,bool),bool),ord_less_eq(fun(U_489,bool)),U_486),hAPP(fun(U_489,bool),fun(U_489,bool),hAPP(U_489,fun(fun(U_489,bool),fun(U_489,bool)),insert(U_489),U_487),U_488)))
          | ~ hBOOL(hAPP(fun(U_489,bool),bool,hAPP(fun(U_489,bool),fun(fun(U_489,bool),bool),ord_less_eq(fun(U_489,bool)),U_486),U_488)) )
        & ( hBOOL(hAPP(fun(U_489,bool),bool,hAPP(fun(U_489,bool),fun(fun(U_489,bool),bool),ord_less_eq(fun(U_489,bool)),U_486),U_488))
          | ~ hBOOL(hAPP(fun(U_489,bool),bool,hAPP(fun(U_489,bool),fun(fun(U_489,bool),bool),ord_less_eq(fun(U_489,bool)),U_486),hAPP(fun(U_489,bool),fun(U_489,bool),hAPP(U_489,fun(fun(U_489,bool),fun(U_489,bool)),insert(U_489),U_487),U_488))) ) )
      | hBOOL(hAPP(fun(U_489,bool),bool,hAPP(U_489,fun(fun(U_489,bool),bool),member(U_489),U_487),U_486)) ),
    inference(variable_rename,[status(thm)],[f_175_1]) ).

fof(f_175_3,plain,
    ( ! [U_486,U_487,U_488,U_489] :
        ( hBOOL(hAPP(fun(U_489,bool),bool,hAPP(fun(U_489,bool),fun(fun(U_489,bool),bool),ord_less_eq(fun(U_489,bool)),U_486),hAPP(fun(U_489,bool),fun(U_489,bool),hAPP(U_489,fun(fun(U_489,bool),fun(U_489,bool)),insert(U_489),U_487),U_488)))
        | ~ hBOOL(hAPP(fun(U_489,bool),bool,hAPP(fun(U_489,bool),fun(fun(U_489,bool),bool),ord_less_eq(fun(U_489,bool)),U_486),U_488))
        | ~ sP21(U_486,U_487,U_488,U_489) )
    & ! [U_486,U_487,U_488,U_489] :
        ( hBOOL(hAPP(fun(U_489,bool),bool,hAPP(fun(U_489,bool),fun(fun(U_489,bool),bool),ord_less_eq(fun(U_489,bool)),U_486),U_488))
        | ~ hBOOL(hAPP(fun(U_489,bool),bool,hAPP(fun(U_489,bool),fun(fun(U_489,bool),bool),ord_less_eq(fun(U_489,bool)),U_486),hAPP(fun(U_489,bool),fun(U_489,bool),hAPP(U_489,fun(fun(U_489,bool),fun(U_489,bool)),insert(U_489),U_487),U_488)))
        | ~ sP21(U_486,U_487,U_488,U_489) )
    & ! [U_486,U_487,U_488,U_489] :
        ( sP21(U_486,U_487,U_488,U_489)
        | hBOOL(hAPP(fun(U_489,bool),bool,hAPP(U_489,fun(fun(U_489,bool),bool),member(U_489),U_487),U_486)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP21])],[f_175_2]) ).

cnf(f_175_4,plain,
    ( sP21(U_486,U_487,U_488,U_489)
    | hBOOL(hAPP(fun(U_489,bool),bool,hAPP(U_489,fun(fun(U_489,bool),bool),member(U_489),U_487),U_486)) ),
    inference(clausify,[status(thm)],[f_175_3]) ).

cnf(f_175_5,plain,
    ( hBOOL(hAPP(fun(U_489,bool),bool,hAPP(fun(U_489,bool),fun(fun(U_489,bool),bool),ord_less_eq(fun(U_489,bool)),U_486),U_488))
    | ~ hBOOL(hAPP(fun(U_489,bool),bool,hAPP(fun(U_489,bool),fun(fun(U_489,bool),bool),ord_less_eq(fun(U_489,bool)),U_486),hAPP(fun(U_489,bool),fun(U_489,bool),hAPP(U_489,fun(fun(U_489,bool),fun(U_489,bool)),insert(U_489),U_487),U_488)))
    | ~ sP21(U_486,U_487,U_488,U_489) ),
    inference(clausify,[status(thm)],[f_175_3]) ).

cnf(f_175_6,plain,
    ( hBOOL(hAPP(fun(U_489,bool),bool,hAPP(fun(U_489,bool),fun(fun(U_489,bool),bool),ord_less_eq(fun(U_489,bool)),U_486),hAPP(fun(U_489,bool),fun(U_489,bool),hAPP(U_489,fun(fun(U_489,bool),fun(U_489,bool)),insert(U_489),U_487),U_488)))
    | ~ hBOOL(hAPP(fun(U_489,bool),bool,hAPP(fun(U_489,bool),fun(fun(U_489,bool),bool),ord_less_eq(fun(U_489,bool)),U_486),U_488))
    | ~ sP21(U_486,U_487,U_488,U_489) ),
    inference(clausify,[status(thm)],[f_175_3]) ).

fof(f_176_1,plain,
    ! [X_b,B_3,A_3,B_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),B_3),B_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),B_1)) ),
    inference(fof_nnf,[status(thm)],[fact_105_subset__insertI2]) ).

fof(f_176_2,plain,
    ! [U_493,U_492,U_491,U_490] :
      ( hBOOL(hAPP(fun(U_493,bool),bool,hAPP(fun(U_493,bool),fun(fun(U_493,bool),bool),ord_less_eq(fun(U_493,bool)),U_491),hAPP(fun(U_493,bool),fun(U_493,bool),hAPP(U_493,fun(fun(U_493,bool),fun(U_493,bool)),insert(U_493),U_492),U_490)))
      | ~ hBOOL(hAPP(fun(U_493,bool),bool,hAPP(fun(U_493,bool),fun(fun(U_493,bool),bool),ord_less_eq(fun(U_493,bool)),U_491),U_490)) ),
    inference(variable_rename,[status(thm)],[f_176_1]) ).

fof(f_176_3,plain,
    ! [U_492,U_490,U_491,U_493] :
      ( hBOOL(hAPP(fun(U_493,bool),bool,hAPP(fun(U_493,bool),fun(fun(U_493,bool),bool),ord_less_eq(fun(U_493,bool)),U_491),hAPP(fun(U_493,bool),fun(U_493,bool),hAPP(U_493,fun(fun(U_493,bool),fun(U_493,bool)),insert(U_493),U_492),U_490)))
      | ~ hBOOL(hAPP(fun(U_493,bool),bool,hAPP(fun(U_493,bool),fun(fun(U_493,bool),bool),ord_less_eq(fun(U_493,bool)),U_491),U_490)) ),
    inference(definitional_conversion,[status(esa)],[f_176_2]) ).

cnf(f_176_4,plain,
    ( hBOOL(hAPP(fun(U_493,bool),bool,hAPP(fun(U_493,bool),fun(fun(U_493,bool),bool),ord_less_eq(fun(U_493,bool)),U_491),hAPP(fun(U_493,bool),fun(U_493,bool),hAPP(U_493,fun(fun(U_493,bool),fun(U_493,bool)),insert(U_493),U_492),U_490)))
    | ~ hBOOL(hAPP(fun(U_493,bool),bool,hAPP(fun(U_493,bool),fun(fun(U_493,bool),bool),ord_less_eq(fun(U_493,bool)),U_491),U_490)) ),
    inference(clausify,[status(thm)],[f_176_3]) ).

fof(f_177_1,plain,
    ! [X_b,A_2,C_2,D_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(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_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)),C_2),D_3)) ),
    inference(fof_nnf,[status(thm)],[fact_106_insert__mono]) ).

fof(f_177_2,plain,
    ! [U_497,U_496,U_495,U_494] :
      ( hBOOL(hAPP(fun(U_497,bool),bool,hAPP(fun(U_497,bool),fun(fun(U_497,bool),bool),ord_less_eq(fun(U_497,bool)),hAPP(fun(U_497,bool),fun(U_497,bool),hAPP(U_497,fun(fun(U_497,bool),fun(U_497,bool)),insert(U_497),U_496),U_495)),hAPP(fun(U_497,bool),fun(U_497,bool),hAPP(U_497,fun(fun(U_497,bool),fun(U_497,bool)),insert(U_497),U_496),U_494)))
      | ~ hBOOL(hAPP(fun(U_497,bool),bool,hAPP(fun(U_497,bool),fun(fun(U_497,bool),bool),ord_less_eq(fun(U_497,bool)),U_495),U_494)) ),
    inference(variable_rename,[status(thm)],[f_177_1]) ).

fof(f_177_3,plain,
    ! [U_497,U_494,U_495,U_496] :
      ( hBOOL(hAPP(fun(U_497,bool),bool,hAPP(fun(U_497,bool),fun(fun(U_497,bool),bool),ord_less_eq(fun(U_497,bool)),hAPP(fun(U_497,bool),fun(U_497,bool),hAPP(U_497,fun(fun(U_497,bool),fun(U_497,bool)),insert(U_497),U_496),U_495)),hAPP(fun(U_497,bool),fun(U_497,bool),hAPP(U_497,fun(fun(U_497,bool),fun(U_497,bool)),insert(U_497),U_496),U_494)))
      | ~ hBOOL(hAPP(fun(U_497,bool),bool,hAPP(fun(U_497,bool),fun(fun(U_497,bool),bool),ord_less_eq(fun(U_497,bool)),U_495),U_494)) ),
    inference(definitional_conversion,[status(esa)],[f_177_2]) ).

cnf(f_177_4,plain,
    ( hBOOL(hAPP(fun(U_497,bool),bool,hAPP(fun(U_497,bool),fun(fun(U_497,bool),bool),ord_less_eq(fun(U_497,bool)),hAPP(fun(U_497,bool),fun(U_497,bool),hAPP(U_497,fun(fun(U_497,bool),fun(U_497,bool)),insert(U_497),U_496),U_495)),hAPP(fun(U_497,bool),fun(U_497,bool),hAPP(U_497,fun(fun(U_497,bool),fun(U_497,bool)),insert(U_497),U_496),U_494)))
    | ~ hBOOL(hAPP(fun(U_497,bool),bool,hAPP(fun(U_497,bool),fun(fun(U_497,bool),bool),ord_less_eq(fun(U_497,bool)),U_495),U_494)) ),
    inference(clausify,[status(thm)],[f_177_3]) ).

fof(f_178_1,plain,
    ! [X_c,X_b,F,A_2,B_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),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_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),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_1)),
    inference(fof_nnf,[status(thm)],[fact_107_image__insert]) ).

fof(f_178_2,plain,
    ! [U_502,U_501,U_500,U_499,U_498] : hAPP(fun(U_502,bool),fun(U_501,bool),hAPP(fun(U_502,U_501),fun(fun(U_502,bool),fun(U_501,bool)),image(U_502,U_501),U_500),hAPP(fun(U_502,bool),fun(U_502,bool),hAPP(U_502,fun(fun(U_502,bool),fun(U_502,bool)),insert(U_502),U_499),U_498)) = hAPP(fun(U_501,bool),fun(U_501,bool),hAPP(U_501,fun(fun(U_501,bool),fun(U_501,bool)),insert(U_501),hAPP(U_502,U_501,U_500,U_499)),hAPP(fun(U_502,bool),fun(U_501,bool),hAPP(fun(U_502,U_501),fun(fun(U_502,bool),fun(U_501,bool)),image(U_502,U_501),U_500),U_498)),
    inference(variable_rename,[status(thm)],[f_178_1]) ).

fof(f_178_3,plain,
    ! [U_498,U_501,U_500,U_499,U_502] : hAPP(fun(U_502,bool),fun(U_501,bool),hAPP(fun(U_502,U_501),fun(fun(U_502,bool),fun(U_501,bool)),image(U_502,U_501),U_500),hAPP(fun(U_502,bool),fun(U_502,bool),hAPP(U_502,fun(fun(U_502,bool),fun(U_502,bool)),insert(U_502),U_499),U_498)) = hAPP(fun(U_501,bool),fun(U_501,bool),hAPP(U_501,fun(fun(U_501,bool),fun(U_501,bool)),insert(U_501),hAPP(U_502,U_501,U_500,U_499)),hAPP(fun(U_502,bool),fun(U_501,bool),hAPP(fun(U_502,U_501),fun(fun(U_502,bool),fun(U_501,bool)),image(U_502,U_501),U_500),U_498)),
    inference(definitional_conversion,[status(esa)],[f_178_2]) ).

cnf(f_178_4,plain,
    hAPP(fun(U_502,bool),fun(U_501,bool),hAPP(fun(U_502,U_501),fun(fun(U_502,bool),fun(U_501,bool)),image(U_502,U_501),U_500),hAPP(fun(U_502,bool),fun(U_502,bool),hAPP(U_502,fun(fun(U_502,bool),fun(U_502,bool)),insert(U_502),U_499),U_498)) = hAPP(fun(U_501,bool),fun(U_501,bool),hAPP(U_501,fun(fun(U_501,bool),fun(U_501,bool)),insert(U_501),hAPP(U_502,U_501,U_500,U_499)),hAPP(fun(U_502,bool),fun(U_501,bool),hAPP(fun(U_502,U_501),fun(fun(U_502,bool),fun(U_501,bool)),image(U_502,U_501),U_500),U_498)),
    inference(clausify,[status(thm)],[f_178_3]) ).

fof(f_179_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_108_insert__image]) ).

fof(f_179_2,plain,
    ! [U_507,U_506,U_505,U_504,U_503] :
      ( hAPP(fun(U_507,bool),fun(U_507,bool),hAPP(U_507,fun(fun(U_507,bool),fun(U_507,bool)),insert(U_507),hAPP(U_506,U_507,U_505,U_504)),hAPP(fun(U_506,bool),fun(U_507,bool),hAPP(fun(U_506,U_507),fun(fun(U_506,bool),fun(U_507,bool)),image(U_506,U_507),U_505),U_503)) = hAPP(fun(U_506,bool),fun(U_507,bool),hAPP(fun(U_506,U_507),fun(fun(U_506,bool),fun(U_507,bool)),image(U_506,U_507),U_505),U_503)
      | ~ hBOOL(hAPP(fun(U_506,bool),bool,hAPP(U_506,fun(fun(U_506,bool),bool),member(U_506),U_504),U_503)) ),
    inference(variable_rename,[status(thm)],[f_179_1]) ).

fof(f_179_3,plain,
    ! [U_504,U_503,U_506,U_505,U_507] :
      ( hAPP(fun(U_507,bool),fun(U_507,bool),hAPP(U_507,fun(fun(U_507,bool),fun(U_507,bool)),insert(U_507),hAPP(U_506,U_507,U_505,U_504)),hAPP(fun(U_506,bool),fun(U_507,bool),hAPP(fun(U_506,U_507),fun(fun(U_506,bool),fun(U_507,bool)),image(U_506,U_507),U_505),U_503)) = hAPP(fun(U_506,bool),fun(U_507,bool),hAPP(fun(U_506,U_507),fun(fun(U_506,bool),fun(U_507,bool)),image(U_506,U_507),U_505),U_503)
      | ~ hBOOL(hAPP(fun(U_506,bool),bool,hAPP(U_506,fun(fun(U_506,bool),bool),member(U_506),U_504),U_503)) ),
    inference(definitional_conversion,[status(esa)],[f_179_2]) ).

cnf(f_179_4,plain,
    ( hAPP(fun(U_507,bool),fun(U_507,bool),hAPP(U_507,fun(fun(U_507,bool),fun(U_507,bool)),insert(U_507),hAPP(U_506,U_507,U_505,U_504)),hAPP(fun(U_506,bool),fun(U_507,bool),hAPP(fun(U_506,U_507),fun(fun(U_506,bool),fun(U_507,bool)),image(U_506,U_507),U_505),U_503)) = hAPP(fun(U_506,bool),fun(U_507,bool),hAPP(fun(U_506,U_507),fun(fun(U_506,bool),fun(U_507,bool)),image(U_506,U_507),U_505),U_503)
    | ~ hBOOL(hAPP(fun(U_506,bool),bool,hAPP(U_506,fun(fun(U_506,bool),bool),member(U_506),U_504),U_503)) ),
    inference(clausify,[status(thm)],[f_179_3]) ).

fof(f_180_1,plain,
    ! [X_b,X_c,B_1,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_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)))
        | ! [AA] :
            ( ti(fun(X_b,bool),B_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),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_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),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_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_109_subset__image__iff]) ).

fof(f_180_2,plain,
    ! [U_514,U_513,U_512,U_511,U_510] :
      ( ( hBOOL(hAPP(fun(U_514,bool),bool,hAPP(fun(U_514,bool),fun(fun(U_514,bool),bool),ord_less_eq(fun(U_514,bool)),U_512),hAPP(fun(U_513,bool),fun(U_514,bool),hAPP(fun(U_513,U_514),fun(fun(U_513,bool),fun(U_514,bool)),image(U_513,U_514),U_511),U_510)))
        | ! [U_509] :
            ( ti(fun(U_514,bool),U_512) != hAPP(fun(U_513,bool),fun(U_514,bool),hAPP(fun(U_513,U_514),fun(fun(U_513,bool),fun(U_514,bool)),image(U_513,U_514),U_511),U_509)
            | ~ hBOOL(hAPP(fun(U_513,bool),bool,hAPP(fun(U_513,bool),fun(fun(U_513,bool),bool),ord_less_eq(fun(U_513,bool)),U_509),U_510)) ) )
      & ( ? [U_508] :
            ( ti(fun(U_514,bool),U_512) = hAPP(fun(U_513,bool),fun(U_514,bool),hAPP(fun(U_513,U_514),fun(fun(U_513,bool),fun(U_514,bool)),image(U_513,U_514),U_511),U_508)
            & hBOOL(hAPP(fun(U_513,bool),bool,hAPP(fun(U_513,bool),fun(fun(U_513,bool),bool),ord_less_eq(fun(U_513,bool)),U_508),U_510)) )
        | ~ hBOOL(hAPP(fun(U_514,bool),bool,hAPP(fun(U_514,bool),fun(fun(U_514,bool),bool),ord_less_eq(fun(U_514,bool)),U_512),hAPP(fun(U_513,bool),fun(U_514,bool),hAPP(fun(U_513,U_514),fun(fun(U_513,bool),fun(U_514,bool)),image(U_513,U_514),U_511),U_510))) ) ),
    inference(variable_rename,[status(thm)],[f_180_1]) ).

fof(f_180_3,plain,
    ( ! [U_524,U_522,U_520,U_518,U_516] :
        ( hBOOL(hAPP(fun(U_524,bool),bool,hAPP(fun(U_524,bool),fun(fun(U_524,bool),bool),ord_less_eq(fun(U_524,bool)),U_520),hAPP(fun(U_522,bool),fun(U_524,bool),hAPP(fun(U_522,U_524),fun(fun(U_522,bool),fun(U_524,bool)),image(U_522,U_524),U_518),U_516)))
        | ! [U_509] :
            ( ti(fun(U_524,bool),U_520) != hAPP(fun(U_522,bool),fun(U_524,bool),hAPP(fun(U_522,U_524),fun(fun(U_522,bool),fun(U_524,bool)),image(U_522,U_524),U_518),U_509)
            | ~ hBOOL(hAPP(fun(U_522,bool),bool,hAPP(fun(U_522,bool),fun(fun(U_522,bool),bool),ord_less_eq(fun(U_522,bool)),U_509),U_516)) ) )
    & ! [U_523,U_521,U_519,U_517,U_515] :
        ( ? [U_508] :
            ( ti(fun(U_523,bool),U_519) = hAPP(fun(U_521,bool),fun(U_523,bool),hAPP(fun(U_521,U_523),fun(fun(U_521,bool),fun(U_523,bool)),image(U_521,U_523),U_517),U_508)
            & hBOOL(hAPP(fun(U_521,bool),bool,hAPP(fun(U_521,bool),fun(fun(U_521,bool),bool),ord_less_eq(fun(U_521,bool)),U_508),U_515)) )
        | ~ hBOOL(hAPP(fun(U_523,bool),bool,hAPP(fun(U_523,bool),fun(fun(U_523,bool),bool),ord_less_eq(fun(U_523,bool)),U_519),hAPP(fun(U_521,bool),fun(U_523,bool),hAPP(fun(U_521,U_523),fun(fun(U_521,bool),fun(U_523,bool)),image(U_521,U_523),U_517),U_515))) ) ),
    inference(miniscope,[status(thm)],[f_180_2]) ).

fof(f_180_4,plain,
    ( ! [U_524,U_522,U_520,U_518,U_516] :
        ( hBOOL(hAPP(fun(U_524,bool),bool,hAPP(fun(U_524,bool),fun(fun(U_524,bool),bool),ord_less_eq(fun(U_524,bool)),U_520),hAPP(fun(U_522,bool),fun(U_524,bool),hAPP(fun(U_522,U_524),fun(fun(U_522,bool),fun(U_524,bool)),image(U_522,U_524),U_518),U_516)))
        | ! [U_509] :
            ( ti(fun(U_524,bool),U_520) != hAPP(fun(U_522,bool),fun(U_524,bool),hAPP(fun(U_522,U_524),fun(fun(U_522,bool),fun(U_524,bool)),image(U_522,U_524),U_518),U_509)
            | ~ hBOOL(hAPP(fun(U_522,bool),bool,hAPP(fun(U_522,bool),fun(fun(U_522,bool),bool),ord_less_eq(fun(U_522,bool)),U_509),U_516)) ) )
    & ! [U_523,U_521,U_519,U_517,U_515] :
        ( ( ti(fun(U_523,bool),U_519) = hAPP(fun(U_521,bool),fun(U_523,bool),hAPP(fun(U_521,U_523),fun(fun(U_521,bool),fun(U_523,bool)),image(U_521,U_523),U_517),sK9(U_523,U_521,U_519,U_517,U_515))
          & hBOOL(hAPP(fun(U_521,bool),bool,hAPP(fun(U_521,bool),fun(fun(U_521,bool),bool),ord_less_eq(fun(U_521,bool)),sK9(U_523,U_521,U_519,U_517,U_515)),U_515)) )
        | ~ hBOOL(hAPP(fun(U_523,bool),bool,hAPP(fun(U_523,bool),fun(fun(U_523,bool),bool),ord_less_eq(fun(U_523,bool)),U_519),hAPP(fun(U_521,bool),fun(U_523,bool),hAPP(fun(U_521,U_523),fun(fun(U_521,bool),fun(U_523,bool)),image(U_521,U_523),U_517),U_515))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_508,sK9(U_523,U_521,U_519,U_517,U_515))],[f_180_3]) ).

fof(f_180_5,plain,
    ( ! [U_519,U_517,U_515,U_521,U_523] :
        ( ti(fun(U_523,bool),U_519) = hAPP(fun(U_521,bool),fun(U_523,bool),hAPP(fun(U_521,U_523),fun(fun(U_521,bool),fun(U_523,bool)),image(U_521,U_523),U_517),sK9(U_523,U_521,U_519,U_517,U_515))
        | ~ sP22(U_519,U_517,U_515,U_521,U_523) )
    & ! [U_519,U_517,U_515,U_521,U_523] :
        ( hBOOL(hAPP(fun(U_521,bool),bool,hAPP(fun(U_521,bool),fun(fun(U_521,bool),bool),ord_less_eq(fun(U_521,bool)),sK9(U_523,U_521,U_519,U_517,U_515)),U_515))
        | ~ sP22(U_519,U_517,U_515,U_521,U_523) )
    & ! [U_509,U_516,U_520,U_518,U_522,U_524] :
        ( hBOOL(hAPP(fun(U_524,bool),bool,hAPP(fun(U_524,bool),fun(fun(U_524,bool),bool),ord_less_eq(fun(U_524,bool)),U_520),hAPP(fun(U_522,bool),fun(U_524,bool),hAPP(fun(U_522,U_524),fun(fun(U_522,bool),fun(U_524,bool)),image(U_522,U_524),U_518),U_516)))
        | ti(fun(U_524,bool),U_520) != hAPP(fun(U_522,bool),fun(U_524,bool),hAPP(fun(U_522,U_524),fun(fun(U_522,bool),fun(U_524,bool)),image(U_522,U_524),U_518),U_509)
        | ~ hBOOL(hAPP(fun(U_522,bool),bool,hAPP(fun(U_522,bool),fun(fun(U_522,bool),bool),ord_less_eq(fun(U_522,bool)),U_509),U_516)) )
    & ! [U_519,U_517,U_515,U_521,U_523] :
        ( sP22(U_519,U_517,U_515,U_521,U_523)
        | ~ hBOOL(hAPP(fun(U_523,bool),bool,hAPP(fun(U_523,bool),fun(fun(U_523,bool),bool),ord_less_eq(fun(U_523,bool)),U_519),hAPP(fun(U_521,bool),fun(U_523,bool),hAPP(fun(U_521,U_523),fun(fun(U_521,bool),fun(U_523,bool)),image(U_521,U_523),U_517),U_515))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP22])],[f_180_4]) ).

cnf(f_180_6,plain,
    ( sP22(U_519,U_517,U_515,U_521,U_523)
    | ~ hBOOL(hAPP(fun(U_523,bool),bool,hAPP(fun(U_523,bool),fun(fun(U_523,bool),bool),ord_less_eq(fun(U_523,bool)),U_519),hAPP(fun(U_521,bool),fun(U_523,bool),hAPP(fun(U_521,U_523),fun(fun(U_521,bool),fun(U_523,bool)),image(U_521,U_523),U_517),U_515))) ),
    inference(clausify,[status(thm)],[f_180_5]) ).

cnf(f_180_7,plain,
    ( hBOOL(hAPP(fun(U_524,bool),bool,hAPP(fun(U_524,bool),fun(fun(U_524,bool),bool),ord_less_eq(fun(U_524,bool)),U_520),hAPP(fun(U_522,bool),fun(U_524,bool),hAPP(fun(U_522,U_524),fun(fun(U_522,bool),fun(U_524,bool)),image(U_522,U_524),U_518),U_516)))
    | ti(fun(U_524,bool),U_520) != hAPP(fun(U_522,bool),fun(U_524,bool),hAPP(fun(U_522,U_524),fun(fun(U_522,bool),fun(U_524,bool)),image(U_522,U_524),U_518),U_509)
    | ~ hBOOL(hAPP(fun(U_522,bool),bool,hAPP(fun(U_522,bool),fun(fun(U_522,bool),bool),ord_less_eq(fun(U_522,bool)),U_509),U_516)) ),
    inference(clausify,[status(thm)],[f_180_5]) ).

cnf(f_180_8,plain,
    ( hBOOL(hAPP(fun(U_521,bool),bool,hAPP(fun(U_521,bool),fun(fun(U_521,bool),bool),ord_less_eq(fun(U_521,bool)),sK9(U_523,U_521,U_519,U_517,U_515)),U_515))
    | ~ sP22(U_519,U_517,U_515,U_521,U_523) ),
    inference(clausify,[status(thm)],[f_180_5]) ).

cnf(f_180_9,plain,
    ( ti(fun(U_523,bool),U_519) = hAPP(fun(U_521,bool),fun(U_523,bool),hAPP(fun(U_521,U_523),fun(fun(U_521,bool),fun(U_523,bool)),image(U_521,U_523),U_517),sK9(U_523,U_521,U_519,U_517,U_515))
    | ~ sP22(U_519,U_517,U_515,U_521,U_523) ),
    inference(clausify,[status(thm)],[f_180_5]) ).

fof(f_181_1,plain,
    ! [X_c,X_b,F,A_3,B_1] :
      ( 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_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),B_1)) ),
    inference(fof_nnf,[status(thm)],[fact_110_image__mono]) ).

fof(f_181_2,plain,
    ! [U_529,U_528,U_527,U_526,U_525] :
      ( hBOOL(hAPP(fun(U_529,bool),bool,hAPP(fun(U_529,bool),fun(fun(U_529,bool),bool),ord_less_eq(fun(U_529,bool)),hAPP(fun(U_528,bool),fun(U_529,bool),hAPP(fun(U_528,U_529),fun(fun(U_528,bool),fun(U_529,bool)),image(U_528,U_529),U_527),U_526)),hAPP(fun(U_528,bool),fun(U_529,bool),hAPP(fun(U_528,U_529),fun(fun(U_528,bool),fun(U_529,bool)),image(U_528,U_529),U_527),U_525)))
      | ~ hBOOL(hAPP(fun(U_528,bool),bool,hAPP(fun(U_528,bool),fun(fun(U_528,bool),bool),ord_less_eq(fun(U_528,bool)),U_526),U_525)) ),
    inference(variable_rename,[status(thm)],[f_181_1]) ).

fof(f_181_3,plain,
    ! [U_528,U_526,U_525,U_529,U_527] :
      ( hBOOL(hAPP(fun(U_529,bool),bool,hAPP(fun(U_529,bool),fun(fun(U_529,bool),bool),ord_less_eq(fun(U_529,bool)),hAPP(fun(U_528,bool),fun(U_529,bool),hAPP(fun(U_528,U_529),fun(fun(U_528,bool),fun(U_529,bool)),image(U_528,U_529),U_527),U_526)),hAPP(fun(U_528,bool),fun(U_529,bool),hAPP(fun(U_528,U_529),fun(fun(U_528,bool),fun(U_529,bool)),image(U_528,U_529),U_527),U_525)))
      | ~ hBOOL(hAPP(fun(U_528,bool),bool,hAPP(fun(U_528,bool),fun(fun(U_528,bool),bool),ord_less_eq(fun(U_528,bool)),U_526),U_525)) ),
    inference(definitional_conversion,[status(esa)],[f_181_2]) ).

cnf(f_181_4,plain,
    ( hBOOL(hAPP(fun(U_529,bool),bool,hAPP(fun(U_529,bool),fun(fun(U_529,bool),bool),ord_less_eq(fun(U_529,bool)),hAPP(fun(U_528,bool),fun(U_529,bool),hAPP(fun(U_528,U_529),fun(fun(U_528,bool),fun(U_529,bool)),image(U_528,U_529),U_527),U_526)),hAPP(fun(U_528,bool),fun(U_529,bool),hAPP(fun(U_528,U_529),fun(fun(U_528,bool),fun(U_529,bool)),image(U_528,U_529),U_527),U_525)))
    | ~ hBOOL(hAPP(fun(U_528,bool),bool,hAPP(fun(U_528,bool),fun(fun(U_528,bool),bool),ord_less_eq(fun(U_528,bool)),U_526),U_525)) ),
    inference(clausify,[status(thm)],[f_181_3]) ).

fof(f_182_1,plain,
    ! [X_b,X_c,B_3,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_3) = 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_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))) ),
    inference(fof_nnf,[status(thm)],[fact_111_imageE]) ).

fof(f_182_2,plain,
    ! [U_535,U_534,U_533,U_532,U_531] :
      ( ? [U_530] :
          ( hBOOL(hAPP(fun(U_534,bool),bool,hAPP(U_534,fun(fun(U_534,bool),bool),member(U_534),U_530),U_531))
          & ti(U_535,U_533) = hAPP(U_534,U_535,U_532,U_530) )
      | ~ hBOOL(hAPP(fun(U_535,bool),bool,hAPP(U_535,fun(fun(U_535,bool),bool),member(U_535),U_533),hAPP(fun(U_534,bool),fun(U_535,bool),hAPP(fun(U_534,U_535),fun(fun(U_534,bool),fun(U_535,bool)),image(U_534,U_535),U_532),U_531))) ),
    inference(variable_rename,[status(thm)],[f_182_1]) ).

fof(f_182_3,plain,
    ! [U_535,U_534,U_533,U_532,U_531] :
      ( ( hBOOL(hAPP(fun(U_534,bool),bool,hAPP(U_534,fun(fun(U_534,bool),bool),member(U_534),sK10(U_535,U_534,U_533,U_532,U_531)),U_531))
        & ti(U_535,U_533) = hAPP(U_534,U_535,U_532,sK10(U_535,U_534,U_533,U_532,U_531)) )
      | ~ hBOOL(hAPP(fun(U_535,bool),bool,hAPP(U_535,fun(fun(U_535,bool),bool),member(U_535),U_533),hAPP(fun(U_534,bool),fun(U_535,bool),hAPP(fun(U_534,U_535),fun(fun(U_534,bool),fun(U_535,bool)),image(U_534,U_535),U_532),U_531))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_530,sK10(U_535,U_534,U_533,U_532,U_531))],[f_182_2]) ).

fof(f_182_4,plain,
    ( ! [U_533,U_531,U_532,U_534,U_535] :
        ( hBOOL(hAPP(fun(U_534,bool),bool,hAPP(U_534,fun(fun(U_534,bool),bool),member(U_534),sK10(U_535,U_534,U_533,U_532,U_531)),U_531))
        | ~ sP23(U_533,U_531,U_532,U_534,U_535) )
    & ! [U_533,U_531,U_532,U_534,U_535] :
        ( ti(U_535,U_533) = hAPP(U_534,U_535,U_532,sK10(U_535,U_534,U_533,U_532,U_531))
        | ~ sP23(U_533,U_531,U_532,U_534,U_535) )
    & ! [U_533,U_531,U_532,U_534,U_535] :
        ( sP23(U_533,U_531,U_532,U_534,U_535)
        | ~ hBOOL(hAPP(fun(U_535,bool),bool,hAPP(U_535,fun(fun(U_535,bool),bool),member(U_535),U_533),hAPP(fun(U_534,bool),fun(U_535,bool),hAPP(fun(U_534,U_535),fun(fun(U_534,bool),fun(U_535,bool)),image(U_534,U_535),U_532),U_531))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP23])],[f_182_3]) ).

cnf(f_182_5,plain,
    ( sP23(U_533,U_531,U_532,U_534,U_535)
    | ~ hBOOL(hAPP(fun(U_535,bool),bool,hAPP(U_535,fun(fun(U_535,bool),bool),member(U_535),U_533),hAPP(fun(U_534,bool),fun(U_535,bool),hAPP(fun(U_534,U_535),fun(fun(U_534,bool),fun(U_535,bool)),image(U_534,U_535),U_532),U_531))) ),
    inference(clausify,[status(thm)],[f_182_4]) ).

cnf(f_182_6,plain,
    ( ti(U_535,U_533) = hAPP(U_534,U_535,U_532,sK10(U_535,U_534,U_533,U_532,U_531))
    | ~ sP23(U_533,U_531,U_532,U_534,U_535) ),
    inference(clausify,[status(thm)],[f_182_4]) ).

cnf(f_182_7,plain,
    ( hBOOL(hAPP(fun(U_534,bool),bool,hAPP(U_534,fun(fun(U_534,bool),bool),member(U_534),sK10(U_535,U_534,U_533,U_532,U_531)),U_531))
    | ~ sP23(U_533,U_531,U_532,U_534,U_535) ),
    inference(clausify,[status(thm)],[f_182_4]) ).

fof(f_183_1,plain,
    ! [X_b,B_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_1))
      | ? [X_2] :
          ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B_1))
          & 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_112_subsetI]) ).

fof(f_183_2,plain,
    ! [U_539,U_538,U_537] :
      ( hBOOL(hAPP(fun(U_539,bool),bool,hAPP(fun(U_539,bool),fun(fun(U_539,bool),bool),ord_less_eq(fun(U_539,bool)),U_537),U_538))
      | ? [U_536] :
          ( ~ hBOOL(hAPP(fun(U_539,bool),bool,hAPP(U_539,fun(fun(U_539,bool),bool),member(U_539),U_536),U_538))
          & hBOOL(hAPP(fun(U_539,bool),bool,hAPP(U_539,fun(fun(U_539,bool),bool),member(U_539),U_536),U_537)) ) ),
    inference(variable_rename,[status(thm)],[f_183_1]) ).

fof(f_183_3,plain,
    ! [U_539,U_538,U_537] :
      ( hBOOL(hAPP(fun(U_539,bool),bool,hAPP(fun(U_539,bool),fun(fun(U_539,bool),bool),ord_less_eq(fun(U_539,bool)),U_537),U_538))
      | ( ~ hBOOL(hAPP(fun(U_539,bool),bool,hAPP(U_539,fun(fun(U_539,bool),bool),member(U_539),sK11(U_539,U_538,U_537)),U_538))
        & hBOOL(hAPP(fun(U_539,bool),bool,hAPP(U_539,fun(fun(U_539,bool),bool),member(U_539),sK11(U_539,U_538,U_537)),U_537)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_536,sK11(U_539,U_538,U_537))],[f_183_2]) ).

fof(f_183_4,plain,
    ( ! [U_537,U_539,U_538] :
        ( ~ hBOOL(hAPP(fun(U_539,bool),bool,hAPP(U_539,fun(fun(U_539,bool),bool),member(U_539),sK11(U_539,U_538,U_537)),U_538))
        | ~ sP24(U_537,U_539,U_538) )
    & ! [U_537,U_539,U_538] :
        ( hBOOL(hAPP(fun(U_539,bool),bool,hAPP(U_539,fun(fun(U_539,bool),bool),member(U_539),sK11(U_539,U_538,U_537)),U_537))
        | ~ sP24(U_537,U_539,U_538) )
    & ! [U_537,U_539,U_538] :
        ( hBOOL(hAPP(fun(U_539,bool),bool,hAPP(fun(U_539,bool),fun(fun(U_539,bool),bool),ord_less_eq(fun(U_539,bool)),U_537),U_538))
        | sP24(U_537,U_539,U_538) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP24])],[f_183_3]) ).

cnf(f_183_5,plain,
    ( hBOOL(hAPP(fun(U_539,bool),bool,hAPP(fun(U_539,bool),fun(fun(U_539,bool),bool),ord_less_eq(fun(U_539,bool)),U_537),U_538))
    | sP24(U_537,U_539,U_538) ),
    inference(clausify,[status(thm)],[f_183_4]) ).

cnf(f_183_6,plain,
    ( hBOOL(hAPP(fun(U_539,bool),bool,hAPP(U_539,fun(fun(U_539,bool),bool),member(U_539),sK11(U_539,U_538,U_537)),U_537))
    | ~ sP24(U_537,U_539,U_538) ),
    inference(clausify,[status(thm)],[f_183_4]) ).

cnf(f_183_7,plain,
    ( ~ hBOOL(hAPP(fun(U_539,bool),bool,hAPP(U_539,fun(fun(U_539,bool),bool),member(U_539),sK11(U_539,U_538,U_537)),U_538))
    | ~ sP24(U_537,U_539,U_538) ),
    inference(clausify,[status(thm)],[f_183_4]) ).

fof(f_184_1,plain,
    ! [X_c,X_b,F,B_1,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_1))
      | ? [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_1))
          & 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_113_image__subsetI]) ).

fof(f_184_2,plain,
    ! [U_545,U_544,U_543,U_542,U_541] :
      ( hBOOL(hAPP(fun(U_545,bool),bool,hAPP(fun(U_545,bool),fun(fun(U_545,bool),bool),ord_less_eq(fun(U_545,bool)),hAPP(fun(U_544,bool),fun(U_545,bool),hAPP(fun(U_544,U_545),fun(fun(U_544,bool),fun(U_545,bool)),image(U_544,U_545),U_543),U_541)),U_542))
      | ? [U_540] :
          ( ~ hBOOL(hAPP(fun(U_545,bool),bool,hAPP(U_545,fun(fun(U_545,bool),bool),member(U_545),hAPP(U_544,U_545,U_543,U_540)),U_542))
          & hBOOL(hAPP(fun(U_544,bool),bool,hAPP(U_544,fun(fun(U_544,bool),bool),member(U_544),U_540),U_541)) ) ),
    inference(variable_rename,[status(thm)],[f_184_1]) ).

fof(f_184_3,plain,
    ! [U_545,U_544,U_543,U_542,U_541] :
      ( hBOOL(hAPP(fun(U_545,bool),bool,hAPP(fun(U_545,bool),fun(fun(U_545,bool),bool),ord_less_eq(fun(U_545,bool)),hAPP(fun(U_544,bool),fun(U_545,bool),hAPP(fun(U_544,U_545),fun(fun(U_544,bool),fun(U_545,bool)),image(U_544,U_545),U_543),U_541)),U_542))
      | ( ~ hBOOL(hAPP(fun(U_545,bool),bool,hAPP(U_545,fun(fun(U_545,bool),bool),member(U_545),hAPP(U_544,U_545,U_543,sK12(U_545,U_544,U_543,U_542,U_541))),U_542))
        & hBOOL(hAPP(fun(U_544,bool),bool,hAPP(U_544,fun(fun(U_544,bool),bool),member(U_544),sK12(U_545,U_544,U_543,U_542,U_541)),U_541)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_540,sK12(U_545,U_544,U_543,U_542,U_541))],[f_184_2]) ).

fof(f_184_4,plain,
    ( ! [U_541,U_544,U_542,U_543,U_545] :
        ( ~ hBOOL(hAPP(fun(U_545,bool),bool,hAPP(U_545,fun(fun(U_545,bool),bool),member(U_545),hAPP(U_544,U_545,U_543,sK12(U_545,U_544,U_543,U_542,U_541))),U_542))
        | ~ sP25(U_541,U_544,U_542,U_543,U_545) )
    & ! [U_541,U_544,U_542,U_543,U_545] :
        ( hBOOL(hAPP(fun(U_544,bool),bool,hAPP(U_544,fun(fun(U_544,bool),bool),member(U_544),sK12(U_545,U_544,U_543,U_542,U_541)),U_541))
        | ~ sP25(U_541,U_544,U_542,U_543,U_545) )
    & ! [U_541,U_544,U_542,U_543,U_545] :
        ( hBOOL(hAPP(fun(U_545,bool),bool,hAPP(fun(U_545,bool),fun(fun(U_545,bool),bool),ord_less_eq(fun(U_545,bool)),hAPP(fun(U_544,bool),fun(U_545,bool),hAPP(fun(U_544,U_545),fun(fun(U_544,bool),fun(U_545,bool)),image(U_544,U_545),U_543),U_541)),U_542))
        | sP25(U_541,U_544,U_542,U_543,U_545) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP25])],[f_184_3]) ).

cnf(f_184_5,plain,
    ( hBOOL(hAPP(fun(U_545,bool),bool,hAPP(fun(U_545,bool),fun(fun(U_545,bool),bool),ord_less_eq(fun(U_545,bool)),hAPP(fun(U_544,bool),fun(U_545,bool),hAPP(fun(U_544,U_545),fun(fun(U_544,bool),fun(U_545,bool)),image(U_544,U_545),U_543),U_541)),U_542))
    | sP25(U_541,U_544,U_542,U_543,U_545) ),
    inference(clausify,[status(thm)],[f_184_4]) ).

cnf(f_184_6,plain,
    ( hBOOL(hAPP(fun(U_544,bool),bool,hAPP(U_544,fun(fun(U_544,bool),bool),member(U_544),sK12(U_545,U_544,U_543,U_542,U_541)),U_541))
    | ~ sP25(U_541,U_544,U_542,U_543,U_545) ),
    inference(clausify,[status(thm)],[f_184_4]) ).

cnf(f_184_7,plain,
    ( ~ hBOOL(hAPP(fun(U_545,bool),bool,hAPP(U_545,fun(fun(U_545,bool),bool),member(U_545),hAPP(U_544,U_545,U_543,sK12(U_545,U_544,U_543,U_542,U_541))),U_542))
    | ~ sP25(U_541,U_544,U_542,U_543,U_545) ),
    inference(clausify,[status(thm)],[f_184_4]) ).

fof(f_185_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_114_le__funI]) ).

fof(f_185_2,plain,
    ! [U_550,U_549] :
      ( ! [U_548,U_547] :
          ( hBOOL(hAPP(fun(U_550,U_549),bool,hAPP(fun(U_550,U_549),fun(fun(U_550,U_549),bool),ord_less_eq(fun(U_550,U_549)),U_548),U_547))
          | ? [U_546] : ~ hBOOL(hAPP(U_549,bool,hAPP(U_549,fun(U_549,bool),ord_less_eq(U_549),hAPP(U_550,U_549,U_548,U_546)),hAPP(U_550,U_549,U_547,U_546))) )
      | ~ ord(U_549) ),
    inference(variable_rename,[status(thm)],[f_185_1]) ).

fof(f_185_3,plain,
    ! [U_550,U_549] :
      ( ! [U_548,U_547] :
          ( hBOOL(hAPP(fun(U_550,U_549),bool,hAPP(fun(U_550,U_549),fun(fun(U_550,U_549),bool),ord_less_eq(fun(U_550,U_549)),U_548),U_547))
          | ~ hBOOL(hAPP(U_549,bool,hAPP(U_549,fun(U_549,bool),ord_less_eq(U_549),hAPP(U_550,U_549,U_548,sK13(U_550,U_549,U_548,U_547))),hAPP(U_550,U_549,U_547,sK13(U_550,U_549,U_548,U_547)))) )
      | ~ ord(U_549) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_546,sK13(U_550,U_549,U_548,U_547))],[f_185_2]) ).

fof(f_185_4,plain,
    ! [U_549,U_547,U_548,U_550] :
      ( hBOOL(hAPP(fun(U_550,U_549),bool,hAPP(fun(U_550,U_549),fun(fun(U_550,U_549),bool),ord_less_eq(fun(U_550,U_549)),U_548),U_547))
      | ~ hBOOL(hAPP(U_549,bool,hAPP(U_549,fun(U_549,bool),ord_less_eq(U_549),hAPP(U_550,U_549,U_548,sK13(U_550,U_549,U_548,U_547))),hAPP(U_550,U_549,U_547,sK13(U_550,U_549,U_548,U_547))))
      | ~ ord(U_549) ),
    inference(definitional_conversion,[status(esa)],[f_185_3]) ).

cnf(f_185_5,plain,
    ( hBOOL(hAPP(fun(U_550,U_549),bool,hAPP(fun(U_550,U_549),fun(fun(U_550,U_549),bool),ord_less_eq(fun(U_550,U_549)),U_548),U_547))
    | ~ hBOOL(hAPP(U_549,bool,hAPP(U_549,fun(U_549,bool),ord_less_eq(U_549),hAPP(U_550,U_549,U_548,sK13(U_550,U_549,U_548,U_547))),hAPP(U_550,U_549,U_547,sK13(U_550,U_549,U_548,U_547))))
    | ~ ord(U_549) ),
    inference(clausify,[status(thm)],[f_185_4]) ).

fof(f_186_1,plain,
    ! [N_2] :
      ( ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),N_2))
        | ! [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_2)) ) )
      & ( ? [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_2)) )
        | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),N_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_115_finite__nat__set__iff__bounded__le]) ).

fof(f_186_2,plain,
    ! [U_555] :
      ( ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_555))
        | ! [U_554] :
          ? [U_553] :
            ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_553),U_554))
            & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_553),U_555)) ) )
      & ( ? [U_552] :
          ! [U_551] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_551),U_552))
            | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_551),U_555)) )
        | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_555)) ) ),
    inference(variable_rename,[status(thm)],[f_186_1]) ).

fof(f_186_3,plain,
    ( ! [U_557] :
        ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_557))
        | ! [U_554] :
          ? [U_553] :
            ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_553),U_554))
            & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_553),U_557)) ) )
    & ! [U_556] :
        ( ? [U_552] :
          ! [U_551] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_551),U_552))
            | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_551),U_556)) )
        | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_556)) ) ),
    inference(miniscope,[status(thm)],[f_186_2]) ).

fof(f_186_4,plain,
    ( ! [U_557] :
        ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_557))
        | ! [U_554] :
          ? [U_553] :
            ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_553),U_554))
            & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_553),U_557)) ) )
    & ! [U_556] :
        ( ! [U_551] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_551),sK14(U_556)))
            | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_551),U_556)) )
        | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_556)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_552,sK14(U_556))],[f_186_3]) ).

fof(f_186_5,plain,
    ( ! [U_557] :
        ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_557))
        | ! [U_554] :
            ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sK15(U_557,U_554)),U_554))
            & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK15(U_557,U_554)),U_557)) ) )
    & ! [U_556] :
        ( ! [U_551] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_551),sK14(U_556)))
            | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_551),U_556)) )
        | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_556)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_553,sK15(U_557,U_554))],[f_186_4]) ).

fof(f_186_6,plain,
    ( ! [U_554,U_557] :
        ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sK15(U_557,U_554)),U_554))
        | ~ sP26(U_554,U_557) )
    & ! [U_554,U_557] :
        ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK15(U_557,U_554)),U_557))
        | ~ sP26(U_554,U_557) )
    & ! [U_554,U_557] :
        ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_557))
        | sP26(U_554,U_557) )
    & ! [U_551,U_556] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_551),sK14(U_556)))
        | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_551),U_556))
        | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_556)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP26])],[f_186_5]) ).

cnf(f_186_7,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_551),sK14(U_556)))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_551),U_556))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_556)) ),
    inference(clausify,[status(thm)],[f_186_6]) ).

cnf(f_186_8,plain,
    ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_557))
    | sP26(U_554,U_557) ),
    inference(clausify,[status(thm)],[f_186_6]) ).

cnf(f_186_9,plain,
    ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK15(U_557,U_554)),U_557))
    | ~ sP26(U_554,U_557) ),
    inference(clausify,[status(thm)],[f_186_6]) ).

cnf(f_186_10,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sK15(U_557,U_554)),U_554))
    | ~ sP26(U_554,U_557) ),
    inference(clausify,[status(thm)],[f_186_6]) ).

fof(f_187_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_116_assms_I3_J]) ).

fof(f_187_2,plain,
    ! [U_560,U_559] :
      ( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,U_560),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_559)),bot_bot(fun(x_a,bool)))))
      | ? [U_558] :
          ( ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,U_560),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_558)),bot_bot(fun(x_a,bool)))))
          & hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),U_558),u)) )
      | ~ hBOOL(hAPP(com,bool,wt,U_559)) ),
    inference(variable_rename,[status(thm)],[f_187_1]) ).

fof(f_187_3,plain,
    ! [U_560,U_559] :
      ( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,U_560),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_559)),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_560),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,sK16(U_560,U_559))),bot_bot(fun(x_a,bool)))))
        & hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),sK16(U_560,U_559)),u)) )
      | ~ hBOOL(hAPP(com,bool,wt,U_559)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_558,sK16(U_560,U_559))],[f_187_2]) ).

fof(f_187_4,plain,
    ( ! [U_560,U_559] :
        ( ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,U_560),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,sK16(U_560,U_559))),bot_bot(fun(x_a,bool)))))
        | ~ sP27(U_560,U_559) )
    & ! [U_560,U_559] :
        ( hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),sK16(U_560,U_559)),u))
        | ~ sP27(U_560,U_559) )
    & ! [U_560,U_559] :
        ( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,U_560),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_559)),bot_bot(fun(x_a,bool)))))
        | sP27(U_560,U_559)
        | ~ hBOOL(hAPP(com,bool,wt,U_559)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP27])],[f_187_3]) ).

cnf(f_187_5,plain,
    ( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,U_560),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_559)),bot_bot(fun(x_a,bool)))))
    | sP27(U_560,U_559)
    | ~ hBOOL(hAPP(com,bool,wt,U_559)) ),
    inference(clausify,[status(thm)],[f_187_4]) ).

cnf(f_187_6,plain,
    ( hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),sK16(U_560,U_559)),u))
    | ~ sP27(U_560,U_559) ),
    inference(clausify,[status(thm)],[f_187_4]) ).

cnf(f_187_7,plain,
    ( ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,U_560),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,sK16(U_560,U_559))),bot_bot(fun(x_a,bool)))))
    | ~ sP27(U_560,U_559) ),
    inference(clausify,[status(thm)],[f_187_4]) ).

fof(f_188_1,plain,
    ! [X_b] :
      ( ! [A_2,B_3,C_1,D_1] :
          ( ( ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),B_3))
              | ~ 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_3)) ) )
          | hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3) != 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_117_diff__eq__diff__less__eq]) ).

fof(f_188_2,plain,
    ! [U_565] :
      ( ! [U_564,U_563,U_562,U_561] :
          ( ( ( hBOOL(hAPP(U_565,bool,hAPP(U_565,fun(U_565,bool),ord_less_eq(U_565),U_564),U_563))
              | ~ hBOOL(hAPP(U_565,bool,hAPP(U_565,fun(U_565,bool),ord_less_eq(U_565),U_562),U_561)) )
            & ( hBOOL(hAPP(U_565,bool,hAPP(U_565,fun(U_565,bool),ord_less_eq(U_565),U_562),U_561))
              | ~ hBOOL(hAPP(U_565,bool,hAPP(U_565,fun(U_565,bool),ord_less_eq(U_565),U_564),U_563)) ) )
          | hAPP(U_565,U_565,hAPP(U_565,fun(U_565,U_565),minus_minus(U_565),U_564),U_563) != hAPP(U_565,U_565,hAPP(U_565,fun(U_565,U_565),minus_minus(U_565),U_562),U_561) )
      | ~ ordered_ab_group_add(U_565) ),
    inference(variable_rename,[status(thm)],[f_188_1]) ).

fof(f_188_3,plain,
    ( ! [U_564,U_563,U_561,U_565,U_562] :
        ( hBOOL(hAPP(U_565,bool,hAPP(U_565,fun(U_565,bool),ord_less_eq(U_565),U_564),U_563))
        | ~ hBOOL(hAPP(U_565,bool,hAPP(U_565,fun(U_565,bool),ord_less_eq(U_565),U_562),U_561))
        | ~ sP28(U_564,U_563,U_561,U_565,U_562) )
    & ! [U_564,U_563,U_561,U_565,U_562] :
        ( hBOOL(hAPP(U_565,bool,hAPP(U_565,fun(U_565,bool),ord_less_eq(U_565),U_562),U_561))
        | ~ hBOOL(hAPP(U_565,bool,hAPP(U_565,fun(U_565,bool),ord_less_eq(U_565),U_564),U_563))
        | ~ sP28(U_564,U_563,U_561,U_565,U_562) )
    & ! [U_564,U_563,U_561,U_565,U_562] :
        ( sP28(U_564,U_563,U_561,U_565,U_562)
        | hAPP(U_565,U_565,hAPP(U_565,fun(U_565,U_565),minus_minus(U_565),U_564),U_563) != hAPP(U_565,U_565,hAPP(U_565,fun(U_565,U_565),minus_minus(U_565),U_562),U_561)
        | ~ ordered_ab_group_add(U_565) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP28])],[f_188_2]) ).

cnf(f_188_4,plain,
    ( sP28(U_564,U_563,U_561,U_565,U_562)
    | hAPP(U_565,U_565,hAPP(U_565,fun(U_565,U_565),minus_minus(U_565),U_564),U_563) != hAPP(U_565,U_565,hAPP(U_565,fun(U_565,U_565),minus_minus(U_565),U_562),U_561)
    | ~ ordered_ab_group_add(U_565) ),
    inference(clausify,[status(thm)],[f_188_3]) ).

cnf(f_188_5,plain,
    ( hBOOL(hAPP(U_565,bool,hAPP(U_565,fun(U_565,bool),ord_less_eq(U_565),U_562),U_561))
    | ~ hBOOL(hAPP(U_565,bool,hAPP(U_565,fun(U_565,bool),ord_less_eq(U_565),U_564),U_563))
    | ~ sP28(U_564,U_563,U_561,U_565,U_562) ),
    inference(clausify,[status(thm)],[f_188_3]) ).

cnf(f_188_6,plain,
    ( hBOOL(hAPP(U_565,bool,hAPP(U_565,fun(U_565,bool),ord_less_eq(U_565),U_564),U_563))
    | ~ hBOOL(hAPP(U_565,bool,hAPP(U_565,fun(U_565,bool),ord_less_eq(U_565),U_562),U_561))
    | ~ sP28(U_564,U_563,U_561,U_565,U_562) ),
    inference(clausify,[status(thm)],[f_188_3]) ).

fof(f_189_1,plain,
    ! [M,Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M)),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)),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)),Na))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M)),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_118_less__eq__nat_Osimps_I2_J]) ).

fof(f_189_2,plain,
    ! [U_567,U_566] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_567)),U_566))
        | ~ 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_567)),U_566)) )
      & ( 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_567)),U_566))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_567)),U_566)) ) ),
    inference(variable_rename,[status(thm)],[f_189_1]) ).

fof(f_189_3,plain,
    ( ! [U_571,U_569] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_571)),U_569))
        | ~ 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_571)),U_569)) )
    & ! [U_570,U_568] :
        ( 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_570)),U_568))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_570)),U_568)) ) ),
    inference(miniscope,[status(thm)],[f_189_2]) ).

fof(f_189_4,plain,
    ( ! [U_569,U_571] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_571)),U_569))
        | ~ 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_571)),U_569)) )
    & ! [U_568,U_570] :
        ( 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_570)),U_568))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_570)),U_568)) ) ),
    inference(definitional_conversion,[status(esa)],[f_189_3]) ).

cnf(f_189_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_570)),U_568))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_570)),U_568)) ),
    inference(clausify,[status(thm)],[f_189_4]) ).

cnf(f_189_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_571)),U_569))
    | ~ 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_571)),U_569)) ),
    inference(clausify,[status(thm)],[f_189_4]) ).

fof(f_190_1,plain,
    ! [X_c,X_b,B_1,A_3,F,Z_2,G,F_1] :
      ( hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(fun(X_c,bool),X_b,F_1,B_1)),hAPP(fun(X_c,bool),X_b,F_1,A_3)) = hAPP(fun(X_c,bool),X_b,F_1,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_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))),finite908156982e_idem(X_b,X_c),F),Z_2),G),F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_119_folding__image__simple__idem_Osubset__idem]) ).

fof(f_190_2,plain,
    ! [U_579,U_578,U_577,U_576,U_575,U_574,U_573,U_572] :
      ( hAPP(U_578,U_578,hAPP(U_578,fun(U_578,U_578),U_575,hAPP(fun(U_579,bool),U_578,U_572,U_577)),hAPP(fun(U_579,bool),U_578,U_572,U_576)) = hAPP(fun(U_579,bool),U_578,U_572,U_576)
      | ~ hBOOL(hAPP(fun(U_579,bool),bool,hAPP(fun(U_579,bool),fun(fun(U_579,bool),bool),ord_less_eq(fun(U_579,bool)),U_577),U_576))
      | ~ hBOOL(hAPP(fun(U_579,bool),bool,finite_finite(U_579),U_576))
      | ~ hBOOL(hAPP(fun(fun(U_579,bool),U_578),bool,hAPP(fun(U_579,U_578),fun(fun(fun(U_579,bool),U_578),bool),hAPP(U_578,fun(fun(U_579,U_578),fun(fun(fun(U_579,bool),U_578),bool)),hAPP(fun(U_578,fun(U_578,U_578)),fun(U_578,fun(fun(U_579,U_578),fun(fun(fun(U_579,bool),U_578),bool))),finite908156982e_idem(U_578,U_579),U_575),U_574),U_573),U_572)) ),
    inference(variable_rename,[status(thm)],[f_190_1]) ).

fof(f_190_3,plain,
    ! [U_573,U_578,U_572,U_574,U_575,U_576,U_577,U_579] :
      ( hAPP(U_578,U_578,hAPP(U_578,fun(U_578,U_578),U_575,hAPP(fun(U_579,bool),U_578,U_572,U_577)),hAPP(fun(U_579,bool),U_578,U_572,U_576)) = hAPP(fun(U_579,bool),U_578,U_572,U_576)
      | ~ hBOOL(hAPP(fun(U_579,bool),bool,hAPP(fun(U_579,bool),fun(fun(U_579,bool),bool),ord_less_eq(fun(U_579,bool)),U_577),U_576))
      | ~ hBOOL(hAPP(fun(U_579,bool),bool,finite_finite(U_579),U_576))
      | ~ hBOOL(hAPP(fun(fun(U_579,bool),U_578),bool,hAPP(fun(U_579,U_578),fun(fun(fun(U_579,bool),U_578),bool),hAPP(U_578,fun(fun(U_579,U_578),fun(fun(fun(U_579,bool),U_578),bool)),hAPP(fun(U_578,fun(U_578,U_578)),fun(U_578,fun(fun(U_579,U_578),fun(fun(fun(U_579,bool),U_578),bool))),finite908156982e_idem(U_578,U_579),U_575),U_574),U_573),U_572)) ),
    inference(definitional_conversion,[status(esa)],[f_190_2]) ).

cnf(f_190_4,plain,
    ( hAPP(U_578,U_578,hAPP(U_578,fun(U_578,U_578),U_575,hAPP(fun(U_579,bool),U_578,U_572,U_577)),hAPP(fun(U_579,bool),U_578,U_572,U_576)) = hAPP(fun(U_579,bool),U_578,U_572,U_576)
    | ~ hBOOL(hAPP(fun(U_579,bool),bool,hAPP(fun(U_579,bool),fun(fun(U_579,bool),bool),ord_less_eq(fun(U_579,bool)),U_577),U_576))
    | ~ hBOOL(hAPP(fun(U_579,bool),bool,finite_finite(U_579),U_576))
    | ~ hBOOL(hAPP(fun(fun(U_579,bool),U_578),bool,hAPP(fun(U_579,U_578),fun(fun(fun(U_579,bool),U_578),bool),hAPP(U_578,fun(fun(U_579,U_578),fun(fun(fun(U_579,bool),U_578),bool)),hAPP(fun(U_578,fun(U_578,U_578)),fun(U_578,fun(fun(U_579,U_578),fun(fun(fun(U_579,bool),U_578),bool))),finite908156982e_idem(U_578,U_579),U_575),U_574),U_573),U_572)) ),
    inference(clausify,[status(thm)],[f_190_3]) ).

fof(f_191_1,plain,
    ! [X_c,X_b,X_1,A_3,F,Z_2,G,F_1] :
      ( hAPP(fun(X_c,bool),X_b,F_1,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_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))),finite908156982e_idem(X_b,X_c),F),Z_2),G),F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_120_folding__image__simple__idem_Oinsert__idem]) ).

fof(f_191_2,plain,
    ! [U_587,U_586,U_585,U_584,U_583,U_582,U_581,U_580] :
      ( hAPP(fun(U_587,bool),U_586,U_580,hAPP(fun(U_587,bool),fun(U_587,bool),hAPP(U_587,fun(fun(U_587,bool),fun(U_587,bool)),insert(U_587),U_585),U_584)) = hAPP(U_586,U_586,hAPP(U_586,fun(U_586,U_586),U_583,hAPP(U_587,U_586,U_581,U_585)),hAPP(fun(U_587,bool),U_586,U_580,U_584))
      | ~ hBOOL(hAPP(fun(U_587,bool),bool,finite_finite(U_587),U_584))
      | ~ hBOOL(hAPP(fun(fun(U_587,bool),U_586),bool,hAPP(fun(U_587,U_586),fun(fun(fun(U_587,bool),U_586),bool),hAPP(U_586,fun(fun(U_587,U_586),fun(fun(fun(U_587,bool),U_586),bool)),hAPP(fun(U_586,fun(U_586,U_586)),fun(U_586,fun(fun(U_587,U_586),fun(fun(fun(U_587,bool),U_586),bool))),finite908156982e_idem(U_586,U_587),U_583),U_582),U_581),U_580)) ),
    inference(variable_rename,[status(thm)],[f_191_1]) ).

fof(f_191_3,plain,
    ! [U_585,U_587,U_583,U_582,U_580,U_586,U_581,U_584] :
      ( hAPP(fun(U_587,bool),U_586,U_580,hAPP(fun(U_587,bool),fun(U_587,bool),hAPP(U_587,fun(fun(U_587,bool),fun(U_587,bool)),insert(U_587),U_585),U_584)) = hAPP(U_586,U_586,hAPP(U_586,fun(U_586,U_586),U_583,hAPP(U_587,U_586,U_581,U_585)),hAPP(fun(U_587,bool),U_586,U_580,U_584))
      | ~ hBOOL(hAPP(fun(U_587,bool),bool,finite_finite(U_587),U_584))
      | ~ hBOOL(hAPP(fun(fun(U_587,bool),U_586),bool,hAPP(fun(U_587,U_586),fun(fun(fun(U_587,bool),U_586),bool),hAPP(U_586,fun(fun(U_587,U_586),fun(fun(fun(U_587,bool),U_586),bool)),hAPP(fun(U_586,fun(U_586,U_586)),fun(U_586,fun(fun(U_587,U_586),fun(fun(fun(U_587,bool),U_586),bool))),finite908156982e_idem(U_586,U_587),U_583),U_582),U_581),U_580)) ),
    inference(definitional_conversion,[status(esa)],[f_191_2]) ).

cnf(f_191_4,plain,
    ( hAPP(fun(U_587,bool),U_586,U_580,hAPP(fun(U_587,bool),fun(U_587,bool),hAPP(U_587,fun(fun(U_587,bool),fun(U_587,bool)),insert(U_587),U_585),U_584)) = hAPP(U_586,U_586,hAPP(U_586,fun(U_586,U_586),U_583,hAPP(U_587,U_586,U_581,U_585)),hAPP(fun(U_587,bool),U_586,U_580,U_584))
    | ~ hBOOL(hAPP(fun(U_587,bool),bool,finite_finite(U_587),U_584))
    | ~ hBOOL(hAPP(fun(fun(U_587,bool),U_586),bool,hAPP(fun(U_587,U_586),fun(fun(fun(U_587,bool),U_586),bool),hAPP(U_586,fun(fun(U_587,U_586),fun(fun(fun(U_587,bool),U_586),bool)),hAPP(fun(U_586,fun(U_586,U_586)),fun(U_586,fun(fun(U_587,U_586),fun(fun(fun(U_587,bool),U_586),bool))),finite908156982e_idem(U_586,U_587),U_583),U_582),U_581),U_580)) ),
    inference(clausify,[status(thm)],[f_191_3]) ).

fof(f_192_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_121_emptyE]) ).

fof(f_192_2,plain,
    ! [U_589,U_588] : ~ hBOOL(hAPP(fun(U_589,bool),bool,hAPP(U_589,fun(fun(U_589,bool),bool),member(U_589),U_588),bot_bot(fun(U_589,bool)))),
    inference(variable_rename,[status(thm)],[f_192_1]) ).

fof(f_192_3,plain,
    ! [U_589,U_588] : ~ hBOOL(hAPP(fun(U_589,bool),bool,hAPP(U_589,fun(fun(U_589,bool),bool),member(U_589),U_588),bot_bot(fun(U_589,bool)))),
    inference(definitional_conversion,[status(esa)],[f_192_2]) ).

cnf(f_192_4,plain,
    ~ hBOOL(hAPP(fun(U_589,bool),bool,hAPP(U_589,fun(fun(U_589,bool),bool),member(U_589),U_588),bot_bot(fun(U_589,bool)))),
    inference(clausify,[status(thm)],[f_192_3]) ).

fof(f_193_1,plain,
    ! [X_b,B_1,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_1)))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) ),
    inference(fof_nnf,[status(thm)],[fact_122_finite__Diff]) ).

fof(f_193_2,plain,
    ! [U_592,U_591,U_590] :
      ( hBOOL(hAPP(fun(U_592,bool),bool,finite_finite(U_592),hAPP(fun(U_592,bool),fun(U_592,bool),hAPP(fun(U_592,bool),fun(fun(U_592,bool),fun(U_592,bool)),minus_minus(fun(U_592,bool)),U_590),U_591)))
      | ~ hBOOL(hAPP(fun(U_592,bool),bool,finite_finite(U_592),U_590)) ),
    inference(variable_rename,[status(thm)],[f_193_1]) ).

fof(f_193_3,plain,
    ! [U_592,U_591,U_590] :
      ( hBOOL(hAPP(fun(U_592,bool),bool,finite_finite(U_592),hAPP(fun(U_592,bool),fun(U_592,bool),hAPP(fun(U_592,bool),fun(fun(U_592,bool),fun(U_592,bool)),minus_minus(fun(U_592,bool)),U_590),U_591)))
      | ~ hBOOL(hAPP(fun(U_592,bool),bool,finite_finite(U_592),U_590)) ),
    inference(definitional_conversion,[status(esa)],[f_193_2]) ).

cnf(f_193_4,plain,
    ( hBOOL(hAPP(fun(U_592,bool),bool,finite_finite(U_592),hAPP(fun(U_592,bool),fun(U_592,bool),hAPP(fun(U_592,bool),fun(fun(U_592,bool),fun(U_592,bool)),minus_minus(fun(U_592,bool)),U_590),U_591)))
    | ~ hBOOL(hAPP(fun(U_592,bool),bool,finite_finite(U_592),U_590)) ),
    inference(clausify,[status(thm)],[f_193_3]) ).

fof(f_194_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_123_finite_OemptyI]) ).

fof(f_194_2,plain,
    ! [U_593] : hBOOL(hAPP(fun(U_593,bool),bool,finite_finite(U_593),bot_bot(fun(U_593,bool)))),
    inference(variable_rename,[status(thm)],[f_194_1]) ).

fof(f_194_3,plain,
    ! [U_593] : hBOOL(hAPP(fun(U_593,bool),bool,finite_finite(U_593),bot_bot(fun(U_593,bool)))),
    inference(definitional_conversion,[status(esa)],[f_194_2]) ).

cnf(f_194_4,plain,
    hBOOL(hAPP(fun(U_593,bool),bool,finite_finite(U_593),bot_bot(fun(U_593,bool)))),
    inference(clausify,[status(thm)],[f_194_3]) ).

fof(f_195_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_124_empty__subsetI]) ).

fof(f_195_2,plain,
    ! [U_595,U_594] : hBOOL(hAPP(fun(U_595,bool),bool,hAPP(fun(U_595,bool),fun(fun(U_595,bool),bool),ord_less_eq(fun(U_595,bool)),bot_bot(fun(U_595,bool))),U_594)),
    inference(variable_rename,[status(thm)],[f_195_1]) ).

fof(f_195_3,plain,
    ! [U_594,U_595] : hBOOL(hAPP(fun(U_595,bool),bool,hAPP(fun(U_595,bool),fun(fun(U_595,bool),bool),ord_less_eq(fun(U_595,bool)),bot_bot(fun(U_595,bool))),U_594)),
    inference(definitional_conversion,[status(esa)],[f_195_2]) ).

cnf(f_195_4,plain,
    hBOOL(hAPP(fun(U_595,bool),bool,hAPP(fun(U_595,bool),fun(fun(U_595,bool),bool),ord_less_eq(fun(U_595,bool)),bot_bot(fun(U_595,bool))),U_594)),
    inference(clausify,[status(thm)],[f_195_3]) ).

fof(f_196_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_125_equals0D]) ).

fof(f_196_2,plain,
    ! [U_598,U_597,U_596] :
      ( ~ hBOOL(hAPP(fun(U_598,bool),bool,hAPP(U_598,fun(fun(U_598,bool),bool),member(U_598),U_597),U_596))
      | ti(fun(U_598,bool),U_596) != bot_bot(fun(U_598,bool)) ),
    inference(variable_rename,[status(thm)],[f_196_1]) ).

fof(f_196_3,plain,
    ! [U_596,U_598,U_597] :
      ( ~ hBOOL(hAPP(fun(U_598,bool),bool,hAPP(U_598,fun(fun(U_598,bool),bool),member(U_598),U_597),U_596))
      | ti(fun(U_598,bool),U_596) != bot_bot(fun(U_598,bool)) ),
    inference(definitional_conversion,[status(esa)],[f_196_2]) ).

cnf(f_196_4,plain,
    ( ~ hBOOL(hAPP(fun(U_598,bool),bool,hAPP(U_598,fun(fun(U_598,bool),bool),member(U_598),U_597),U_596))
    | ti(fun(U_598,bool),U_596) != bot_bot(fun(U_598,bool)) ),
    inference(clausify,[status(thm)],[f_196_3]) ).

fof(f_197_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_126_Collect__empty__eq]) ).

fof(f_197_2,plain,
    ! [U_602,U_601] :
      ( ( hAPP(fun(U_602,bool),fun(U_602,bool),collect(U_602),U_601) = bot_bot(fun(U_602,bool))
        | ? [U_600] : hBOOL(hAPP(U_602,bool,U_601,U_600)) )
      & ( ! [U_599] : ~ hBOOL(hAPP(U_602,bool,U_601,U_599))
        | hAPP(fun(U_602,bool),fun(U_602,bool),collect(U_602),U_601) != bot_bot(fun(U_602,bool)) ) ),
    inference(variable_rename,[status(thm)],[f_197_1]) ).

fof(f_197_3,plain,
    ( ! [U_606,U_604] :
        ( hAPP(fun(U_606,bool),fun(U_606,bool),collect(U_606),U_604) = bot_bot(fun(U_606,bool))
        | ? [U_600] : hBOOL(hAPP(U_606,bool,U_604,U_600)) )
    & ! [U_605,U_603] :
        ( ! [U_599] : ~ hBOOL(hAPP(U_605,bool,U_603,U_599))
        | hAPP(fun(U_605,bool),fun(U_605,bool),collect(U_605),U_603) != bot_bot(fun(U_605,bool)) ) ),
    inference(miniscope,[status(thm)],[f_197_2]) ).

fof(f_197_4,plain,
    ( ! [U_606,U_604] :
        ( hAPP(fun(U_606,bool),fun(U_606,bool),collect(U_606),U_604) = bot_bot(fun(U_606,bool))
        | hBOOL(hAPP(U_606,bool,U_604,sK17(U_606,U_604))) )
    & ! [U_605,U_603] :
        ( ! [U_599] : ~ hBOOL(hAPP(U_605,bool,U_603,U_599))
        | hAPP(fun(U_605,bool),fun(U_605,bool),collect(U_605),U_603) != bot_bot(fun(U_605,bool)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_600,sK17(U_606,U_604))],[f_197_3]) ).

fof(f_197_5,plain,
    ( ! [U_604,U_606] :
        ( hAPP(fun(U_606,bool),fun(U_606,bool),collect(U_606),U_604) = bot_bot(fun(U_606,bool))
        | hBOOL(hAPP(U_606,bool,U_604,sK17(U_606,U_604))) )
    & ! [U_599,U_605,U_603] :
        ( ~ hBOOL(hAPP(U_605,bool,U_603,U_599))
        | hAPP(fun(U_605,bool),fun(U_605,bool),collect(U_605),U_603) != bot_bot(fun(U_605,bool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_197_4]) ).

cnf(f_197_6,plain,
    ( ~ hBOOL(hAPP(U_605,bool,U_603,U_599))
    | hAPP(fun(U_605,bool),fun(U_605,bool),collect(U_605),U_603) != bot_bot(fun(U_605,bool)) ),
    inference(clausify,[status(thm)],[f_197_5]) ).

cnf(f_197_7,plain,
    ( hAPP(fun(U_606,bool),fun(U_606,bool),collect(U_606),U_604) = bot_bot(fun(U_606,bool))
    | hBOOL(hAPP(U_606,bool,U_604,sK17(U_606,U_604))) ),
    inference(clausify,[status(thm)],[f_197_5]) ).

fof(f_198_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_127_Diff__cancel]) ).

fof(f_198_2,plain,
    ! [U_608,U_607] : hAPP(fun(U_608,bool),fun(U_608,bool),hAPP(fun(U_608,bool),fun(fun(U_608,bool),fun(U_608,bool)),minus_minus(fun(U_608,bool)),U_607),U_607) = bot_bot(fun(U_608,bool)),
    inference(variable_rename,[status(thm)],[f_198_1]) ).

fof(f_198_3,plain,
    ! [U_608,U_607] : hAPP(fun(U_608,bool),fun(U_608,bool),hAPP(fun(U_608,bool),fun(fun(U_608,bool),fun(U_608,bool)),minus_minus(fun(U_608,bool)),U_607),U_607) = bot_bot(fun(U_608,bool)),
    inference(definitional_conversion,[status(esa)],[f_198_2]) ).

cnf(f_198_4,plain,
    hAPP(fun(U_608,bool),fun(U_608,bool),hAPP(fun(U_608,bool),fun(fun(U_608,bool),fun(U_608,bool)),minus_minus(fun(U_608,bool)),U_607),U_607) = bot_bot(fun(U_608,bool)),
    inference(clausify,[status(thm)],[f_198_3]) ).

fof(f_199_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_128_Diff__empty]) ).

fof(f_199_2,plain,
    ! [U_610,U_609] : hAPP(fun(U_610,bool),fun(U_610,bool),hAPP(fun(U_610,bool),fun(fun(U_610,bool),fun(U_610,bool)),minus_minus(fun(U_610,bool)),U_609),bot_bot(fun(U_610,bool))) = ti(fun(U_610,bool),U_609),
    inference(variable_rename,[status(thm)],[f_199_1]) ).

fof(f_199_3,plain,
    ! [U_609,U_610] : hAPP(fun(U_610,bool),fun(U_610,bool),hAPP(fun(U_610,bool),fun(fun(U_610,bool),fun(U_610,bool)),minus_minus(fun(U_610,bool)),U_609),bot_bot(fun(U_610,bool))) = ti(fun(U_610,bool),U_609),
    inference(definitional_conversion,[status(esa)],[f_199_2]) ).

cnf(f_199_4,plain,
    hAPP(fun(U_610,bool),fun(U_610,bool),hAPP(fun(U_610,bool),fun(fun(U_610,bool),fun(U_610,bool)),minus_minus(fun(U_610,bool)),U_609),bot_bot(fun(U_610,bool))) = ti(fun(U_610,bool),U_609),
    inference(clausify,[status(thm)],[f_199_3]) ).

fof(f_200_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_129_empty__iff]) ).

fof(f_200_2,plain,
    ! [U_612,U_611] : ~ hBOOL(hAPP(fun(U_612,bool),bool,hAPP(U_612,fun(fun(U_612,bool),bool),member(U_612),U_611),bot_bot(fun(U_612,bool)))),
    inference(variable_rename,[status(thm)],[f_200_1]) ).

fof(f_200_3,plain,
    ! [U_611,U_612] : ~ hBOOL(hAPP(fun(U_612,bool),bool,hAPP(U_612,fun(fun(U_612,bool),bool),member(U_612),U_611),bot_bot(fun(U_612,bool)))),
    inference(definitional_conversion,[status(esa)],[f_200_2]) ).

cnf(f_200_4,plain,
    ~ hBOOL(hAPP(fun(U_612,bool),bool,hAPP(U_612,fun(fun(U_612,bool),bool),member(U_612),U_611),bot_bot(fun(U_612,bool)))),
    inference(clausify,[status(thm)],[f_200_3]) ).

fof(f_201_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_130_empty__Collect__eq]) ).

fof(f_201_2,plain,
    ! [U_616,U_615] :
      ( ( bot_bot(fun(U_616,bool)) = hAPP(fun(U_616,bool),fun(U_616,bool),collect(U_616),U_615)
        | ? [U_614] : hBOOL(hAPP(U_616,bool,U_615,U_614)) )
      & ( ! [U_613] : ~ hBOOL(hAPP(U_616,bool,U_615,U_613))
        | bot_bot(fun(U_616,bool)) != hAPP(fun(U_616,bool),fun(U_616,bool),collect(U_616),U_615) ) ),
    inference(variable_rename,[status(thm)],[f_201_1]) ).

fof(f_201_3,plain,
    ( ! [U_620,U_618] :
        ( bot_bot(fun(U_620,bool)) = hAPP(fun(U_620,bool),fun(U_620,bool),collect(U_620),U_618)
        | ? [U_614] : hBOOL(hAPP(U_620,bool,U_618,U_614)) )
    & ! [U_619,U_617] :
        ( ! [U_613] : ~ hBOOL(hAPP(U_619,bool,U_617,U_613))
        | bot_bot(fun(U_619,bool)) != hAPP(fun(U_619,bool),fun(U_619,bool),collect(U_619),U_617) ) ),
    inference(miniscope,[status(thm)],[f_201_2]) ).

fof(f_201_4,plain,
    ( ! [U_620,U_618] :
        ( bot_bot(fun(U_620,bool)) = hAPP(fun(U_620,bool),fun(U_620,bool),collect(U_620),U_618)
        | hBOOL(hAPP(U_620,bool,U_618,sK18(U_620,U_618))) )
    & ! [U_619,U_617] :
        ( ! [U_613] : ~ hBOOL(hAPP(U_619,bool,U_617,U_613))
        | bot_bot(fun(U_619,bool)) != hAPP(fun(U_619,bool),fun(U_619,bool),collect(U_619),U_617) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_614,sK18(U_620,U_618))],[f_201_3]) ).

fof(f_201_5,plain,
    ( ! [U_620,U_618] :
        ( bot_bot(fun(U_620,bool)) = hAPP(fun(U_620,bool),fun(U_620,bool),collect(U_620),U_618)
        | hBOOL(hAPP(U_620,bool,U_618,sK18(U_620,U_618))) )
    & ! [U_613,U_619,U_617] :
        ( ~ hBOOL(hAPP(U_619,bool,U_617,U_613))
        | bot_bot(fun(U_619,bool)) != hAPP(fun(U_619,bool),fun(U_619,bool),collect(U_619),U_617) ) ),
    inference(definitional_conversion,[status(esa)],[f_201_4]) ).

cnf(f_201_6,plain,
    ( ~ hBOOL(hAPP(U_619,bool,U_617,U_613))
    | bot_bot(fun(U_619,bool)) != hAPP(fun(U_619,bool),fun(U_619,bool),collect(U_619),U_617) ),
    inference(clausify,[status(thm)],[f_201_5]) ).

cnf(f_201_7,plain,
    ( bot_bot(fun(U_620,bool)) = hAPP(fun(U_620,bool),fun(U_620,bool),collect(U_620),U_618)
    | hBOOL(hAPP(U_620,bool,U_618,sK18(U_620,U_618))) ),
    inference(clausify,[status(thm)],[f_201_5]) ).

fof(f_202_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_131_empty__Diff]) ).

fof(f_202_2,plain,
    ! [U_622,U_621] : hAPP(fun(U_622,bool),fun(U_622,bool),hAPP(fun(U_622,bool),fun(fun(U_622,bool),fun(U_622,bool)),minus_minus(fun(U_622,bool)),bot_bot(fun(U_622,bool))),U_621) = bot_bot(fun(U_622,bool)),
    inference(variable_rename,[status(thm)],[f_202_1]) ).

fof(f_202_3,plain,
    ! [U_621,U_622] : hAPP(fun(U_622,bool),fun(U_622,bool),hAPP(fun(U_622,bool),fun(fun(U_622,bool),fun(U_622,bool)),minus_minus(fun(U_622,bool)),bot_bot(fun(U_622,bool))),U_621) = bot_bot(fun(U_622,bool)),
    inference(definitional_conversion,[status(esa)],[f_202_2]) ).

cnf(f_202_4,plain,
    hAPP(fun(U_622,bool),fun(U_622,bool),hAPP(fun(U_622,bool),fun(fun(U_622,bool),fun(U_622,bool)),minus_minus(fun(U_622,bool)),bot_bot(fun(U_622,bool))),U_621) = bot_bot(fun(U_622,bool)),
    inference(clausify,[status(thm)],[f_202_3]) ).

fof(f_203_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_132_ex__in__conv]) ).

fof(f_203_2,plain,
    ! [U_626,U_625] :
      ( ( ? [U_624] : hBOOL(hAPP(fun(U_626,bool),bool,hAPP(U_626,fun(fun(U_626,bool),bool),member(U_626),U_624),U_625))
        | ti(fun(U_626,bool),U_625) = bot_bot(fun(U_626,bool)) )
      & ( ti(fun(U_626,bool),U_625) != bot_bot(fun(U_626,bool))
        | ! [U_623] : ~ hBOOL(hAPP(fun(U_626,bool),bool,hAPP(U_626,fun(fun(U_626,bool),bool),member(U_626),U_623),U_625)) ) ),
    inference(variable_rename,[status(thm)],[f_203_1]) ).

fof(f_203_3,plain,
    ( ! [U_630,U_628] :
        ( ? [U_624] : hBOOL(hAPP(fun(U_630,bool),bool,hAPP(U_630,fun(fun(U_630,bool),bool),member(U_630),U_624),U_628))
        | ti(fun(U_630,bool),U_628) = bot_bot(fun(U_630,bool)) )
    & ! [U_629,U_627] :
        ( ti(fun(U_629,bool),U_627) != bot_bot(fun(U_629,bool))
        | ! [U_623] : ~ hBOOL(hAPP(fun(U_629,bool),bool,hAPP(U_629,fun(fun(U_629,bool),bool),member(U_629),U_623),U_627)) ) ),
    inference(miniscope,[status(thm)],[f_203_2]) ).

fof(f_203_4,plain,
    ( ! [U_630,U_628] :
        ( hBOOL(hAPP(fun(U_630,bool),bool,hAPP(U_630,fun(fun(U_630,bool),bool),member(U_630),sK19(U_630,U_628)),U_628))
        | ti(fun(U_630,bool),U_628) = bot_bot(fun(U_630,bool)) )
    & ! [U_629,U_627] :
        ( ti(fun(U_629,bool),U_627) != bot_bot(fun(U_629,bool))
        | ! [U_623] : ~ hBOOL(hAPP(fun(U_629,bool),bool,hAPP(U_629,fun(fun(U_629,bool),bool),member(U_629),U_623),U_627)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_624,sK19(U_630,U_628))],[f_203_3]) ).

fof(f_203_5,plain,
    ( ! [U_628,U_630] :
        ( hBOOL(hAPP(fun(U_630,bool),bool,hAPP(U_630,fun(fun(U_630,bool),bool),member(U_630),sK19(U_630,U_628)),U_628))
        | ti(fun(U_630,bool),U_628) = bot_bot(fun(U_630,bool)) )
    & ! [U_623,U_627,U_629] :
        ( ti(fun(U_629,bool),U_627) != bot_bot(fun(U_629,bool))
        | ~ hBOOL(hAPP(fun(U_629,bool),bool,hAPP(U_629,fun(fun(U_629,bool),bool),member(U_629),U_623),U_627)) ) ),
    inference(definitional_conversion,[status(esa)],[f_203_4]) ).

cnf(f_203_6,plain,
    ( ti(fun(U_629,bool),U_627) != bot_bot(fun(U_629,bool))
    | ~ hBOOL(hAPP(fun(U_629,bool),bool,hAPP(U_629,fun(fun(U_629,bool),bool),member(U_629),U_623),U_627)) ),
    inference(clausify,[status(thm)],[f_203_5]) ).

cnf(f_203_7,plain,
    ( hBOOL(hAPP(fun(U_630,bool),bool,hAPP(U_630,fun(fun(U_630,bool),bool),member(U_630),sK19(U_630,U_628)),U_628))
    | ti(fun(U_630,bool),U_628) = bot_bot(fun(U_630,bool)) ),
    inference(clausify,[status(thm)],[f_203_5]) ).

fof(f_204_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_133_all__not__in__conv]) ).

fof(f_204_2,plain,
    ! [U_634,U_633] :
      ( ( ! [U_632] : ~ hBOOL(hAPP(fun(U_634,bool),bool,hAPP(U_634,fun(fun(U_634,bool),bool),member(U_634),U_632),U_633))
        | ti(fun(U_634,bool),U_633) != bot_bot(fun(U_634,bool)) )
      & ( ti(fun(U_634,bool),U_633) = bot_bot(fun(U_634,bool))
        | ? [U_631] : hBOOL(hAPP(fun(U_634,bool),bool,hAPP(U_634,fun(fun(U_634,bool),bool),member(U_634),U_631),U_633)) ) ),
    inference(variable_rename,[status(thm)],[f_204_1]) ).

fof(f_204_3,plain,
    ( ! [U_638,U_636] :
        ( ! [U_632] : ~ hBOOL(hAPP(fun(U_638,bool),bool,hAPP(U_638,fun(fun(U_638,bool),bool),member(U_638),U_632),U_636))
        | ti(fun(U_638,bool),U_636) != bot_bot(fun(U_638,bool)) )
    & ! [U_637,U_635] :
        ( ti(fun(U_637,bool),U_635) = bot_bot(fun(U_637,bool))
        | ? [U_631] : hBOOL(hAPP(fun(U_637,bool),bool,hAPP(U_637,fun(fun(U_637,bool),bool),member(U_637),U_631),U_635)) ) ),
    inference(miniscope,[status(thm)],[f_204_2]) ).

fof(f_204_4,plain,
    ( ! [U_638,U_636] :
        ( ! [U_632] : ~ hBOOL(hAPP(fun(U_638,bool),bool,hAPP(U_638,fun(fun(U_638,bool),bool),member(U_638),U_632),U_636))
        | ti(fun(U_638,bool),U_636) != bot_bot(fun(U_638,bool)) )
    & ! [U_637,U_635] :
        ( ti(fun(U_637,bool),U_635) = bot_bot(fun(U_637,bool))
        | hBOOL(hAPP(fun(U_637,bool),bool,hAPP(U_637,fun(fun(U_637,bool),bool),member(U_637),sK20(U_637,U_635)),U_635)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_631,sK20(U_637,U_635))],[f_204_3]) ).

fof(f_204_5,plain,
    ( ! [U_632,U_636,U_638] :
        ( ~ hBOOL(hAPP(fun(U_638,bool),bool,hAPP(U_638,fun(fun(U_638,bool),bool),member(U_638),U_632),U_636))
        | ti(fun(U_638,bool),U_636) != bot_bot(fun(U_638,bool)) )
    & ! [U_635,U_637] :
        ( ti(fun(U_637,bool),U_635) = bot_bot(fun(U_637,bool))
        | hBOOL(hAPP(fun(U_637,bool),bool,hAPP(U_637,fun(fun(U_637,bool),bool),member(U_637),sK20(U_637,U_635)),U_635)) ) ),
    inference(definitional_conversion,[status(esa)],[f_204_4]) ).

cnf(f_204_6,plain,
    ( ti(fun(U_637,bool),U_635) = bot_bot(fun(U_637,bool))
    | hBOOL(hAPP(fun(U_637,bool),bool,hAPP(U_637,fun(fun(U_637,bool),bool),member(U_637),sK20(U_637,U_635)),U_635)) ),
    inference(clausify,[status(thm)],[f_204_5]) ).

cnf(f_204_7,plain,
    ( ~ hBOOL(hAPP(fun(U_638,bool),bool,hAPP(U_638,fun(fun(U_638,bool),bool),member(U_638),U_632),U_636))
    | ti(fun(U_638,bool),U_636) != bot_bot(fun(U_638,bool)) ),
    inference(clausify,[status(thm)],[f_204_5]) ).

fof(f_205_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_134_bot__apply]) ).

fof(f_205_2,plain,
    ! [U_641,U_640] :
      ( ! [U_639] : hAPP(U_641,U_640,bot_bot(fun(U_641,U_640)),U_639) = bot_bot(U_640)
      | ~ bot(U_640) ),
    inference(variable_rename,[status(thm)],[f_205_1]) ).

fof(f_205_3,plain,
    ! [U_639,U_640,U_641] :
      ( hAPP(U_641,U_640,bot_bot(fun(U_641,U_640)),U_639) = bot_bot(U_640)
      | ~ bot(U_640) ),
    inference(definitional_conversion,[status(esa)],[f_205_2]) ).

cnf(f_205_4,plain,
    ( hAPP(U_641,U_640,bot_bot(fun(U_641,U_640)),U_639) = bot_bot(U_640)
    | ~ bot(U_640) ),
    inference(clausify,[status(thm)],[f_205_3]) ).

fof(f_206_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_135_empty__def]) ).

fof(f_206_2,plain,
    ! [U_642] : bot_bot(fun(U_642,bool)) = hAPP(fun(U_642,bool),fun(U_642,bool),collect(U_642),hAPP(bool,fun(U_642,bool),combk(bool,U_642),fFalse)),
    inference(variable_rename,[status(thm)],[f_206_1]) ).

fof(f_206_3,plain,
    ! [U_642] : bot_bot(fun(U_642,bool)) = hAPP(fun(U_642,bool),fun(U_642,bool),collect(U_642),hAPP(bool,fun(U_642,bool),combk(bool,U_642),fFalse)),
    inference(definitional_conversion,[status(esa)],[f_206_2]) ).

cnf(f_206_4,plain,
    bot_bot(fun(U_642,bool)) = hAPP(fun(U_642,bool),fun(U_642,bool),collect(U_642),hAPP(bool,fun(U_642,bool),combk(bool,U_642),fFalse)),
    inference(clausify,[status(thm)],[f_206_3]) ).

fof(f_207_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_136_bot__fun__def]) ).

fof(f_207_2,plain,
    ! [U_645,U_644] :
      ( ! [U_643] : hAPP(U_645,U_644,bot_bot(fun(U_645,U_644)),U_643) = bot_bot(U_644)
      | ~ bot(U_644) ),
    inference(variable_rename,[status(thm)],[f_207_1]) ).

fof(f_207_3,plain,
    ! [U_643,U_644,U_645] :
      ( hAPP(U_645,U_644,bot_bot(fun(U_645,U_644)),U_643) = bot_bot(U_644)
      | ~ bot(U_644) ),
    inference(definitional_conversion,[status(esa)],[f_207_2]) ).

cnf(f_207_4,plain,
    ( hAPP(U_645,U_644,bot_bot(fun(U_645,U_644)),U_643) = bot_bot(U_644)
    | ~ bot(U_644) ),
    inference(clausify,[status(thm)],[f_207_3]) ).

fof(f_208_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_137_insert__Diff]) ).

fof(f_208_2,plain,
    ! [U_648,U_647,U_646] :
      ( hAPP(fun(U_648,bool),fun(U_648,bool),hAPP(U_648,fun(fun(U_648,bool),fun(U_648,bool)),insert(U_648),U_647),hAPP(fun(U_648,bool),fun(U_648,bool),hAPP(fun(U_648,bool),fun(fun(U_648,bool),fun(U_648,bool)),minus_minus(fun(U_648,bool)),U_646),hAPP(fun(U_648,bool),fun(U_648,bool),hAPP(U_648,fun(fun(U_648,bool),fun(U_648,bool)),insert(U_648),U_647),bot_bot(fun(U_648,bool))))) = ti(fun(U_648,bool),U_646)
      | ~ hBOOL(hAPP(fun(U_648,bool),bool,hAPP(U_648,fun(fun(U_648,bool),bool),member(U_648),U_647),U_646)) ),
    inference(variable_rename,[status(thm)],[f_208_1]) ).

fof(f_208_3,plain,
    ! [U_646,U_648,U_647] :
      ( hAPP(fun(U_648,bool),fun(U_648,bool),hAPP(U_648,fun(fun(U_648,bool),fun(U_648,bool)),insert(U_648),U_647),hAPP(fun(U_648,bool),fun(U_648,bool),hAPP(fun(U_648,bool),fun(fun(U_648,bool),fun(U_648,bool)),minus_minus(fun(U_648,bool)),U_646),hAPP(fun(U_648,bool),fun(U_648,bool),hAPP(U_648,fun(fun(U_648,bool),fun(U_648,bool)),insert(U_648),U_647),bot_bot(fun(U_648,bool))))) = ti(fun(U_648,bool),U_646)
      | ~ hBOOL(hAPP(fun(U_648,bool),bool,hAPP(U_648,fun(fun(U_648,bool),bool),member(U_648),U_647),U_646)) ),
    inference(definitional_conversion,[status(esa)],[f_208_2]) ).

cnf(f_208_4,plain,
    ( hAPP(fun(U_648,bool),fun(U_648,bool),hAPP(U_648,fun(fun(U_648,bool),fun(U_648,bool)),insert(U_648),U_647),hAPP(fun(U_648,bool),fun(U_648,bool),hAPP(fun(U_648,bool),fun(fun(U_648,bool),fun(U_648,bool)),minus_minus(fun(U_648,bool)),U_646),hAPP(fun(U_648,bool),fun(U_648,bool),hAPP(U_648,fun(fun(U_648,bool),fun(U_648,bool)),insert(U_648),U_647),bot_bot(fun(U_648,bool))))) = ti(fun(U_648,bool),U_646)
    | ~ hBOOL(hAPP(fun(U_648,bool),bool,hAPP(U_648,fun(fun(U_648,bool),bool),member(U_648),U_647),U_646)) ),
    inference(clausify,[status(thm)],[f_208_3]) ).

fof(f_209_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_138_Diff__insert__absorb]) ).

fof(f_209_2,plain,
    ! [U_651,U_650,U_649] :
      ( hAPP(fun(U_651,bool),fun(U_651,bool),hAPP(fun(U_651,bool),fun(fun(U_651,bool),fun(U_651,bool)),minus_minus(fun(U_651,bool)),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_650),U_649)),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_650),bot_bot(fun(U_651,bool)))) = ti(fun(U_651,bool),U_649)
      | hBOOL(hAPP(fun(U_651,bool),bool,hAPP(U_651,fun(fun(U_651,bool),bool),member(U_651),U_650),U_649)) ),
    inference(variable_rename,[status(thm)],[f_209_1]) ).

fof(f_209_3,plain,
    ! [U_650,U_651,U_649] :
      ( hAPP(fun(U_651,bool),fun(U_651,bool),hAPP(fun(U_651,bool),fun(fun(U_651,bool),fun(U_651,bool)),minus_minus(fun(U_651,bool)),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_650),U_649)),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_650),bot_bot(fun(U_651,bool)))) = ti(fun(U_651,bool),U_649)
      | hBOOL(hAPP(fun(U_651,bool),bool,hAPP(U_651,fun(fun(U_651,bool),bool),member(U_651),U_650),U_649)) ),
    inference(definitional_conversion,[status(esa)],[f_209_2]) ).

cnf(f_209_4,plain,
    ( hAPP(fun(U_651,bool),fun(U_651,bool),hAPP(fun(U_651,bool),fun(fun(U_651,bool),fun(U_651,bool)),minus_minus(fun(U_651,bool)),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_650),U_649)),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_650),bot_bot(fun(U_651,bool)))) = ti(fun(U_651,bool),U_649)
    | hBOOL(hAPP(fun(U_651,bool),bool,hAPP(U_651,fun(fun(U_651,bool),bool),member(U_651),U_650),U_649)) ),
    inference(clausify,[status(thm)],[f_209_3]) ).

fof(f_210_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_139_insert__Diff__single]) ).

fof(f_210_2,plain,
    ! [U_654,U_653,U_652] : hAPP(fun(U_654,bool),fun(U_654,bool),hAPP(U_654,fun(fun(U_654,bool),fun(U_654,bool)),insert(U_654),U_653),hAPP(fun(U_654,bool),fun(U_654,bool),hAPP(fun(U_654,bool),fun(fun(U_654,bool),fun(U_654,bool)),minus_minus(fun(U_654,bool)),U_652),hAPP(fun(U_654,bool),fun(U_654,bool),hAPP(U_654,fun(fun(U_654,bool),fun(U_654,bool)),insert(U_654),U_653),bot_bot(fun(U_654,bool))))) = hAPP(fun(U_654,bool),fun(U_654,bool),hAPP(U_654,fun(fun(U_654,bool),fun(U_654,bool)),insert(U_654),U_653),U_652),
    inference(variable_rename,[status(thm)],[f_210_1]) ).

fof(f_210_3,plain,
    ! [U_654,U_653,U_652] : hAPP(fun(U_654,bool),fun(U_654,bool),hAPP(U_654,fun(fun(U_654,bool),fun(U_654,bool)),insert(U_654),U_653),hAPP(fun(U_654,bool),fun(U_654,bool),hAPP(fun(U_654,bool),fun(fun(U_654,bool),fun(U_654,bool)),minus_minus(fun(U_654,bool)),U_652),hAPP(fun(U_654,bool),fun(U_654,bool),hAPP(U_654,fun(fun(U_654,bool),fun(U_654,bool)),insert(U_654),U_653),bot_bot(fun(U_654,bool))))) = hAPP(fun(U_654,bool),fun(U_654,bool),hAPP(U_654,fun(fun(U_654,bool),fun(U_654,bool)),insert(U_654),U_653),U_652),
    inference(definitional_conversion,[status(esa)],[f_210_2]) ).

cnf(f_210_4,plain,
    hAPP(fun(U_654,bool),fun(U_654,bool),hAPP(U_654,fun(fun(U_654,bool),fun(U_654,bool)),insert(U_654),U_653),hAPP(fun(U_654,bool),fun(U_654,bool),hAPP(fun(U_654,bool),fun(fun(U_654,bool),fun(U_654,bool)),minus_minus(fun(U_654,bool)),U_652),hAPP(fun(U_654,bool),fun(U_654,bool),hAPP(U_654,fun(fun(U_654,bool),fun(U_654,bool)),insert(U_654),U_653),bot_bot(fun(U_654,bool))))) = hAPP(fun(U_654,bool),fun(U_654,bool),hAPP(U_654,fun(fun(U_654,bool),fun(U_654,bool)),insert(U_654),U_653),U_652),
    inference(clausify,[status(thm)],[f_210_3]) ).

fof(f_211_1,plain,
    ! [X_b,A_3,A_2,B_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),A_2),B_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)),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_1),
    inference(fof_nnf,[status(thm)],[fact_140_Diff__insert2]) ).

fof(f_211_2,plain,
    ! [U_658,U_657,U_656,U_655] : hAPP(fun(U_658,bool),fun(U_658,bool),hAPP(fun(U_658,bool),fun(fun(U_658,bool),fun(U_658,bool)),minus_minus(fun(U_658,bool)),U_657),hAPP(fun(U_658,bool),fun(U_658,bool),hAPP(U_658,fun(fun(U_658,bool),fun(U_658,bool)),insert(U_658),U_656),U_655)) = hAPP(fun(U_658,bool),fun(U_658,bool),hAPP(fun(U_658,bool),fun(fun(U_658,bool),fun(U_658,bool)),minus_minus(fun(U_658,bool)),hAPP(fun(U_658,bool),fun(U_658,bool),hAPP(fun(U_658,bool),fun(fun(U_658,bool),fun(U_658,bool)),minus_minus(fun(U_658,bool)),U_657),hAPP(fun(U_658,bool),fun(U_658,bool),hAPP(U_658,fun(fun(U_658,bool),fun(U_658,bool)),insert(U_658),U_656),bot_bot(fun(U_658,bool))))),U_655),
    inference(variable_rename,[status(thm)],[f_211_1]) ).

fof(f_211_3,plain,
    ! [U_655,U_657,U_658,U_656] : hAPP(fun(U_658,bool),fun(U_658,bool),hAPP(fun(U_658,bool),fun(fun(U_658,bool),fun(U_658,bool)),minus_minus(fun(U_658,bool)),U_657),hAPP(fun(U_658,bool),fun(U_658,bool),hAPP(U_658,fun(fun(U_658,bool),fun(U_658,bool)),insert(U_658),U_656),U_655)) = hAPP(fun(U_658,bool),fun(U_658,bool),hAPP(fun(U_658,bool),fun(fun(U_658,bool),fun(U_658,bool)),minus_minus(fun(U_658,bool)),hAPP(fun(U_658,bool),fun(U_658,bool),hAPP(fun(U_658,bool),fun(fun(U_658,bool),fun(U_658,bool)),minus_minus(fun(U_658,bool)),U_657),hAPP(fun(U_658,bool),fun(U_658,bool),hAPP(U_658,fun(fun(U_658,bool),fun(U_658,bool)),insert(U_658),U_656),bot_bot(fun(U_658,bool))))),U_655),
    inference(definitional_conversion,[status(esa)],[f_211_2]) ).

cnf(f_211_4,plain,
    hAPP(fun(U_658,bool),fun(U_658,bool),hAPP(fun(U_658,bool),fun(fun(U_658,bool),fun(U_658,bool)),minus_minus(fun(U_658,bool)),U_657),hAPP(fun(U_658,bool),fun(U_658,bool),hAPP(U_658,fun(fun(U_658,bool),fun(U_658,bool)),insert(U_658),U_656),U_655)) = hAPP(fun(U_658,bool),fun(U_658,bool),hAPP(fun(U_658,bool),fun(fun(U_658,bool),fun(U_658,bool)),minus_minus(fun(U_658,bool)),hAPP(fun(U_658,bool),fun(U_658,bool),hAPP(fun(U_658,bool),fun(fun(U_658,bool),fun(U_658,bool)),minus_minus(fun(U_658,bool)),U_657),hAPP(fun(U_658,bool),fun(U_658,bool),hAPP(U_658,fun(fun(U_658,bool),fun(U_658,bool)),insert(U_658),U_656),bot_bot(fun(U_658,bool))))),U_655),
    inference(clausify,[status(thm)],[f_211_3]) ).

fof(f_212_1,plain,
    ! [X_b,A_3,A_2,B_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),A_2),B_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)),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_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),bot_bot(fun(X_b,bool)))),
    inference(fof_nnf,[status(thm)],[fact_141_Diff__insert]) ).

fof(f_212_2,plain,
    ! [U_662,U_661,U_660,U_659] : hAPP(fun(U_662,bool),fun(U_662,bool),hAPP(fun(U_662,bool),fun(fun(U_662,bool),fun(U_662,bool)),minus_minus(fun(U_662,bool)),U_661),hAPP(fun(U_662,bool),fun(U_662,bool),hAPP(U_662,fun(fun(U_662,bool),fun(U_662,bool)),insert(U_662),U_660),U_659)) = hAPP(fun(U_662,bool),fun(U_662,bool),hAPP(fun(U_662,bool),fun(fun(U_662,bool),fun(U_662,bool)),minus_minus(fun(U_662,bool)),hAPP(fun(U_662,bool),fun(U_662,bool),hAPP(fun(U_662,bool),fun(fun(U_662,bool),fun(U_662,bool)),minus_minus(fun(U_662,bool)),U_661),U_659)),hAPP(fun(U_662,bool),fun(U_662,bool),hAPP(U_662,fun(fun(U_662,bool),fun(U_662,bool)),insert(U_662),U_660),bot_bot(fun(U_662,bool)))),
    inference(variable_rename,[status(thm)],[f_212_1]) ).

fof(f_212_3,plain,
    ! [U_661,U_662,U_659,U_660] : hAPP(fun(U_662,bool),fun(U_662,bool),hAPP(fun(U_662,bool),fun(fun(U_662,bool),fun(U_662,bool)),minus_minus(fun(U_662,bool)),U_661),hAPP(fun(U_662,bool),fun(U_662,bool),hAPP(U_662,fun(fun(U_662,bool),fun(U_662,bool)),insert(U_662),U_660),U_659)) = hAPP(fun(U_662,bool),fun(U_662,bool),hAPP(fun(U_662,bool),fun(fun(U_662,bool),fun(U_662,bool)),minus_minus(fun(U_662,bool)),hAPP(fun(U_662,bool),fun(U_662,bool),hAPP(fun(U_662,bool),fun(fun(U_662,bool),fun(U_662,bool)),minus_minus(fun(U_662,bool)),U_661),U_659)),hAPP(fun(U_662,bool),fun(U_662,bool),hAPP(U_662,fun(fun(U_662,bool),fun(U_662,bool)),insert(U_662),U_660),bot_bot(fun(U_662,bool)))),
    inference(definitional_conversion,[status(esa)],[f_212_2]) ).

cnf(f_212_4,plain,
    hAPP(fun(U_662,bool),fun(U_662,bool),hAPP(fun(U_662,bool),fun(fun(U_662,bool),fun(U_662,bool)),minus_minus(fun(U_662,bool)),U_661),hAPP(fun(U_662,bool),fun(U_662,bool),hAPP(U_662,fun(fun(U_662,bool),fun(U_662,bool)),insert(U_662),U_660),U_659)) = hAPP(fun(U_662,bool),fun(U_662,bool),hAPP(fun(U_662,bool),fun(fun(U_662,bool),fun(U_662,bool)),minus_minus(fun(U_662,bool)),hAPP(fun(U_662,bool),fun(U_662,bool),hAPP(fun(U_662,bool),fun(fun(U_662,bool),fun(U_662,bool)),minus_minus(fun(U_662,bool)),U_661),U_659)),hAPP(fun(U_662,bool),fun(U_662,bool),hAPP(U_662,fun(fun(U_662,bool),fun(U_662,bool)),insert(U_662),U_660),bot_bot(fun(U_662,bool)))),
    inference(clausify,[status(thm)],[f_212_3]) ).

fof(f_213_1,plain,
    ! [X_c,X_b,X_1,F,Z_2,G,F_1] :
      ( 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_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))),finite908156982e_idem(X_b,X_c),F),Z_2),G),F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_142_folding__image__simple__idem_Oidem]) ).

fof(f_213_2,plain,
    ! [U_669,U_668,U_667,U_666,U_665,U_664,U_663] :
      ( hAPP(U_668,U_668,hAPP(U_668,fun(U_668,U_668),U_666,U_667),U_667) = ti(U_668,U_667)
      | ~ hBOOL(hAPP(fun(fun(U_669,bool),U_668),bool,hAPP(fun(U_669,U_668),fun(fun(fun(U_669,bool),U_668),bool),hAPP(U_668,fun(fun(U_669,U_668),fun(fun(fun(U_669,bool),U_668),bool)),hAPP(fun(U_668,fun(U_668,U_668)),fun(U_668,fun(fun(U_669,U_668),fun(fun(fun(U_669,bool),U_668),bool))),finite908156982e_idem(U_668,U_669),U_666),U_665),U_664),U_663)) ),
    inference(variable_rename,[status(thm)],[f_213_1]) ).

fof(f_213_3,plain,
    ! [U_669,U_668,U_667,U_666] :
      ( ! [U_665,U_664,U_663] : ~ hBOOL(hAPP(fun(fun(U_669,bool),U_668),bool,hAPP(fun(U_669,U_668),fun(fun(fun(U_669,bool),U_668),bool),hAPP(U_668,fun(fun(U_669,U_668),fun(fun(fun(U_669,bool),U_668),bool)),hAPP(fun(U_668,fun(U_668,U_668)),fun(U_668,fun(fun(U_669,U_668),fun(fun(fun(U_669,bool),U_668),bool))),finite908156982e_idem(U_668,U_669),U_666),U_665),U_664),U_663))
      | hAPP(U_668,U_668,hAPP(U_668,fun(U_668,U_668),U_666,U_667),U_667) = ti(U_668,U_667) ),
    inference(miniscope,[status(thm)],[f_213_2]) ).

fof(f_213_4,plain,
    ! [U_663,U_664,U_665,U_666,U_667,U_668,U_669] :
      ( ~ hBOOL(hAPP(fun(fun(U_669,bool),U_668),bool,hAPP(fun(U_669,U_668),fun(fun(fun(U_669,bool),U_668),bool),hAPP(U_668,fun(fun(U_669,U_668),fun(fun(fun(U_669,bool),U_668),bool)),hAPP(fun(U_668,fun(U_668,U_668)),fun(U_668,fun(fun(U_669,U_668),fun(fun(fun(U_669,bool),U_668),bool))),finite908156982e_idem(U_668,U_669),U_666),U_665),U_664),U_663))
      | hAPP(U_668,U_668,hAPP(U_668,fun(U_668,U_668),U_666,U_667),U_667) = ti(U_668,U_667) ),
    inference(definitional_conversion,[status(esa)],[f_213_3]) ).

cnf(f_213_5,plain,
    ( ~ hBOOL(hAPP(fun(fun(U_669,bool),U_668),bool,hAPP(fun(U_669,U_668),fun(fun(fun(U_669,bool),U_668),bool),hAPP(U_668,fun(fun(U_669,U_668),fun(fun(fun(U_669,bool),U_668),bool)),hAPP(fun(U_668,fun(U_668,U_668)),fun(U_668,fun(fun(U_669,U_668),fun(fun(fun(U_669,bool),U_668),bool))),finite908156982e_idem(U_668,U_669),U_666),U_665),U_664),U_663))
    | hAPP(U_668,U_668,hAPP(U_668,fun(U_668,U_668),U_666,U_667),U_667) = ti(U_668,U_667) ),
    inference(clausify,[status(thm)],[f_213_4]) ).

fof(f_214_1,plain,
    ! [X_b,A_3,X_1,B_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),B_1)))
      | ~ 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_1)) ),
    inference(fof_nnf,[status(thm)],[fact_143_diff__single__insert]) ).

fof(f_214_2,plain,
    ! [U_673,U_672,U_671,U_670] :
      ( hBOOL(hAPP(fun(U_673,bool),bool,hAPP(fun(U_673,bool),fun(fun(U_673,bool),bool),ord_less_eq(fun(U_673,bool)),U_672),hAPP(fun(U_673,bool),fun(U_673,bool),hAPP(U_673,fun(fun(U_673,bool),fun(U_673,bool)),insert(U_673),U_671),U_670)))
      | ~ hBOOL(hAPP(fun(U_673,bool),bool,hAPP(U_673,fun(fun(U_673,bool),bool),member(U_673),U_671),U_672))
      | ~ hBOOL(hAPP(fun(U_673,bool),bool,hAPP(fun(U_673,bool),fun(fun(U_673,bool),bool),ord_less_eq(fun(U_673,bool)),hAPP(fun(U_673,bool),fun(U_673,bool),hAPP(fun(U_673,bool),fun(fun(U_673,bool),fun(U_673,bool)),minus_minus(fun(U_673,bool)),U_672),hAPP(fun(U_673,bool),fun(U_673,bool),hAPP(U_673,fun(fun(U_673,bool),fun(U_673,bool)),insert(U_673),U_671),bot_bot(fun(U_673,bool))))),U_670)) ),
    inference(variable_rename,[status(thm)],[f_214_1]) ).

fof(f_214_3,plain,
    ! [U_673,U_670,U_671,U_672] :
      ( hBOOL(hAPP(fun(U_673,bool),bool,hAPP(fun(U_673,bool),fun(fun(U_673,bool),bool),ord_less_eq(fun(U_673,bool)),U_672),hAPP(fun(U_673,bool),fun(U_673,bool),hAPP(U_673,fun(fun(U_673,bool),fun(U_673,bool)),insert(U_673),U_671),U_670)))
      | ~ hBOOL(hAPP(fun(U_673,bool),bool,hAPP(U_673,fun(fun(U_673,bool),bool),member(U_673),U_671),U_672))
      | ~ hBOOL(hAPP(fun(U_673,bool),bool,hAPP(fun(U_673,bool),fun(fun(U_673,bool),bool),ord_less_eq(fun(U_673,bool)),hAPP(fun(U_673,bool),fun(U_673,bool),hAPP(fun(U_673,bool),fun(fun(U_673,bool),fun(U_673,bool)),minus_minus(fun(U_673,bool)),U_672),hAPP(fun(U_673,bool),fun(U_673,bool),hAPP(U_673,fun(fun(U_673,bool),fun(U_673,bool)),insert(U_673),U_671),bot_bot(fun(U_673,bool))))),U_670)) ),
    inference(definitional_conversion,[status(esa)],[f_214_2]) ).

cnf(f_214_4,plain,
    ( hBOOL(hAPP(fun(U_673,bool),bool,hAPP(fun(U_673,bool),fun(fun(U_673,bool),bool),ord_less_eq(fun(U_673,bool)),U_672),hAPP(fun(U_673,bool),fun(U_673,bool),hAPP(U_673,fun(fun(U_673,bool),fun(U_673,bool)),insert(U_673),U_671),U_670)))
    | ~ hBOOL(hAPP(fun(U_673,bool),bool,hAPP(U_673,fun(fun(U_673,bool),bool),member(U_673),U_671),U_672))
    | ~ hBOOL(hAPP(fun(U_673,bool),bool,hAPP(fun(U_673,bool),fun(fun(U_673,bool),bool),ord_less_eq(fun(U_673,bool)),hAPP(fun(U_673,bool),fun(U_673,bool),hAPP(fun(U_673,bool),fun(fun(U_673,bool),fun(U_673,bool)),minus_minus(fun(U_673,bool)),U_672),hAPP(fun(U_673,bool),fun(U_673,bool),hAPP(U_673,fun(fun(U_673,bool),fun(U_673,bool)),insert(U_673),U_671),bot_bot(fun(U_673,bool))))),U_670)) ),
    inference(clausify,[status(thm)],[f_214_3]) ).

fof(f_215_1,plain,
    ! [X_b,A_3,X_1,B_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),B_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),B_1))
          & ~ 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_1))
          & 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_1))
            | 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_1))
            | ~ 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_1))) ) ),
    inference(fof_nnf,[status(thm)],[fact_144_subset__insert__iff]) ).

fof(f_215_2,plain,
    ! [U_677,U_676,U_675,U_674] :
      ( ( hBOOL(hAPP(fun(U_677,bool),bool,hAPP(fun(U_677,bool),fun(fun(U_677,bool),bool),ord_less_eq(fun(U_677,bool)),U_676),hAPP(fun(U_677,bool),fun(U_677,bool),hAPP(U_677,fun(fun(U_677,bool),fun(U_677,bool)),insert(U_677),U_675),U_674)))
        | ( ~ hBOOL(hAPP(fun(U_677,bool),bool,hAPP(fun(U_677,bool),fun(fun(U_677,bool),bool),ord_less_eq(fun(U_677,bool)),U_676),U_674))
          & ~ hBOOL(hAPP(fun(U_677,bool),bool,hAPP(U_677,fun(fun(U_677,bool),bool),member(U_677),U_675),U_676)) )
        | ( ~ hBOOL(hAPP(fun(U_677,bool),bool,hAPP(fun(U_677,bool),fun(fun(U_677,bool),bool),ord_less_eq(fun(U_677,bool)),hAPP(fun(U_677,bool),fun(U_677,bool),hAPP(fun(U_677,bool),fun(fun(U_677,bool),fun(U_677,bool)),minus_minus(fun(U_677,bool)),U_676),hAPP(fun(U_677,bool),fun(U_677,bool),hAPP(U_677,fun(fun(U_677,bool),fun(U_677,bool)),insert(U_677),U_675),bot_bot(fun(U_677,bool))))),U_674))
          & hBOOL(hAPP(fun(U_677,bool),bool,hAPP(U_677,fun(fun(U_677,bool),bool),member(U_677),U_675),U_676)) ) )
      & ( ( ( hBOOL(hAPP(fun(U_677,bool),bool,hAPP(fun(U_677,bool),fun(fun(U_677,bool),bool),ord_less_eq(fun(U_677,bool)),U_676),U_674))
            | hBOOL(hAPP(fun(U_677,bool),bool,hAPP(U_677,fun(fun(U_677,bool),bool),member(U_677),U_675),U_676)) )
          & ( hBOOL(hAPP(fun(U_677,bool),bool,hAPP(fun(U_677,bool),fun(fun(U_677,bool),bool),ord_less_eq(fun(U_677,bool)),hAPP(fun(U_677,bool),fun(U_677,bool),hAPP(fun(U_677,bool),fun(fun(U_677,bool),fun(U_677,bool)),minus_minus(fun(U_677,bool)),U_676),hAPP(fun(U_677,bool),fun(U_677,bool),hAPP(U_677,fun(fun(U_677,bool),fun(U_677,bool)),insert(U_677),U_675),bot_bot(fun(U_677,bool))))),U_674))
            | ~ hBOOL(hAPP(fun(U_677,bool),bool,hAPP(U_677,fun(fun(U_677,bool),bool),member(U_677),U_675),U_676)) ) )
        | ~ hBOOL(hAPP(fun(U_677,bool),bool,hAPP(fun(U_677,bool),fun(fun(U_677,bool),bool),ord_less_eq(fun(U_677,bool)),U_676),hAPP(fun(U_677,bool),fun(U_677,bool),hAPP(U_677,fun(fun(U_677,bool),fun(U_677,bool)),insert(U_677),U_675),U_674))) ) ),
    inference(variable_rename,[status(thm)],[f_215_1]) ).

fof(f_215_3,plain,
    ( ! [U_685,U_683,U_681,U_679] :
        ( hBOOL(hAPP(fun(U_685,bool),bool,hAPP(fun(U_685,bool),fun(fun(U_685,bool),bool),ord_less_eq(fun(U_685,bool)),U_683),hAPP(fun(U_685,bool),fun(U_685,bool),hAPP(U_685,fun(fun(U_685,bool),fun(U_685,bool)),insert(U_685),U_681),U_679)))
        | ( ~ hBOOL(hAPP(fun(U_685,bool),bool,hAPP(fun(U_685,bool),fun(fun(U_685,bool),bool),ord_less_eq(fun(U_685,bool)),U_683),U_679))
          & ~ hBOOL(hAPP(fun(U_685,bool),bool,hAPP(U_685,fun(fun(U_685,bool),bool),member(U_685),U_681),U_683)) )
        | ( ~ hBOOL(hAPP(fun(U_685,bool),bool,hAPP(fun(U_685,bool),fun(fun(U_685,bool),bool),ord_less_eq(fun(U_685,bool)),hAPP(fun(U_685,bool),fun(U_685,bool),hAPP(fun(U_685,bool),fun(fun(U_685,bool),fun(U_685,bool)),minus_minus(fun(U_685,bool)),U_683),hAPP(fun(U_685,bool),fun(U_685,bool),hAPP(U_685,fun(fun(U_685,bool),fun(U_685,bool)),insert(U_685),U_681),bot_bot(fun(U_685,bool))))),U_679))
          & hBOOL(hAPP(fun(U_685,bool),bool,hAPP(U_685,fun(fun(U_685,bool),bool),member(U_685),U_681),U_683)) ) )
    & ! [U_684,U_682,U_680,U_678] :
        ( ( ( hBOOL(hAPP(fun(U_684,bool),bool,hAPP(fun(U_684,bool),fun(fun(U_684,bool),bool),ord_less_eq(fun(U_684,bool)),U_682),U_678))
            | hBOOL(hAPP(fun(U_684,bool),bool,hAPP(U_684,fun(fun(U_684,bool),bool),member(U_684),U_680),U_682)) )
          & ( hBOOL(hAPP(fun(U_684,bool),bool,hAPP(fun(U_684,bool),fun(fun(U_684,bool),bool),ord_less_eq(fun(U_684,bool)),hAPP(fun(U_684,bool),fun(U_684,bool),hAPP(fun(U_684,bool),fun(fun(U_684,bool),fun(U_684,bool)),minus_minus(fun(U_684,bool)),U_682),hAPP(fun(U_684,bool),fun(U_684,bool),hAPP(U_684,fun(fun(U_684,bool),fun(U_684,bool)),insert(U_684),U_680),bot_bot(fun(U_684,bool))))),U_678))
            | ~ hBOOL(hAPP(fun(U_684,bool),bool,hAPP(U_684,fun(fun(U_684,bool),bool),member(U_684),U_680),U_682)) ) )
        | ~ hBOOL(hAPP(fun(U_684,bool),bool,hAPP(fun(U_684,bool),fun(fun(U_684,bool),bool),ord_less_eq(fun(U_684,bool)),U_682),hAPP(fun(U_684,bool),fun(U_684,bool),hAPP(U_684,fun(fun(U_684,bool),fun(U_684,bool)),insert(U_684),U_680),U_678))) ) ),
    inference(miniscope,[status(thm)],[f_215_2]) ).

fof(f_215_4,plain,
    ( ! [U_679,U_681,U_683,U_685] :
        ( ~ hBOOL(hAPP(fun(U_685,bool),bool,hAPP(fun(U_685,bool),fun(fun(U_685,bool),bool),ord_less_eq(fun(U_685,bool)),U_683),U_679))
        | ~ sP31(U_679,U_681,U_683,U_685) )
    & ! [U_679,U_681,U_683,U_685] :
        ( ~ hBOOL(hAPP(fun(U_685,bool),bool,hAPP(U_685,fun(fun(U_685,bool),bool),member(U_685),U_681),U_683))
        | ~ sP31(U_679,U_681,U_683,U_685) )
    & ! [U_679,U_681,U_683,U_685] :
        ( ~ hBOOL(hAPP(fun(U_685,bool),bool,hAPP(fun(U_685,bool),fun(fun(U_685,bool),bool),ord_less_eq(fun(U_685,bool)),hAPP(fun(U_685,bool),fun(U_685,bool),hAPP(fun(U_685,bool),fun(fun(U_685,bool),fun(U_685,bool)),minus_minus(fun(U_685,bool)),U_683),hAPP(fun(U_685,bool),fun(U_685,bool),hAPP(U_685,fun(fun(U_685,bool),fun(U_685,bool)),insert(U_685),U_681),bot_bot(fun(U_685,bool))))),U_679))
        | ~ sP30(U_679,U_681,U_683,U_685) )
    & ! [U_679,U_681,U_683,U_685] :
        ( hBOOL(hAPP(fun(U_685,bool),bool,hAPP(U_685,fun(fun(U_685,bool),bool),member(U_685),U_681),U_683))
        | ~ sP30(U_679,U_681,U_683,U_685) )
    & ! [U_684,U_678,U_682,U_680] :
        ( hBOOL(hAPP(fun(U_684,bool),bool,hAPP(fun(U_684,bool),fun(fun(U_684,bool),bool),ord_less_eq(fun(U_684,bool)),U_682),U_678))
        | hBOOL(hAPP(fun(U_684,bool),bool,hAPP(U_684,fun(fun(U_684,bool),bool),member(U_684),U_680),U_682))
        | ~ sP29(U_684,U_678,U_682,U_680) )
    & ! [U_684,U_678,U_682,U_680] :
        ( hBOOL(hAPP(fun(U_684,bool),bool,hAPP(fun(U_684,bool),fun(fun(U_684,bool),bool),ord_less_eq(fun(U_684,bool)),hAPP(fun(U_684,bool),fun(U_684,bool),hAPP(fun(U_684,bool),fun(fun(U_684,bool),fun(U_684,bool)),minus_minus(fun(U_684,bool)),U_682),hAPP(fun(U_684,bool),fun(U_684,bool),hAPP(U_684,fun(fun(U_684,bool),fun(U_684,bool)),insert(U_684),U_680),bot_bot(fun(U_684,bool))))),U_678))
        | ~ hBOOL(hAPP(fun(U_684,bool),bool,hAPP(U_684,fun(fun(U_684,bool),bool),member(U_684),U_680),U_682))
        | ~ sP29(U_684,U_678,U_682,U_680) )
    & ! [U_679,U_681,U_683,U_685] :
        ( hBOOL(hAPP(fun(U_685,bool),bool,hAPP(fun(U_685,bool),fun(fun(U_685,bool),bool),ord_less_eq(fun(U_685,bool)),U_683),hAPP(fun(U_685,bool),fun(U_685,bool),hAPP(U_685,fun(fun(U_685,bool),fun(U_685,bool)),insert(U_685),U_681),U_679)))
        | sP31(U_679,U_681,U_683,U_685)
        | sP30(U_679,U_681,U_683,U_685) )
    & ! [U_684,U_678,U_682,U_680] :
        ( sP29(U_684,U_678,U_682,U_680)
        | ~ hBOOL(hAPP(fun(U_684,bool),bool,hAPP(fun(U_684,bool),fun(fun(U_684,bool),bool),ord_less_eq(fun(U_684,bool)),U_682),hAPP(fun(U_684,bool),fun(U_684,bool),hAPP(U_684,fun(fun(U_684,bool),fun(U_684,bool)),insert(U_684),U_680),U_678))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP29,sP30,sP31])],[f_215_3]) ).

cnf(f_215_5,plain,
    ( sP29(U_684,U_678,U_682,U_680)
    | ~ hBOOL(hAPP(fun(U_684,bool),bool,hAPP(fun(U_684,bool),fun(fun(U_684,bool),bool),ord_less_eq(fun(U_684,bool)),U_682),hAPP(fun(U_684,bool),fun(U_684,bool),hAPP(U_684,fun(fun(U_684,bool),fun(U_684,bool)),insert(U_684),U_680),U_678))) ),
    inference(clausify,[status(thm)],[f_215_4]) ).

cnf(f_215_6,plain,
    ( hBOOL(hAPP(fun(U_685,bool),bool,hAPP(fun(U_685,bool),fun(fun(U_685,bool),bool),ord_less_eq(fun(U_685,bool)),U_683),hAPP(fun(U_685,bool),fun(U_685,bool),hAPP(U_685,fun(fun(U_685,bool),fun(U_685,bool)),insert(U_685),U_681),U_679)))
    | sP31(U_679,U_681,U_683,U_685)
    | sP30(U_679,U_681,U_683,U_685) ),
    inference(clausify,[status(thm)],[f_215_4]) ).

cnf(f_215_7,plain,
    ( hBOOL(hAPP(fun(U_684,bool),bool,hAPP(fun(U_684,bool),fun(fun(U_684,bool),bool),ord_less_eq(fun(U_684,bool)),hAPP(fun(U_684,bool),fun(U_684,bool),hAPP(fun(U_684,bool),fun(fun(U_684,bool),fun(U_684,bool)),minus_minus(fun(U_684,bool)),U_682),hAPP(fun(U_684,bool),fun(U_684,bool),hAPP(U_684,fun(fun(U_684,bool),fun(U_684,bool)),insert(U_684),U_680),bot_bot(fun(U_684,bool))))),U_678))
    | ~ hBOOL(hAPP(fun(U_684,bool),bool,hAPP(U_684,fun(fun(U_684,bool),bool),member(U_684),U_680),U_682))
    | ~ sP29(U_684,U_678,U_682,U_680) ),
    inference(clausify,[status(thm)],[f_215_4]) ).

cnf(f_215_8,plain,
    ( hBOOL(hAPP(fun(U_684,bool),bool,hAPP(fun(U_684,bool),fun(fun(U_684,bool),bool),ord_less_eq(fun(U_684,bool)),U_682),U_678))
    | hBOOL(hAPP(fun(U_684,bool),bool,hAPP(U_684,fun(fun(U_684,bool),bool),member(U_684),U_680),U_682))
    | ~ sP29(U_684,U_678,U_682,U_680) ),
    inference(clausify,[status(thm)],[f_215_4]) ).

cnf(f_215_9,plain,
    ( hBOOL(hAPP(fun(U_685,bool),bool,hAPP(U_685,fun(fun(U_685,bool),bool),member(U_685),U_681),U_683))
    | ~ sP30(U_679,U_681,U_683,U_685) ),
    inference(clausify,[status(thm)],[f_215_4]) ).

cnf(f_215_10,plain,
    ( ~ hBOOL(hAPP(fun(U_685,bool),bool,hAPP(fun(U_685,bool),fun(fun(U_685,bool),bool),ord_less_eq(fun(U_685,bool)),hAPP(fun(U_685,bool),fun(U_685,bool),hAPP(fun(U_685,bool),fun(fun(U_685,bool),fun(U_685,bool)),minus_minus(fun(U_685,bool)),U_683),hAPP(fun(U_685,bool),fun(U_685,bool),hAPP(U_685,fun(fun(U_685,bool),fun(U_685,bool)),insert(U_685),U_681),bot_bot(fun(U_685,bool))))),U_679))
    | ~ sP30(U_679,U_681,U_683,U_685) ),
    inference(clausify,[status(thm)],[f_215_4]) ).

cnf(f_215_11,plain,
    ( ~ hBOOL(hAPP(fun(U_685,bool),bool,hAPP(U_685,fun(fun(U_685,bool),bool),member(U_685),U_681),U_683))
    | ~ sP31(U_679,U_681,U_683,U_685) ),
    inference(clausify,[status(thm)],[f_215_4]) ).

cnf(f_215_12,plain,
    ( ~ hBOOL(hAPP(fun(U_685,bool),bool,hAPP(fun(U_685,bool),fun(fun(U_685,bool),bool),ord_less_eq(fun(U_685,bool)),U_683),U_679))
    | ~ sP31(U_679,U_681,U_683,U_685) ),
    inference(clausify,[status(thm)],[f_215_4]) ).

fof(f_216_1,plain,
    ! [X_b,A_3,B_1] :
      ( ( ( 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_1)))
          | ~ 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_1))) ) )
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_1)) ),
    inference(fof_nnf,[status(thm)],[fact_145_finite__Diff2]) ).

fof(f_216_2,plain,
    ! [U_688,U_687,U_686] :
      ( ( ( hBOOL(hAPP(fun(U_688,bool),bool,finite_finite(U_688),hAPP(fun(U_688,bool),fun(U_688,bool),hAPP(fun(U_688,bool),fun(fun(U_688,bool),fun(U_688,bool)),minus_minus(fun(U_688,bool)),U_687),U_686)))
          | ~ hBOOL(hAPP(fun(U_688,bool),bool,finite_finite(U_688),U_687)) )
        & ( hBOOL(hAPP(fun(U_688,bool),bool,finite_finite(U_688),U_687))
          | ~ hBOOL(hAPP(fun(U_688,bool),bool,finite_finite(U_688),hAPP(fun(U_688,bool),fun(U_688,bool),hAPP(fun(U_688,bool),fun(fun(U_688,bool),fun(U_688,bool)),minus_minus(fun(U_688,bool)),U_687),U_686))) ) )
      | ~ hBOOL(hAPP(fun(U_688,bool),bool,finite_finite(U_688),U_686)) ),
    inference(variable_rename,[status(thm)],[f_216_1]) ).

fof(f_216_3,plain,
    ( ! [U_687,U_688,U_686] :
        ( hBOOL(hAPP(fun(U_688,bool),bool,finite_finite(U_688),hAPP(fun(U_688,bool),fun(U_688,bool),hAPP(fun(U_688,bool),fun(fun(U_688,bool),fun(U_688,bool)),minus_minus(fun(U_688,bool)),U_687),U_686)))
        | ~ hBOOL(hAPP(fun(U_688,bool),bool,finite_finite(U_688),U_687))
        | ~ sP32(U_687,U_688,U_686) )
    & ! [U_687,U_688,U_686] :
        ( hBOOL(hAPP(fun(U_688,bool),bool,finite_finite(U_688),U_687))
        | ~ hBOOL(hAPP(fun(U_688,bool),bool,finite_finite(U_688),hAPP(fun(U_688,bool),fun(U_688,bool),hAPP(fun(U_688,bool),fun(fun(U_688,bool),fun(U_688,bool)),minus_minus(fun(U_688,bool)),U_687),U_686)))
        | ~ sP32(U_687,U_688,U_686) )
    & ! [U_687,U_688,U_686] :
        ( sP32(U_687,U_688,U_686)
        | ~ hBOOL(hAPP(fun(U_688,bool),bool,finite_finite(U_688),U_686)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP32])],[f_216_2]) ).

cnf(f_216_4,plain,
    ( sP32(U_687,U_688,U_686)
    | ~ hBOOL(hAPP(fun(U_688,bool),bool,finite_finite(U_688),U_686)) ),
    inference(clausify,[status(thm)],[f_216_3]) ).

cnf(f_216_5,plain,
    ( hBOOL(hAPP(fun(U_688,bool),bool,finite_finite(U_688),U_687))
    | ~ hBOOL(hAPP(fun(U_688,bool),bool,finite_finite(U_688),hAPP(fun(U_688,bool),fun(U_688,bool),hAPP(fun(U_688,bool),fun(fun(U_688,bool),fun(U_688,bool)),minus_minus(fun(U_688,bool)),U_687),U_686)))
    | ~ sP32(U_687,U_688,U_686) ),
    inference(clausify,[status(thm)],[f_216_3]) ).

cnf(f_216_6,plain,
    ( hBOOL(hAPP(fun(U_688,bool),bool,finite_finite(U_688),hAPP(fun(U_688,bool),fun(U_688,bool),hAPP(fun(U_688,bool),fun(fun(U_688,bool),fun(U_688,bool)),minus_minus(fun(U_688,bool)),U_687),U_686)))
    | ~ hBOOL(hAPP(fun(U_688,bool),bool,finite_finite(U_688),U_687))
    | ~ sP32(U_687,U_688,U_686) ),
    inference(clausify,[status(thm)],[f_216_3]) ).

fof(f_217_1,plain,
    ! [X_b,A_3,X_1,B_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)),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_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_1)
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_1)) ),
    inference(fof_nnf,[status(thm)],[fact_146_insert__Diff1]) ).

fof(f_217_2,plain,
    ! [U_692,U_691,U_690,U_689] :
      ( hAPP(fun(U_692,bool),fun(U_692,bool),hAPP(fun(U_692,bool),fun(fun(U_692,bool),fun(U_692,bool)),minus_minus(fun(U_692,bool)),hAPP(fun(U_692,bool),fun(U_692,bool),hAPP(U_692,fun(fun(U_692,bool),fun(U_692,bool)),insert(U_692),U_690),U_691)),U_689) = hAPP(fun(U_692,bool),fun(U_692,bool),hAPP(fun(U_692,bool),fun(fun(U_692,bool),fun(U_692,bool)),minus_minus(fun(U_692,bool)),U_691),U_689)
      | ~ hBOOL(hAPP(fun(U_692,bool),bool,hAPP(U_692,fun(fun(U_692,bool),bool),member(U_692),U_690),U_689)) ),
    inference(variable_rename,[status(thm)],[f_217_1]) ).

fof(f_217_3,plain,
    ! [U_689,U_692,U_690,U_691] :
      ( hAPP(fun(U_692,bool),fun(U_692,bool),hAPP(fun(U_692,bool),fun(fun(U_692,bool),fun(U_692,bool)),minus_minus(fun(U_692,bool)),hAPP(fun(U_692,bool),fun(U_692,bool),hAPP(U_692,fun(fun(U_692,bool),fun(U_692,bool)),insert(U_692),U_690),U_691)),U_689) = hAPP(fun(U_692,bool),fun(U_692,bool),hAPP(fun(U_692,bool),fun(fun(U_692,bool),fun(U_692,bool)),minus_minus(fun(U_692,bool)),U_691),U_689)
      | ~ hBOOL(hAPP(fun(U_692,bool),bool,hAPP(U_692,fun(fun(U_692,bool),bool),member(U_692),U_690),U_689)) ),
    inference(definitional_conversion,[status(esa)],[f_217_2]) ).

cnf(f_217_4,plain,
    ( hAPP(fun(U_692,bool),fun(U_692,bool),hAPP(fun(U_692,bool),fun(fun(U_692,bool),fun(U_692,bool)),minus_minus(fun(U_692,bool)),hAPP(fun(U_692,bool),fun(U_692,bool),hAPP(U_692,fun(fun(U_692,bool),fun(U_692,bool)),insert(U_692),U_690),U_691)),U_689) = hAPP(fun(U_692,bool),fun(U_692,bool),hAPP(fun(U_692,bool),fun(fun(U_692,bool),fun(U_692,bool)),minus_minus(fun(U_692,bool)),U_691),U_689)
    | ~ hBOOL(hAPP(fun(U_692,bool),bool,hAPP(U_692,fun(fun(U_692,bool),bool),member(U_692),U_690),U_689)) ),
    inference(clausify,[status(thm)],[f_217_3]) ).

fof(f_218_1,plain,
    ! [X_b,A_3,X_1,B_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)),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_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),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_1))
        | hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_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)),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_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_1)
        | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_147_insert__Diff__if]) ).

fof(f_218_2,plain,
    ! [U_696,U_695,U_694,U_693] :
      ( ( hAPP(fun(U_696,bool),fun(U_696,bool),hAPP(fun(U_696,bool),fun(fun(U_696,bool),fun(U_696,bool)),minus_minus(fun(U_696,bool)),hAPP(fun(U_696,bool),fun(U_696,bool),hAPP(U_696,fun(fun(U_696,bool),fun(U_696,bool)),insert(U_696),U_694),U_695)),U_693) = hAPP(fun(U_696,bool),fun(U_696,bool),hAPP(U_696,fun(fun(U_696,bool),fun(U_696,bool)),insert(U_696),U_694),hAPP(fun(U_696,bool),fun(U_696,bool),hAPP(fun(U_696,bool),fun(fun(U_696,bool),fun(U_696,bool)),minus_minus(fun(U_696,bool)),U_695),U_693))
        | hBOOL(hAPP(fun(U_696,bool),bool,hAPP(U_696,fun(fun(U_696,bool),bool),member(U_696),U_694),U_693)) )
      & ( hAPP(fun(U_696,bool),fun(U_696,bool),hAPP(fun(U_696,bool),fun(fun(U_696,bool),fun(U_696,bool)),minus_minus(fun(U_696,bool)),hAPP(fun(U_696,bool),fun(U_696,bool),hAPP(U_696,fun(fun(U_696,bool),fun(U_696,bool)),insert(U_696),U_694),U_695)),U_693) = hAPP(fun(U_696,bool),fun(U_696,bool),hAPP(fun(U_696,bool),fun(fun(U_696,bool),fun(U_696,bool)),minus_minus(fun(U_696,bool)),U_695),U_693)
        | ~ hBOOL(hAPP(fun(U_696,bool),bool,hAPP(U_696,fun(fun(U_696,bool),bool),member(U_696),U_694),U_693)) ) ),
    inference(variable_rename,[status(thm)],[f_218_1]) ).

fof(f_218_3,plain,
    ( ! [U_704,U_702,U_700,U_698] :
        ( hAPP(fun(U_704,bool),fun(U_704,bool),hAPP(fun(U_704,bool),fun(fun(U_704,bool),fun(U_704,bool)),minus_minus(fun(U_704,bool)),hAPP(fun(U_704,bool),fun(U_704,bool),hAPP(U_704,fun(fun(U_704,bool),fun(U_704,bool)),insert(U_704),U_700),U_702)),U_698) = hAPP(fun(U_704,bool),fun(U_704,bool),hAPP(U_704,fun(fun(U_704,bool),fun(U_704,bool)),insert(U_704),U_700),hAPP(fun(U_704,bool),fun(U_704,bool),hAPP(fun(U_704,bool),fun(fun(U_704,bool),fun(U_704,bool)),minus_minus(fun(U_704,bool)),U_702),U_698))
        | hBOOL(hAPP(fun(U_704,bool),bool,hAPP(U_704,fun(fun(U_704,bool),bool),member(U_704),U_700),U_698)) )
    & ! [U_703,U_701,U_699,U_697] :
        ( hAPP(fun(U_703,bool),fun(U_703,bool),hAPP(fun(U_703,bool),fun(fun(U_703,bool),fun(U_703,bool)),minus_minus(fun(U_703,bool)),hAPP(fun(U_703,bool),fun(U_703,bool),hAPP(U_703,fun(fun(U_703,bool),fun(U_703,bool)),insert(U_703),U_699),U_701)),U_697) = hAPP(fun(U_703,bool),fun(U_703,bool),hAPP(fun(U_703,bool),fun(fun(U_703,bool),fun(U_703,bool)),minus_minus(fun(U_703,bool)),U_701),U_697)
        | ~ hBOOL(hAPP(fun(U_703,bool),bool,hAPP(U_703,fun(fun(U_703,bool),bool),member(U_703),U_699),U_697)) ) ),
    inference(miniscope,[status(thm)],[f_218_2]) ).

fof(f_218_4,plain,
    ( ! [U_700,U_698,U_702,U_704] :
        ( hAPP(fun(U_704,bool),fun(U_704,bool),hAPP(fun(U_704,bool),fun(fun(U_704,bool),fun(U_704,bool)),minus_minus(fun(U_704,bool)),hAPP(fun(U_704,bool),fun(U_704,bool),hAPP(U_704,fun(fun(U_704,bool),fun(U_704,bool)),insert(U_704),U_700),U_702)),U_698) = hAPP(fun(U_704,bool),fun(U_704,bool),hAPP(U_704,fun(fun(U_704,bool),fun(U_704,bool)),insert(U_704),U_700),hAPP(fun(U_704,bool),fun(U_704,bool),hAPP(fun(U_704,bool),fun(fun(U_704,bool),fun(U_704,bool)),minus_minus(fun(U_704,bool)),U_702),U_698))
        | hBOOL(hAPP(fun(U_704,bool),bool,hAPP(U_704,fun(fun(U_704,bool),bool),member(U_704),U_700),U_698)) )
    & ! [U_703,U_697,U_701,U_699] :
        ( hAPP(fun(U_703,bool),fun(U_703,bool),hAPP(fun(U_703,bool),fun(fun(U_703,bool),fun(U_703,bool)),minus_minus(fun(U_703,bool)),hAPP(fun(U_703,bool),fun(U_703,bool),hAPP(U_703,fun(fun(U_703,bool),fun(U_703,bool)),insert(U_703),U_699),U_701)),U_697) = hAPP(fun(U_703,bool),fun(U_703,bool),hAPP(fun(U_703,bool),fun(fun(U_703,bool),fun(U_703,bool)),minus_minus(fun(U_703,bool)),U_701),U_697)
        | ~ hBOOL(hAPP(fun(U_703,bool),bool,hAPP(U_703,fun(fun(U_703,bool),bool),member(U_703),U_699),U_697)) ) ),
    inference(definitional_conversion,[status(esa)],[f_218_3]) ).

cnf(f_218_5,plain,
    ( hAPP(fun(U_703,bool),fun(U_703,bool),hAPP(fun(U_703,bool),fun(fun(U_703,bool),fun(U_703,bool)),minus_minus(fun(U_703,bool)),hAPP(fun(U_703,bool),fun(U_703,bool),hAPP(U_703,fun(fun(U_703,bool),fun(U_703,bool)),insert(U_703),U_699),U_701)),U_697) = hAPP(fun(U_703,bool),fun(U_703,bool),hAPP(fun(U_703,bool),fun(fun(U_703,bool),fun(U_703,bool)),minus_minus(fun(U_703,bool)),U_701),U_697)
    | ~ hBOOL(hAPP(fun(U_703,bool),bool,hAPP(U_703,fun(fun(U_703,bool),bool),member(U_703),U_699),U_697)) ),
    inference(clausify,[status(thm)],[f_218_4]) ).

cnf(f_218_6,plain,
    ( hAPP(fun(U_704,bool),fun(U_704,bool),hAPP(fun(U_704,bool),fun(fun(U_704,bool),fun(U_704,bool)),minus_minus(fun(U_704,bool)),hAPP(fun(U_704,bool),fun(U_704,bool),hAPP(U_704,fun(fun(U_704,bool),fun(U_704,bool)),insert(U_704),U_700),U_702)),U_698) = hAPP(fun(U_704,bool),fun(U_704,bool),hAPP(U_704,fun(fun(U_704,bool),fun(U_704,bool)),insert(U_704),U_700),hAPP(fun(U_704,bool),fun(U_704,bool),hAPP(fun(U_704,bool),fun(fun(U_704,bool),fun(U_704,bool)),minus_minus(fun(U_704,bool)),U_702),U_698))
    | hBOOL(hAPP(fun(U_704,bool),bool,hAPP(U_704,fun(fun(U_704,bool),bool),member(U_704),U_700),U_698)) ),
    inference(clausify,[status(thm)],[f_218_4]) ).

fof(f_219_1,plain,
    ! [X_b,C_2,A_3,B_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)),B_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)),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_1),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_1)) ),
    inference(fof_nnf,[status(thm)],[fact_148_double__diff]) ).

fof(f_219_2,plain,
    ! [U_708,U_707,U_706,U_705] :
      ( hAPP(fun(U_708,bool),fun(U_708,bool),hAPP(fun(U_708,bool),fun(fun(U_708,bool),fun(U_708,bool)),minus_minus(fun(U_708,bool)),U_705),hAPP(fun(U_708,bool),fun(U_708,bool),hAPP(fun(U_708,bool),fun(fun(U_708,bool),fun(U_708,bool)),minus_minus(fun(U_708,bool)),U_707),U_706)) = ti(fun(U_708,bool),U_706)
      | ~ hBOOL(hAPP(fun(U_708,bool),bool,hAPP(fun(U_708,bool),fun(fun(U_708,bool),bool),ord_less_eq(fun(U_708,bool)),U_705),U_707))
      | ~ hBOOL(hAPP(fun(U_708,bool),bool,hAPP(fun(U_708,bool),fun(fun(U_708,bool),bool),ord_less_eq(fun(U_708,bool)),U_706),U_705)) ),
    inference(variable_rename,[status(thm)],[f_219_1]) ).

fof(f_219_3,plain,
    ! [U_706,U_708,U_707,U_705] :
      ( hAPP(fun(U_708,bool),fun(U_708,bool),hAPP(fun(U_708,bool),fun(fun(U_708,bool),fun(U_708,bool)),minus_minus(fun(U_708,bool)),U_705),hAPP(fun(U_708,bool),fun(U_708,bool),hAPP(fun(U_708,bool),fun(fun(U_708,bool),fun(U_708,bool)),minus_minus(fun(U_708,bool)),U_707),U_706)) = ti(fun(U_708,bool),U_706)
      | ~ hBOOL(hAPP(fun(U_708,bool),bool,hAPP(fun(U_708,bool),fun(fun(U_708,bool),bool),ord_less_eq(fun(U_708,bool)),U_705),U_707))
      | ~ hBOOL(hAPP(fun(U_708,bool),bool,hAPP(fun(U_708,bool),fun(fun(U_708,bool),bool),ord_less_eq(fun(U_708,bool)),U_706),U_705)) ),
    inference(definitional_conversion,[status(esa)],[f_219_2]) ).

cnf(f_219_4,plain,
    ( hAPP(fun(U_708,bool),fun(U_708,bool),hAPP(fun(U_708,bool),fun(fun(U_708,bool),fun(U_708,bool)),minus_minus(fun(U_708,bool)),U_705),hAPP(fun(U_708,bool),fun(U_708,bool),hAPP(fun(U_708,bool),fun(fun(U_708,bool),fun(U_708,bool)),minus_minus(fun(U_708,bool)),U_707),U_706)) = ti(fun(U_708,bool),U_706)
    | ~ hBOOL(hAPP(fun(U_708,bool),bool,hAPP(fun(U_708,bool),fun(fun(U_708,bool),bool),ord_less_eq(fun(U_708,bool)),U_705),U_707))
    | ~ hBOOL(hAPP(fun(U_708,bool),bool,hAPP(fun(U_708,bool),fun(fun(U_708,bool),bool),ord_less_eq(fun(U_708,bool)),U_706),U_705)) ),
    inference(clausify,[status(thm)],[f_219_3]) ).

fof(f_220_1,plain,
    ! [X_b,D_3,B_1,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_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)),C_2),D_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)),D_3),B_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),C_2)) ),
    inference(fof_nnf,[status(thm)],[fact_149_Diff__mono]) ).

fof(f_220_2,plain,
    ! [U_713,U_712,U_711,U_710,U_709] :
      ( hBOOL(hAPP(fun(U_713,bool),bool,hAPP(fun(U_713,bool),fun(fun(U_713,bool),bool),ord_less_eq(fun(U_713,bool)),hAPP(fun(U_713,bool),fun(U_713,bool),hAPP(fun(U_713,bool),fun(fun(U_713,bool),fun(U_713,bool)),minus_minus(fun(U_713,bool)),U_710),U_711)),hAPP(fun(U_713,bool),fun(U_713,bool),hAPP(fun(U_713,bool),fun(fun(U_713,bool),fun(U_713,bool)),minus_minus(fun(U_713,bool)),U_709),U_712)))
      | ~ hBOOL(hAPP(fun(U_713,bool),bool,hAPP(fun(U_713,bool),fun(fun(U_713,bool),bool),ord_less_eq(fun(U_713,bool)),U_712),U_711))
      | ~ hBOOL(hAPP(fun(U_713,bool),bool,hAPP(fun(U_713,bool),fun(fun(U_713,bool),bool),ord_less_eq(fun(U_713,bool)),U_710),U_709)) ),
    inference(variable_rename,[status(thm)],[f_220_1]) ).

fof(f_220_3,plain,
    ! [U_709,U_710,U_713,U_711,U_712] :
      ( hBOOL(hAPP(fun(U_713,bool),bool,hAPP(fun(U_713,bool),fun(fun(U_713,bool),bool),ord_less_eq(fun(U_713,bool)),hAPP(fun(U_713,bool),fun(U_713,bool),hAPP(fun(U_713,bool),fun(fun(U_713,bool),fun(U_713,bool)),minus_minus(fun(U_713,bool)),U_710),U_711)),hAPP(fun(U_713,bool),fun(U_713,bool),hAPP(fun(U_713,bool),fun(fun(U_713,bool),fun(U_713,bool)),minus_minus(fun(U_713,bool)),U_709),U_712)))
      | ~ hBOOL(hAPP(fun(U_713,bool),bool,hAPP(fun(U_713,bool),fun(fun(U_713,bool),bool),ord_less_eq(fun(U_713,bool)),U_712),U_711))
      | ~ hBOOL(hAPP(fun(U_713,bool),bool,hAPP(fun(U_713,bool),fun(fun(U_713,bool),bool),ord_less_eq(fun(U_713,bool)),U_710),U_709)) ),
    inference(definitional_conversion,[status(esa)],[f_220_2]) ).

cnf(f_220_4,plain,
    ( hBOOL(hAPP(fun(U_713,bool),bool,hAPP(fun(U_713,bool),fun(fun(U_713,bool),bool),ord_less_eq(fun(U_713,bool)),hAPP(fun(U_713,bool),fun(U_713,bool),hAPP(fun(U_713,bool),fun(fun(U_713,bool),fun(U_713,bool)),minus_minus(fun(U_713,bool)),U_710),U_711)),hAPP(fun(U_713,bool),fun(U_713,bool),hAPP(fun(U_713,bool),fun(fun(U_713,bool),fun(U_713,bool)),minus_minus(fun(U_713,bool)),U_709),U_712)))
    | ~ hBOOL(hAPP(fun(U_713,bool),bool,hAPP(fun(U_713,bool),fun(fun(U_713,bool),bool),ord_less_eq(fun(U_713,bool)),U_712),U_711))
    | ~ hBOOL(hAPP(fun(U_713,bool),bool,hAPP(fun(U_713,bool),fun(fun(U_713,bool),bool),ord_less_eq(fun(U_713,bool)),U_710),U_709)) ),
    inference(clausify,[status(thm)],[f_220_3]) ).

fof(f_221_1,plain,
    ! [X_b,A_3,B_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)),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_1)),A_3)),
    inference(fof_nnf,[status(thm)],[fact_150_Diff__subset]) ).

fof(f_221_2,plain,
    ! [U_716,U_715,U_714] : hBOOL(hAPP(fun(U_716,bool),bool,hAPP(fun(U_716,bool),fun(fun(U_716,bool),bool),ord_less_eq(fun(U_716,bool)),hAPP(fun(U_716,bool),fun(U_716,bool),hAPP(fun(U_716,bool),fun(fun(U_716,bool),fun(U_716,bool)),minus_minus(fun(U_716,bool)),U_715),U_714)),U_715)),
    inference(variable_rename,[status(thm)],[f_221_1]) ).

fof(f_221_3,plain,
    ! [U_715,U_714,U_716] : hBOOL(hAPP(fun(U_716,bool),bool,hAPP(fun(U_716,bool),fun(fun(U_716,bool),bool),ord_less_eq(fun(U_716,bool)),hAPP(fun(U_716,bool),fun(U_716,bool),hAPP(fun(U_716,bool),fun(fun(U_716,bool),fun(U_716,bool)),minus_minus(fun(U_716,bool)),U_715),U_714)),U_715)),
    inference(definitional_conversion,[status(esa)],[f_221_2]) ).

cnf(f_221_4,plain,
    hBOOL(hAPP(fun(U_716,bool),bool,hAPP(fun(U_716,bool),fun(fun(U_716,bool),bool),ord_less_eq(fun(U_716,bool)),hAPP(fun(U_716,bool),fun(U_716,bool),hAPP(fun(U_716,bool),fun(fun(U_716,bool),fun(U_716,bool)),minus_minus(fun(U_716,bool)),U_715),U_714)),U_715)),
    inference(clausify,[status(thm)],[f_221_3]) ).

fof(f_222_1,plain,
    ! [X_b,A_2,B_3] :
      ( ti(X_b,A_2) = ti(X_b,B_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),B_3),bot_bot(fun(X_b,bool))) ),
    inference(fof_nnf,[status(thm)],[fact_151_singleton__inject]) ).

fof(f_222_2,plain,
    ! [U_719,U_718,U_717] :
      ( ti(U_719,U_718) = ti(U_719,U_717)
      | hAPP(fun(U_719,bool),fun(U_719,bool),hAPP(U_719,fun(fun(U_719,bool),fun(U_719,bool)),insert(U_719),U_718),bot_bot(fun(U_719,bool))) != hAPP(fun(U_719,bool),fun(U_719,bool),hAPP(U_719,fun(fun(U_719,bool),fun(U_719,bool)),insert(U_719),U_717),bot_bot(fun(U_719,bool))) ),
    inference(variable_rename,[status(thm)],[f_222_1]) ).

fof(f_222_3,plain,
    ! [U_717,U_718,U_719] :
      ( ti(U_719,U_718) = ti(U_719,U_717)
      | hAPP(fun(U_719,bool),fun(U_719,bool),hAPP(U_719,fun(fun(U_719,bool),fun(U_719,bool)),insert(U_719),U_718),bot_bot(fun(U_719,bool))) != hAPP(fun(U_719,bool),fun(U_719,bool),hAPP(U_719,fun(fun(U_719,bool),fun(U_719,bool)),insert(U_719),U_717),bot_bot(fun(U_719,bool))) ),
    inference(definitional_conversion,[status(esa)],[f_222_2]) ).

cnf(f_222_4,plain,
    ( ti(U_719,U_718) = ti(U_719,U_717)
    | hAPP(fun(U_719,bool),fun(U_719,bool),hAPP(U_719,fun(fun(U_719,bool),fun(U_719,bool)),insert(U_719),U_718),bot_bot(fun(U_719,bool))) != hAPP(fun(U_719,bool),fun(U_719,bool),hAPP(U_719,fun(fun(U_719,bool),fun(U_719,bool)),insert(U_719),U_717),bot_bot(fun(U_719,bool))) ),
    inference(clausify,[status(thm)],[f_222_3]) ).

fof(f_223_1,plain,
    ! [X_b,B_3,A_2] :
      ( ti(X_b,B_3) = 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_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))))) ),
    inference(fof_nnf,[status(thm)],[fact_152_singletonE]) ).

fof(f_223_2,plain,
    ! [U_722,U_721,U_720] :
      ( ti(U_722,U_721) = ti(U_722,U_720)
      | ~ hBOOL(hAPP(fun(U_722,bool),bool,hAPP(U_722,fun(fun(U_722,bool),bool),member(U_722),U_721),hAPP(fun(U_722,bool),fun(U_722,bool),hAPP(U_722,fun(fun(U_722,bool),fun(U_722,bool)),insert(U_722),U_720),bot_bot(fun(U_722,bool))))) ),
    inference(variable_rename,[status(thm)],[f_223_1]) ).

fof(f_223_3,plain,
    ! [U_720,U_721,U_722] :
      ( ti(U_722,U_721) = ti(U_722,U_720)
      | ~ hBOOL(hAPP(fun(U_722,bool),bool,hAPP(U_722,fun(fun(U_722,bool),bool),member(U_722),U_721),hAPP(fun(U_722,bool),fun(U_722,bool),hAPP(U_722,fun(fun(U_722,bool),fun(U_722,bool)),insert(U_722),U_720),bot_bot(fun(U_722,bool))))) ),
    inference(definitional_conversion,[status(esa)],[f_223_2]) ).

cnf(f_223_4,plain,
    ( ti(U_722,U_721) = ti(U_722,U_720)
    | ~ hBOOL(hAPP(fun(U_722,bool),bool,hAPP(U_722,fun(fun(U_722,bool),bool),member(U_722),U_721),hAPP(fun(U_722,bool),fun(U_722,bool),hAPP(U_722,fun(fun(U_722,bool),fun(U_722,bool)),insert(U_722),U_720),bot_bot(fun(U_722,bool))))) ),
    inference(clausify,[status(thm)],[f_223_3]) ).

fof(f_224_1,plain,
    ! [X_b,A_2,B_3,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_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),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_3) != ti(X_b,C_1)
            | ti(X_b,A_2) != ti(X_b,D_1) )
          & ( ti(X_b,B_3) != ti(X_b,D_1)
            | ti(X_b,A_2) != ti(X_b,C_1) ) ) )
      & ( ( ti(X_b,B_3) = ti(X_b,C_1)
          & ti(X_b,A_2) = ti(X_b,D_1) )
        | ( ti(X_b,B_3) = 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_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),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_153_doubleton__eq__iff]) ).

fof(f_224_2,plain,
    ! [U_727,U_726,U_725,U_724,U_723] :
      ( ( 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_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_725),bot_bot(fun(U_727,bool)))) = 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),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_723),bot_bot(fun(U_727,bool))))
        | ( ( ti(U_727,U_725) != ti(U_727,U_724)
            | ti(U_727,U_726) != ti(U_727,U_723) )
          & ( ti(U_727,U_725) != ti(U_727,U_723)
            | ti(U_727,U_726) != ti(U_727,U_724) ) ) )
      & ( ( ti(U_727,U_725) = ti(U_727,U_724)
          & ti(U_727,U_726) = ti(U_727,U_723) )
        | ( ti(U_727,U_725) = ti(U_727,U_723)
          & ti(U_727,U_726) = ti(U_727,U_724) )
        | 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_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_725),bot_bot(fun(U_727,bool)))) != 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),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_723),bot_bot(fun(U_727,bool)))) ) ),
    inference(variable_rename,[status(thm)],[f_224_1]) ).

fof(f_224_3,plain,
    ( ! [U_737,U_735,U_733,U_731,U_729] :
        ( hAPP(fun(U_737,bool),fun(U_737,bool),hAPP(U_737,fun(fun(U_737,bool),fun(U_737,bool)),insert(U_737),U_735),hAPP(fun(U_737,bool),fun(U_737,bool),hAPP(U_737,fun(fun(U_737,bool),fun(U_737,bool)),insert(U_737),U_733),bot_bot(fun(U_737,bool)))) = hAPP(fun(U_737,bool),fun(U_737,bool),hAPP(U_737,fun(fun(U_737,bool),fun(U_737,bool)),insert(U_737),U_731),hAPP(fun(U_737,bool),fun(U_737,bool),hAPP(U_737,fun(fun(U_737,bool),fun(U_737,bool)),insert(U_737),U_729),bot_bot(fun(U_737,bool))))
        | ( ( ti(U_737,U_733) != ti(U_737,U_731)
            | ti(U_737,U_735) != ti(U_737,U_729) )
          & ( ti(U_737,U_733) != ti(U_737,U_729)
            | ti(U_737,U_735) != ti(U_737,U_731) ) ) )
    & ! [U_736,U_734,U_732,U_730,U_728] :
        ( ( ti(U_736,U_732) = ti(U_736,U_730)
          & ti(U_736,U_734) = ti(U_736,U_728) )
        | ( ti(U_736,U_732) = ti(U_736,U_728)
          & ti(U_736,U_734) = ti(U_736,U_730) )
        | 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_734),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_732),bot_bot(fun(U_736,bool)))) != 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_730),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_728),bot_bot(fun(U_736,bool)))) ) ),
    inference(miniscope,[status(thm)],[f_224_2]) ).

fof(f_224_4,plain,
    ( ! [U_729,U_733,U_737,U_731,U_735] :
        ( ti(U_737,U_733) != ti(U_737,U_731)
        | ti(U_737,U_735) != ti(U_737,U_729)
        | ~ sP35(U_729,U_733,U_737,U_731,U_735) )
    & ! [U_729,U_733,U_737,U_731,U_735] :
        ( ti(U_737,U_733) != ti(U_737,U_729)
        | ti(U_737,U_735) != ti(U_737,U_731)
        | ~ sP35(U_729,U_733,U_737,U_731,U_735) )
    & ! [U_736,U_728,U_732,U_730,U_734] :
        ( ti(U_736,U_732) = ti(U_736,U_730)
        | ~ sP34(U_736,U_728,U_732,U_730,U_734) )
    & ! [U_736,U_728,U_732,U_730,U_734] :
        ( ti(U_736,U_734) = ti(U_736,U_728)
        | ~ sP34(U_736,U_728,U_732,U_730,U_734) )
    & ! [U_736,U_728,U_732,U_730,U_734] :
        ( ti(U_736,U_732) = ti(U_736,U_728)
        | ~ sP33(U_736,U_728,U_732,U_730,U_734) )
    & ! [U_736,U_728,U_732,U_730,U_734] :
        ( ti(U_736,U_734) = ti(U_736,U_730)
        | ~ sP33(U_736,U_728,U_732,U_730,U_734) )
    & ! [U_729,U_733,U_737,U_731,U_735] :
        ( hAPP(fun(U_737,bool),fun(U_737,bool),hAPP(U_737,fun(fun(U_737,bool),fun(U_737,bool)),insert(U_737),U_735),hAPP(fun(U_737,bool),fun(U_737,bool),hAPP(U_737,fun(fun(U_737,bool),fun(U_737,bool)),insert(U_737),U_733),bot_bot(fun(U_737,bool)))) = hAPP(fun(U_737,bool),fun(U_737,bool),hAPP(U_737,fun(fun(U_737,bool),fun(U_737,bool)),insert(U_737),U_731),hAPP(fun(U_737,bool),fun(U_737,bool),hAPP(U_737,fun(fun(U_737,bool),fun(U_737,bool)),insert(U_737),U_729),bot_bot(fun(U_737,bool))))
        | sP35(U_729,U_733,U_737,U_731,U_735) )
    & ! [U_736,U_728,U_732,U_730,U_734] :
        ( sP34(U_736,U_728,U_732,U_730,U_734)
        | sP33(U_736,U_728,U_732,U_730,U_734)
        | 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_734),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_732),bot_bot(fun(U_736,bool)))) != 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_730),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_728),bot_bot(fun(U_736,bool)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP33,sP34,sP35])],[f_224_3]) ).

cnf(f_224_5,plain,
    ( sP34(U_736,U_728,U_732,U_730,U_734)
    | sP33(U_736,U_728,U_732,U_730,U_734)
    | 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_734),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_732),bot_bot(fun(U_736,bool)))) != 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_730),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_728),bot_bot(fun(U_736,bool)))) ),
    inference(clausify,[status(thm)],[f_224_4]) ).

cnf(f_224_6,plain,
    ( hAPP(fun(U_737,bool),fun(U_737,bool),hAPP(U_737,fun(fun(U_737,bool),fun(U_737,bool)),insert(U_737),U_735),hAPP(fun(U_737,bool),fun(U_737,bool),hAPP(U_737,fun(fun(U_737,bool),fun(U_737,bool)),insert(U_737),U_733),bot_bot(fun(U_737,bool)))) = hAPP(fun(U_737,bool),fun(U_737,bool),hAPP(U_737,fun(fun(U_737,bool),fun(U_737,bool)),insert(U_737),U_731),hAPP(fun(U_737,bool),fun(U_737,bool),hAPP(U_737,fun(fun(U_737,bool),fun(U_737,bool)),insert(U_737),U_729),bot_bot(fun(U_737,bool))))
    | sP35(U_729,U_733,U_737,U_731,U_735) ),
    inference(clausify,[status(thm)],[f_224_4]) ).

cnf(f_224_7,plain,
    ( ti(U_736,U_734) = ti(U_736,U_730)
    | ~ sP33(U_736,U_728,U_732,U_730,U_734) ),
    inference(clausify,[status(thm)],[f_224_4]) ).

cnf(f_224_8,plain,
    ( ti(U_736,U_732) = ti(U_736,U_728)
    | ~ sP33(U_736,U_728,U_732,U_730,U_734) ),
    inference(clausify,[status(thm)],[f_224_4]) ).

cnf(f_224_9,plain,
    ( ti(U_736,U_734) = ti(U_736,U_728)
    | ~ sP34(U_736,U_728,U_732,U_730,U_734) ),
    inference(clausify,[status(thm)],[f_224_4]) ).

cnf(f_224_10,plain,
    ( ti(U_736,U_732) = ti(U_736,U_730)
    | ~ sP34(U_736,U_728,U_732,U_730,U_734) ),
    inference(clausify,[status(thm)],[f_224_4]) ).

cnf(f_224_11,plain,
    ( ti(U_737,U_733) != ti(U_737,U_729)
    | ti(U_737,U_735) != ti(U_737,U_731)
    | ~ sP35(U_729,U_733,U_737,U_731,U_735) ),
    inference(clausify,[status(thm)],[f_224_4]) ).

cnf(f_224_12,plain,
    ( ti(U_737,U_733) != ti(U_737,U_731)
    | ti(U_737,U_735) != ti(U_737,U_729)
    | ~ sP35(U_729,U_733,U_737,U_731,U_735) ),
    inference(clausify,[status(thm)],[f_224_4]) ).

fof(f_225_1,plain,
    ! [X_b,B_3,A_2] :
      ( ( 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(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_3) != ti(X_b,A_2) )
      & ( ti(X_b,B_3) = 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_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))))) ) ),
    inference(fof_nnf,[status(thm)],[fact_154_singleton__iff]) ).

fof(f_225_2,plain,
    ! [U_740,U_739,U_738] :
      ( ( hBOOL(hAPP(fun(U_740,bool),bool,hAPP(U_740,fun(fun(U_740,bool),bool),member(U_740),U_739),hAPP(fun(U_740,bool),fun(U_740,bool),hAPP(U_740,fun(fun(U_740,bool),fun(U_740,bool)),insert(U_740),U_738),bot_bot(fun(U_740,bool)))))
        | ti(U_740,U_739) != ti(U_740,U_738) )
      & ( ti(U_740,U_739) = ti(U_740,U_738)
        | ~ hBOOL(hAPP(fun(U_740,bool),bool,hAPP(U_740,fun(fun(U_740,bool),bool),member(U_740),U_739),hAPP(fun(U_740,bool),fun(U_740,bool),hAPP(U_740,fun(fun(U_740,bool),fun(U_740,bool)),insert(U_740),U_738),bot_bot(fun(U_740,bool))))) ) ),
    inference(variable_rename,[status(thm)],[f_225_1]) ).

fof(f_225_3,plain,
    ( ! [U_746,U_744,U_742] :
        ( hBOOL(hAPP(fun(U_746,bool),bool,hAPP(U_746,fun(fun(U_746,bool),bool),member(U_746),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_742),bot_bot(fun(U_746,bool)))))
        | ti(U_746,U_744) != ti(U_746,U_742) )
    & ! [U_745,U_743,U_741] :
        ( ti(U_745,U_743) = ti(U_745,U_741)
        | ~ hBOOL(hAPP(fun(U_745,bool),bool,hAPP(U_745,fun(fun(U_745,bool),bool),member(U_745),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_741),bot_bot(fun(U_745,bool))))) ) ),
    inference(miniscope,[status(thm)],[f_225_2]) ).

fof(f_225_4,plain,
    ( ! [U_744,U_746,U_742] :
        ( hBOOL(hAPP(fun(U_746,bool),bool,hAPP(U_746,fun(fun(U_746,bool),bool),member(U_746),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_742),bot_bot(fun(U_746,bool)))))
        | ti(U_746,U_744) != ti(U_746,U_742) )
    & ! [U_743,U_745,U_741] :
        ( ti(U_745,U_743) = ti(U_745,U_741)
        | ~ hBOOL(hAPP(fun(U_745,bool),bool,hAPP(U_745,fun(fun(U_745,bool),bool),member(U_745),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_741),bot_bot(fun(U_745,bool))))) ) ),
    inference(definitional_conversion,[status(esa)],[f_225_3]) ).

cnf(f_225_5,plain,
    ( ti(U_745,U_743) = ti(U_745,U_741)
    | ~ hBOOL(hAPP(fun(U_745,bool),bool,hAPP(U_745,fun(fun(U_745,bool),bool),member(U_745),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_741),bot_bot(fun(U_745,bool))))) ),
    inference(clausify,[status(thm)],[f_225_4]) ).

cnf(f_225_6,plain,
    ( hBOOL(hAPP(fun(U_746,bool),bool,hAPP(U_746,fun(fun(U_746,bool),bool),member(U_746),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_742),bot_bot(fun(U_746,bool)))))
    | ti(U_746,U_744) != ti(U_746,U_742) ),
    inference(clausify,[status(thm)],[f_225_4]) ).

fof(f_226_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_155_insert__not__empty]) ).

fof(f_226_2,plain,
    ! [U_749,U_748,U_747] : hAPP(fun(U_749,bool),fun(U_749,bool),hAPP(U_749,fun(fun(U_749,bool),fun(U_749,bool)),insert(U_749),U_748),U_747) != bot_bot(fun(U_749,bool)),
    inference(variable_rename,[status(thm)],[f_226_1]) ).

fof(f_226_3,plain,
    ! [U_748,U_749,U_747] : hAPP(fun(U_749,bool),fun(U_749,bool),hAPP(U_749,fun(fun(U_749,bool),fun(U_749,bool)),insert(U_749),U_748),U_747) != bot_bot(fun(U_749,bool)),
    inference(definitional_conversion,[status(esa)],[f_226_2]) ).

cnf(f_226_4,plain,
    hAPP(fun(U_749,bool),fun(U_749,bool),hAPP(U_749,fun(fun(U_749,bool),fun(U_749,bool)),insert(U_749),U_748),U_747) != bot_bot(fun(U_749,bool)),
    inference(clausify,[status(thm)],[f_226_3]) ).

fof(f_227_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_156_empty__not__insert]) ).

fof(f_227_2,plain,
    ! [U_752,U_751,U_750] : bot_bot(fun(U_752,bool)) != hAPP(fun(U_752,bool),fun(U_752,bool),hAPP(U_752,fun(fun(U_752,bool),fun(U_752,bool)),insert(U_752),U_751),U_750),
    inference(variable_rename,[status(thm)],[f_227_1]) ).

fof(f_227_3,plain,
    ! [U_752,U_751,U_750] : bot_bot(fun(U_752,bool)) != hAPP(fun(U_752,bool),fun(U_752,bool),hAPP(U_752,fun(fun(U_752,bool),fun(U_752,bool)),insert(U_752),U_751),U_750),
    inference(definitional_conversion,[status(esa)],[f_227_2]) ).

cnf(f_227_4,plain,
    bot_bot(fun(U_752,bool)) != hAPP(fun(U_752,bool),fun(U_752,bool),hAPP(U_752,fun(fun(U_752,bool),fun(U_752,bool)),insert(U_752),U_751),U_750),
    inference(clausify,[status(thm)],[f_227_3]) ).

fof(f_228_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_157_subset__empty]) ).

fof(f_228_2,plain,
    ! [U_754,U_753] :
      ( ( hBOOL(hAPP(fun(U_754,bool),bool,hAPP(fun(U_754,bool),fun(fun(U_754,bool),bool),ord_less_eq(fun(U_754,bool)),U_753),bot_bot(fun(U_754,bool))))
        | ti(fun(U_754,bool),U_753) != bot_bot(fun(U_754,bool)) )
      & ( ti(fun(U_754,bool),U_753) = bot_bot(fun(U_754,bool))
        | ~ hBOOL(hAPP(fun(U_754,bool),bool,hAPP(fun(U_754,bool),fun(fun(U_754,bool),bool),ord_less_eq(fun(U_754,bool)),U_753),bot_bot(fun(U_754,bool)))) ) ),
    inference(variable_rename,[status(thm)],[f_228_1]) ).

fof(f_228_3,plain,
    ( ! [U_758,U_756] :
        ( hBOOL(hAPP(fun(U_758,bool),bool,hAPP(fun(U_758,bool),fun(fun(U_758,bool),bool),ord_less_eq(fun(U_758,bool)),U_756),bot_bot(fun(U_758,bool))))
        | ti(fun(U_758,bool),U_756) != bot_bot(fun(U_758,bool)) )
    & ! [U_757,U_755] :
        ( ti(fun(U_757,bool),U_755) = bot_bot(fun(U_757,bool))
        | ~ hBOOL(hAPP(fun(U_757,bool),bool,hAPP(fun(U_757,bool),fun(fun(U_757,bool),bool),ord_less_eq(fun(U_757,bool)),U_755),bot_bot(fun(U_757,bool)))) ) ),
    inference(miniscope,[status(thm)],[f_228_2]) ).

fof(f_228_4,plain,
    ( ! [U_756,U_758] :
        ( hBOOL(hAPP(fun(U_758,bool),bool,hAPP(fun(U_758,bool),fun(fun(U_758,bool),bool),ord_less_eq(fun(U_758,bool)),U_756),bot_bot(fun(U_758,bool))))
        | ti(fun(U_758,bool),U_756) != bot_bot(fun(U_758,bool)) )
    & ! [U_755,U_757] :
        ( ti(fun(U_757,bool),U_755) = bot_bot(fun(U_757,bool))
        | ~ hBOOL(hAPP(fun(U_757,bool),bool,hAPP(fun(U_757,bool),fun(fun(U_757,bool),bool),ord_less_eq(fun(U_757,bool)),U_755),bot_bot(fun(U_757,bool)))) ) ),
    inference(definitional_conversion,[status(esa)],[f_228_3]) ).

cnf(f_228_5,plain,
    ( ti(fun(U_757,bool),U_755) = bot_bot(fun(U_757,bool))
    | ~ hBOOL(hAPP(fun(U_757,bool),bool,hAPP(fun(U_757,bool),fun(fun(U_757,bool),bool),ord_less_eq(fun(U_757,bool)),U_755),bot_bot(fun(U_757,bool)))) ),
    inference(clausify,[status(thm)],[f_228_4]) ).

cnf(f_228_6,plain,
    ( hBOOL(hAPP(fun(U_758,bool),bool,hAPP(fun(U_758,bool),fun(fun(U_758,bool),bool),ord_less_eq(fun(U_758,bool)),U_756),bot_bot(fun(U_758,bool))))
    | ti(fun(U_758,bool),U_756) != bot_bot(fun(U_758,bool)) ),
    inference(clausify,[status(thm)],[f_228_4]) ).

fof(f_229_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_158_image__is__empty]) ).

fof(f_229_2,plain,
    ! [U_762,U_761,U_760,U_759] :
      ( ( hAPP(fun(U_762,bool),fun(U_761,bool),hAPP(fun(U_762,U_761),fun(fun(U_762,bool),fun(U_761,bool)),image(U_762,U_761),U_760),U_759) = bot_bot(fun(U_761,bool))
        | ti(fun(U_762,bool),U_759) != bot_bot(fun(U_762,bool)) )
      & ( ti(fun(U_762,bool),U_759) = bot_bot(fun(U_762,bool))
        | hAPP(fun(U_762,bool),fun(U_761,bool),hAPP(fun(U_762,U_761),fun(fun(U_762,bool),fun(U_761,bool)),image(U_762,U_761),U_760),U_759) != bot_bot(fun(U_761,bool)) ) ),
    inference(variable_rename,[status(thm)],[f_229_1]) ).

fof(f_229_3,plain,
    ( ! [U_770,U_768,U_766,U_764] :
        ( hAPP(fun(U_770,bool),fun(U_768,bool),hAPP(fun(U_770,U_768),fun(fun(U_770,bool),fun(U_768,bool)),image(U_770,U_768),U_766),U_764) = bot_bot(fun(U_768,bool))
        | ti(fun(U_770,bool),U_764) != bot_bot(fun(U_770,bool)) )
    & ! [U_769,U_767,U_765,U_763] :
        ( ti(fun(U_769,bool),U_763) = bot_bot(fun(U_769,bool))
        | hAPP(fun(U_769,bool),fun(U_767,bool),hAPP(fun(U_769,U_767),fun(fun(U_769,bool),fun(U_767,bool)),image(U_769,U_767),U_765),U_763) != bot_bot(fun(U_767,bool)) ) ),
    inference(miniscope,[status(thm)],[f_229_2]) ).

fof(f_229_4,plain,
    ( ! [U_766,U_764,U_768,U_770] :
        ( hAPP(fun(U_770,bool),fun(U_768,bool),hAPP(fun(U_770,U_768),fun(fun(U_770,bool),fun(U_768,bool)),image(U_770,U_768),U_766),U_764) = bot_bot(fun(U_768,bool))
        | ti(fun(U_770,bool),U_764) != bot_bot(fun(U_770,bool)) )
    & ! [U_763,U_767,U_765,U_769] :
        ( ti(fun(U_769,bool),U_763) = bot_bot(fun(U_769,bool))
        | hAPP(fun(U_769,bool),fun(U_767,bool),hAPP(fun(U_769,U_767),fun(fun(U_769,bool),fun(U_767,bool)),image(U_769,U_767),U_765),U_763) != bot_bot(fun(U_767,bool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_229_3]) ).

cnf(f_229_5,plain,
    ( ti(fun(U_769,bool),U_763) = bot_bot(fun(U_769,bool))
    | hAPP(fun(U_769,bool),fun(U_767,bool),hAPP(fun(U_769,U_767),fun(fun(U_769,bool),fun(U_767,bool)),image(U_769,U_767),U_765),U_763) != bot_bot(fun(U_767,bool)) ),
    inference(clausify,[status(thm)],[f_229_4]) ).

cnf(f_229_6,plain,
    ( hAPP(fun(U_770,bool),fun(U_768,bool),hAPP(fun(U_770,U_768),fun(fun(U_770,bool),fun(U_768,bool)),image(U_770,U_768),U_766),U_764) = bot_bot(fun(U_768,bool))
    | ti(fun(U_770,bool),U_764) != bot_bot(fun(U_770,bool)) ),
    inference(clausify,[status(thm)],[f_229_4]) ).

fof(f_230_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_159_image__empty]) ).

fof(f_230_2,plain,
    ! [U_773,U_772,U_771] : hAPP(fun(U_773,bool),fun(U_772,bool),hAPP(fun(U_773,U_772),fun(fun(U_773,bool),fun(U_772,bool)),image(U_773,U_772),U_771),bot_bot(fun(U_773,bool))) = bot_bot(fun(U_772,bool)),
    inference(variable_rename,[status(thm)],[f_230_1]) ).

fof(f_230_3,plain,
    ! [U_772,U_771,U_773] : hAPP(fun(U_773,bool),fun(U_772,bool),hAPP(fun(U_773,U_772),fun(fun(U_773,bool),fun(U_772,bool)),image(U_773,U_772),U_771),bot_bot(fun(U_773,bool))) = bot_bot(fun(U_772,bool)),
    inference(definitional_conversion,[status(esa)],[f_230_2]) ).

cnf(f_230_4,plain,
    hAPP(fun(U_773,bool),fun(U_772,bool),hAPP(fun(U_773,U_772),fun(fun(U_773,bool),fun(U_772,bool)),image(U_773,U_772),U_771),bot_bot(fun(U_773,bool))) = bot_bot(fun(U_772,bool)),
    inference(clausify,[status(thm)],[f_230_3]) ).

fof(f_231_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_160_empty__is__image]) ).

fof(f_231_2,plain,
    ! [U_777,U_776,U_775,U_774] :
      ( ( bot_bot(fun(U_777,bool)) = hAPP(fun(U_776,bool),fun(U_777,bool),hAPP(fun(U_776,U_777),fun(fun(U_776,bool),fun(U_777,bool)),image(U_776,U_777),U_775),U_774)
        | ti(fun(U_776,bool),U_774) != bot_bot(fun(U_776,bool)) )
      & ( ti(fun(U_776,bool),U_774) = bot_bot(fun(U_776,bool))
        | bot_bot(fun(U_777,bool)) != hAPP(fun(U_776,bool),fun(U_777,bool),hAPP(fun(U_776,U_777),fun(fun(U_776,bool),fun(U_777,bool)),image(U_776,U_777),U_775),U_774) ) ),
    inference(variable_rename,[status(thm)],[f_231_1]) ).

fof(f_231_3,plain,
    ( ! [U_785,U_783,U_781,U_779] :
        ( bot_bot(fun(U_785,bool)) = hAPP(fun(U_783,bool),fun(U_785,bool),hAPP(fun(U_783,U_785),fun(fun(U_783,bool),fun(U_785,bool)),image(U_783,U_785),U_781),U_779)
        | ti(fun(U_783,bool),U_779) != bot_bot(fun(U_783,bool)) )
    & ! [U_784,U_782,U_780,U_778] :
        ( ti(fun(U_782,bool),U_778) = bot_bot(fun(U_782,bool))
        | bot_bot(fun(U_784,bool)) != hAPP(fun(U_782,bool),fun(U_784,bool),hAPP(fun(U_782,U_784),fun(fun(U_782,bool),fun(U_784,bool)),image(U_782,U_784),U_780),U_778) ) ),
    inference(miniscope,[status(thm)],[f_231_2]) ).

fof(f_231_4,plain,
    ( ! [U_781,U_779,U_783,U_785] :
        ( bot_bot(fun(U_785,bool)) = hAPP(fun(U_783,bool),fun(U_785,bool),hAPP(fun(U_783,U_785),fun(fun(U_783,bool),fun(U_785,bool)),image(U_783,U_785),U_781),U_779)
        | ti(fun(U_783,bool),U_779) != bot_bot(fun(U_783,bool)) )
    & ! [U_778,U_782,U_780,U_784] :
        ( ti(fun(U_782,bool),U_778) = bot_bot(fun(U_782,bool))
        | bot_bot(fun(U_784,bool)) != hAPP(fun(U_782,bool),fun(U_784,bool),hAPP(fun(U_782,U_784),fun(fun(U_782,bool),fun(U_784,bool)),image(U_782,U_784),U_780),U_778) ) ),
    inference(definitional_conversion,[status(esa)],[f_231_3]) ).

cnf(f_231_5,plain,
    ( ti(fun(U_782,bool),U_778) = bot_bot(fun(U_782,bool))
    | bot_bot(fun(U_784,bool)) != hAPP(fun(U_782,bool),fun(U_784,bool),hAPP(fun(U_782,U_784),fun(fun(U_782,bool),fun(U_784,bool)),image(U_782,U_784),U_780),U_778) ),
    inference(clausify,[status(thm)],[f_231_4]) ).

cnf(f_231_6,plain,
    ( bot_bot(fun(U_785,bool)) = hAPP(fun(U_783,bool),fun(U_785,bool),hAPP(fun(U_783,U_785),fun(fun(U_783,bool),fun(U_785,bool)),image(U_783,U_785),U_781),U_779)
    | ti(fun(U_783,bool),U_779) != bot_bot(fun(U_783,bool)) ),
    inference(clausify,[status(thm)],[f_231_4]) ).

fof(f_232_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_161_le__bot]) ).

fof(f_232_2,plain,
    ! [U_787] :
      ( ! [U_786] :
          ( ti(U_787,U_786) = bot_bot(U_787)
          | ~ hBOOL(hAPP(U_787,bool,hAPP(U_787,fun(U_787,bool),ord_less_eq(U_787),U_786),bot_bot(U_787))) )
      | ~ bot(U_787) ),
    inference(variable_rename,[status(thm)],[f_232_1]) ).

fof(f_232_3,plain,
    ! [U_787,U_786] :
      ( ti(U_787,U_786) = bot_bot(U_787)
      | ~ hBOOL(hAPP(U_787,bool,hAPP(U_787,fun(U_787,bool),ord_less_eq(U_787),U_786),bot_bot(U_787)))
      | ~ bot(U_787) ),
    inference(definitional_conversion,[status(esa)],[f_232_2]) ).

cnf(f_232_4,plain,
    ( ti(U_787,U_786) = bot_bot(U_787)
    | ~ hBOOL(hAPP(U_787,bool,hAPP(U_787,fun(U_787,bool),ord_less_eq(U_787),U_786),bot_bot(U_787)))
    | ~ bot(U_787) ),
    inference(clausify,[status(thm)],[f_232_3]) ).

fof(f_233_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_162_bot__unique]) ).

fof(f_233_2,plain,
    ! [U_789] :
      ( ! [U_788] :
          ( ( hBOOL(hAPP(U_789,bool,hAPP(U_789,fun(U_789,bool),ord_less_eq(U_789),U_788),bot_bot(U_789)))
            | ti(U_789,U_788) != bot_bot(U_789) )
          & ( ti(U_789,U_788) = bot_bot(U_789)
            | ~ hBOOL(hAPP(U_789,bool,hAPP(U_789,fun(U_789,bool),ord_less_eq(U_789),U_788),bot_bot(U_789))) ) )
      | ~ bot(U_789) ),
    inference(variable_rename,[status(thm)],[f_233_1]) ).

fof(f_233_3,plain,
    ! [U_789] :
      ( ( ! [U_791] :
            ( hBOOL(hAPP(U_789,bool,hAPP(U_789,fun(U_789,bool),ord_less_eq(U_789),U_791),bot_bot(U_789)))
            | ti(U_789,U_791) != bot_bot(U_789) )
        & ! [U_790] :
            ( ti(U_789,U_790) = bot_bot(U_789)
            | ~ hBOOL(hAPP(U_789,bool,hAPP(U_789,fun(U_789,bool),ord_less_eq(U_789),U_790),bot_bot(U_789))) ) )
      | ~ bot(U_789) ),
    inference(miniscope,[status(thm)],[f_233_2]) ).

fof(f_233_4,plain,
    ( ! [U_789,U_791,U_790] :
        ( hBOOL(hAPP(U_789,bool,hAPP(U_789,fun(U_789,bool),ord_less_eq(U_789),U_791),bot_bot(U_789)))
        | ti(U_789,U_791) != bot_bot(U_789)
        | ~ sP36(U_789,U_791,U_790) )
    & ! [U_789,U_791,U_790] :
        ( ti(U_789,U_790) = bot_bot(U_789)
        | ~ hBOOL(hAPP(U_789,bool,hAPP(U_789,fun(U_789,bool),ord_less_eq(U_789),U_790),bot_bot(U_789)))
        | ~ sP36(U_789,U_791,U_790) )
    & ! [U_789,U_791,U_790] :
        ( sP36(U_789,U_791,U_790)
        | ~ bot(U_789) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP36])],[f_233_3]) ).

cnf(f_233_5,plain,
    ( sP36(U_789,U_791,U_790)
    | ~ bot(U_789) ),
    inference(clausify,[status(thm)],[f_233_4]) ).

cnf(f_233_6,plain,
    ( ti(U_789,U_790) = bot_bot(U_789)
    | ~ hBOOL(hAPP(U_789,bool,hAPP(U_789,fun(U_789,bool),ord_less_eq(U_789),U_790),bot_bot(U_789)))
    | ~ sP36(U_789,U_791,U_790) ),
    inference(clausify,[status(thm)],[f_233_4]) ).

cnf(f_233_7,plain,
    ( hBOOL(hAPP(U_789,bool,hAPP(U_789,fun(U_789,bool),ord_less_eq(U_789),U_791),bot_bot(U_789)))
    | ti(U_789,U_791) != bot_bot(U_789)
    | ~ sP36(U_789,U_791,U_790) ),
    inference(clausify,[status(thm)],[f_233_4]) ).

fof(f_234_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_163_bot__least]) ).

fof(f_234_2,plain,
    ! [U_793] :
      ( ! [U_792] : hBOOL(hAPP(U_793,bool,hAPP(U_793,fun(U_793,bool),ord_less_eq(U_793),bot_bot(U_793)),U_792))
      | ~ bot(U_793) ),
    inference(variable_rename,[status(thm)],[f_234_1]) ).

fof(f_234_3,plain,
    ! [U_792,U_793] :
      ( hBOOL(hAPP(U_793,bool,hAPP(U_793,fun(U_793,bool),ord_less_eq(U_793),bot_bot(U_793)),U_792))
      | ~ bot(U_793) ),
    inference(definitional_conversion,[status(esa)],[f_234_2]) ).

cnf(f_234_4,plain,
    ( hBOOL(hAPP(U_793,bool,hAPP(U_793,fun(U_793,bool),ord_less_eq(U_793),bot_bot(U_793)),U_792))
    | ~ bot(U_793) ),
    inference(clausify,[status(thm)],[f_234_3]) ).

fof(f_235_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_164_Collect__conv__if]) ).

fof(f_235_2,plain,
    ! [U_796,U_795,U_794] :
      ( ( hAPP(fun(U_796,bool),fun(U_796,bool),collect(U_796),hAPP(fun(U_796,bool),fun(U_796,bool),hAPP(fun(U_796,fun(bool,bool)),fun(fun(U_796,bool),fun(U_796,bool)),combs(U_796,bool,bool),hAPP(fun(U_796,bool),fun(U_796,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_796,bool),fun(U_796,fun(bool,bool))),combb(bool,fun(bool,bool),U_796),fconj),hAPP(U_796,fun(U_796,bool),hAPP(fun(U_796,fun(U_796,bool)),fun(U_796,fun(U_796,bool)),combc(U_796,U_796,bool),fequal(U_796)),U_794))),U_795)) = bot_bot(fun(U_796,bool))
        | hBOOL(hAPP(U_796,bool,U_795,U_794)) )
      & ( hAPP(fun(U_796,bool),fun(U_796,bool),collect(U_796),hAPP(fun(U_796,bool),fun(U_796,bool),hAPP(fun(U_796,fun(bool,bool)),fun(fun(U_796,bool),fun(U_796,bool)),combs(U_796,bool,bool),hAPP(fun(U_796,bool),fun(U_796,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_796,bool),fun(U_796,fun(bool,bool))),combb(bool,fun(bool,bool),U_796),fconj),hAPP(U_796,fun(U_796,bool),hAPP(fun(U_796,fun(U_796,bool)),fun(U_796,fun(U_796,bool)),combc(U_796,U_796,bool),fequal(U_796)),U_794))),U_795)) = hAPP(fun(U_796,bool),fun(U_796,bool),hAPP(U_796,fun(fun(U_796,bool),fun(U_796,bool)),insert(U_796),U_794),bot_bot(fun(U_796,bool)))
        | ~ hBOOL(hAPP(U_796,bool,U_795,U_794)) ) ),
    inference(variable_rename,[status(thm)],[f_235_1]) ).

fof(f_235_3,plain,
    ( ! [U_802,U_800,U_798] :
        ( hAPP(fun(U_802,bool),fun(U_802,bool),collect(U_802),hAPP(fun(U_802,bool),fun(U_802,bool),hAPP(fun(U_802,fun(bool,bool)),fun(fun(U_802,bool),fun(U_802,bool)),combs(U_802,bool,bool),hAPP(fun(U_802,bool),fun(U_802,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_802,bool),fun(U_802,fun(bool,bool))),combb(bool,fun(bool,bool),U_802),fconj),hAPP(U_802,fun(U_802,bool),hAPP(fun(U_802,fun(U_802,bool)),fun(U_802,fun(U_802,bool)),combc(U_802,U_802,bool),fequal(U_802)),U_798))),U_800)) = bot_bot(fun(U_802,bool))
        | hBOOL(hAPP(U_802,bool,U_800,U_798)) )
    & ! [U_801,U_799,U_797] :
        ( hAPP(fun(U_801,bool),fun(U_801,bool),collect(U_801),hAPP(fun(U_801,bool),fun(U_801,bool),hAPP(fun(U_801,fun(bool,bool)),fun(fun(U_801,bool),fun(U_801,bool)),combs(U_801,bool,bool),hAPP(fun(U_801,bool),fun(U_801,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_801,bool),fun(U_801,fun(bool,bool))),combb(bool,fun(bool,bool),U_801),fconj),hAPP(U_801,fun(U_801,bool),hAPP(fun(U_801,fun(U_801,bool)),fun(U_801,fun(U_801,bool)),combc(U_801,U_801,bool),fequal(U_801)),U_797))),U_799)) = hAPP(fun(U_801,bool),fun(U_801,bool),hAPP(U_801,fun(fun(U_801,bool),fun(U_801,bool)),insert(U_801),U_797),bot_bot(fun(U_801,bool)))
        | ~ hBOOL(hAPP(U_801,bool,U_799,U_797)) ) ),
    inference(miniscope,[status(thm)],[f_235_2]) ).

fof(f_235_4,plain,
    ( ! [U_800,U_802,U_798] :
        ( hAPP(fun(U_802,bool),fun(U_802,bool),collect(U_802),hAPP(fun(U_802,bool),fun(U_802,bool),hAPP(fun(U_802,fun(bool,bool)),fun(fun(U_802,bool),fun(U_802,bool)),combs(U_802,bool,bool),hAPP(fun(U_802,bool),fun(U_802,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_802,bool),fun(U_802,fun(bool,bool))),combb(bool,fun(bool,bool),U_802),fconj),hAPP(U_802,fun(U_802,bool),hAPP(fun(U_802,fun(U_802,bool)),fun(U_802,fun(U_802,bool)),combc(U_802,U_802,bool),fequal(U_802)),U_798))),U_800)) = bot_bot(fun(U_802,bool))
        | hBOOL(hAPP(U_802,bool,U_800,U_798)) )
    & ! [U_801,U_799,U_797] :
        ( hAPP(fun(U_801,bool),fun(U_801,bool),collect(U_801),hAPP(fun(U_801,bool),fun(U_801,bool),hAPP(fun(U_801,fun(bool,bool)),fun(fun(U_801,bool),fun(U_801,bool)),combs(U_801,bool,bool),hAPP(fun(U_801,bool),fun(U_801,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_801,bool),fun(U_801,fun(bool,bool))),combb(bool,fun(bool,bool),U_801),fconj),hAPP(U_801,fun(U_801,bool),hAPP(fun(U_801,fun(U_801,bool)),fun(U_801,fun(U_801,bool)),combc(U_801,U_801,bool),fequal(U_801)),U_797))),U_799)) = hAPP(fun(U_801,bool),fun(U_801,bool),hAPP(U_801,fun(fun(U_801,bool),fun(U_801,bool)),insert(U_801),U_797),bot_bot(fun(U_801,bool)))
        | ~ hBOOL(hAPP(U_801,bool,U_799,U_797)) ) ),
    inference(definitional_conversion,[status(esa)],[f_235_3]) ).

cnf(f_235_5,plain,
    ( hAPP(fun(U_801,bool),fun(U_801,bool),collect(U_801),hAPP(fun(U_801,bool),fun(U_801,bool),hAPP(fun(U_801,fun(bool,bool)),fun(fun(U_801,bool),fun(U_801,bool)),combs(U_801,bool,bool),hAPP(fun(U_801,bool),fun(U_801,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_801,bool),fun(U_801,fun(bool,bool))),combb(bool,fun(bool,bool),U_801),fconj),hAPP(U_801,fun(U_801,bool),hAPP(fun(U_801,fun(U_801,bool)),fun(U_801,fun(U_801,bool)),combc(U_801,U_801,bool),fequal(U_801)),U_797))),U_799)) = hAPP(fun(U_801,bool),fun(U_801,bool),hAPP(U_801,fun(fun(U_801,bool),fun(U_801,bool)),insert(U_801),U_797),bot_bot(fun(U_801,bool)))
    | ~ hBOOL(hAPP(U_801,bool,U_799,U_797)) ),
    inference(clausify,[status(thm)],[f_235_4]) ).

cnf(f_235_6,plain,
    ( hAPP(fun(U_802,bool),fun(U_802,bool),collect(U_802),hAPP(fun(U_802,bool),fun(U_802,bool),hAPP(fun(U_802,fun(bool,bool)),fun(fun(U_802,bool),fun(U_802,bool)),combs(U_802,bool,bool),hAPP(fun(U_802,bool),fun(U_802,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_802,bool),fun(U_802,fun(bool,bool))),combb(bool,fun(bool,bool),U_802),fconj),hAPP(U_802,fun(U_802,bool),hAPP(fun(U_802,fun(U_802,bool)),fun(U_802,fun(U_802,bool)),combc(U_802,U_802,bool),fequal(U_802)),U_798))),U_800)) = bot_bot(fun(U_802,bool))
    | hBOOL(hAPP(U_802,bool,U_800,U_798)) ),
    inference(clausify,[status(thm)],[f_235_4]) ).

fof(f_236_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_165_Collect__conv__if2]) ).

fof(f_236_2,plain,
    ! [U_805,U_804,U_803] :
      ( ( hAPP(fun(U_805,bool),fun(U_805,bool),collect(U_805),hAPP(fun(U_805,bool),fun(U_805,bool),hAPP(fun(U_805,fun(bool,bool)),fun(fun(U_805,bool),fun(U_805,bool)),combs(U_805,bool,bool),hAPP(fun(U_805,bool),fun(U_805,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_805,bool),fun(U_805,fun(bool,bool))),combb(bool,fun(bool,bool),U_805),fconj),hAPP(U_805,fun(U_805,bool),fequal(U_805),U_803))),U_804)) = bot_bot(fun(U_805,bool))
        | hBOOL(hAPP(U_805,bool,U_804,U_803)) )
      & ( hAPP(fun(U_805,bool),fun(U_805,bool),collect(U_805),hAPP(fun(U_805,bool),fun(U_805,bool),hAPP(fun(U_805,fun(bool,bool)),fun(fun(U_805,bool),fun(U_805,bool)),combs(U_805,bool,bool),hAPP(fun(U_805,bool),fun(U_805,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_805,bool),fun(U_805,fun(bool,bool))),combb(bool,fun(bool,bool),U_805),fconj),hAPP(U_805,fun(U_805,bool),fequal(U_805),U_803))),U_804)) = hAPP(fun(U_805,bool),fun(U_805,bool),hAPP(U_805,fun(fun(U_805,bool),fun(U_805,bool)),insert(U_805),U_803),bot_bot(fun(U_805,bool)))
        | ~ hBOOL(hAPP(U_805,bool,U_804,U_803)) ) ),
    inference(variable_rename,[status(thm)],[f_236_1]) ).

fof(f_236_3,plain,
    ( ! [U_811,U_809,U_807] :
        ( hAPP(fun(U_811,bool),fun(U_811,bool),collect(U_811),hAPP(fun(U_811,bool),fun(U_811,bool),hAPP(fun(U_811,fun(bool,bool)),fun(fun(U_811,bool),fun(U_811,bool)),combs(U_811,bool,bool),hAPP(fun(U_811,bool),fun(U_811,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_811,bool),fun(U_811,fun(bool,bool))),combb(bool,fun(bool,bool),U_811),fconj),hAPP(U_811,fun(U_811,bool),fequal(U_811),U_807))),U_809)) = bot_bot(fun(U_811,bool))
        | hBOOL(hAPP(U_811,bool,U_809,U_807)) )
    & ! [U_810,U_808,U_806] :
        ( hAPP(fun(U_810,bool),fun(U_810,bool),collect(U_810),hAPP(fun(U_810,bool),fun(U_810,bool),hAPP(fun(U_810,fun(bool,bool)),fun(fun(U_810,bool),fun(U_810,bool)),combs(U_810,bool,bool),hAPP(fun(U_810,bool),fun(U_810,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_810,bool),fun(U_810,fun(bool,bool))),combb(bool,fun(bool,bool),U_810),fconj),hAPP(U_810,fun(U_810,bool),fequal(U_810),U_806))),U_808)) = hAPP(fun(U_810,bool),fun(U_810,bool),hAPP(U_810,fun(fun(U_810,bool),fun(U_810,bool)),insert(U_810),U_806),bot_bot(fun(U_810,bool)))
        | ~ hBOOL(hAPP(U_810,bool,U_808,U_806)) ) ),
    inference(miniscope,[status(thm)],[f_236_2]) ).

fof(f_236_4,plain,
    ( ! [U_807,U_809,U_811] :
        ( hAPP(fun(U_811,bool),fun(U_811,bool),collect(U_811),hAPP(fun(U_811,bool),fun(U_811,bool),hAPP(fun(U_811,fun(bool,bool)),fun(fun(U_811,bool),fun(U_811,bool)),combs(U_811,bool,bool),hAPP(fun(U_811,bool),fun(U_811,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_811,bool),fun(U_811,fun(bool,bool))),combb(bool,fun(bool,bool),U_811),fconj),hAPP(U_811,fun(U_811,bool),fequal(U_811),U_807))),U_809)) = bot_bot(fun(U_811,bool))
        | hBOOL(hAPP(U_811,bool,U_809,U_807)) )
    & ! [U_810,U_808,U_806] :
        ( hAPP(fun(U_810,bool),fun(U_810,bool),collect(U_810),hAPP(fun(U_810,bool),fun(U_810,bool),hAPP(fun(U_810,fun(bool,bool)),fun(fun(U_810,bool),fun(U_810,bool)),combs(U_810,bool,bool),hAPP(fun(U_810,bool),fun(U_810,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_810,bool),fun(U_810,fun(bool,bool))),combb(bool,fun(bool,bool),U_810),fconj),hAPP(U_810,fun(U_810,bool),fequal(U_810),U_806))),U_808)) = hAPP(fun(U_810,bool),fun(U_810,bool),hAPP(U_810,fun(fun(U_810,bool),fun(U_810,bool)),insert(U_810),U_806),bot_bot(fun(U_810,bool)))
        | ~ hBOOL(hAPP(U_810,bool,U_808,U_806)) ) ),
    inference(definitional_conversion,[status(esa)],[f_236_3]) ).

cnf(f_236_5,plain,
    ( hAPP(fun(U_810,bool),fun(U_810,bool),collect(U_810),hAPP(fun(U_810,bool),fun(U_810,bool),hAPP(fun(U_810,fun(bool,bool)),fun(fun(U_810,bool),fun(U_810,bool)),combs(U_810,bool,bool),hAPP(fun(U_810,bool),fun(U_810,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_810,bool),fun(U_810,fun(bool,bool))),combb(bool,fun(bool,bool),U_810),fconj),hAPP(U_810,fun(U_810,bool),fequal(U_810),U_806))),U_808)) = hAPP(fun(U_810,bool),fun(U_810,bool),hAPP(U_810,fun(fun(U_810,bool),fun(U_810,bool)),insert(U_810),U_806),bot_bot(fun(U_810,bool)))
    | ~ hBOOL(hAPP(U_810,bool,U_808,U_806)) ),
    inference(clausify,[status(thm)],[f_236_4]) ).

cnf(f_236_6,plain,
    ( hAPP(fun(U_811,bool),fun(U_811,bool),collect(U_811),hAPP(fun(U_811,bool),fun(U_811,bool),hAPP(fun(U_811,fun(bool,bool)),fun(fun(U_811,bool),fun(U_811,bool)),combs(U_811,bool,bool),hAPP(fun(U_811,bool),fun(U_811,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_811,bool),fun(U_811,fun(bool,bool))),combb(bool,fun(bool,bool),U_811),fconj),hAPP(U_811,fun(U_811,bool),fequal(U_811),U_807))),U_809)) = bot_bot(fun(U_811,bool))
    | hBOOL(hAPP(U_811,bool,U_809,U_807)) ),
    inference(clausify,[status(thm)],[f_236_4]) ).

fof(f_237_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_166_singleton__conv]) ).

fof(f_237_2,plain,
    ! [U_813,U_812] : hAPP(fun(U_813,bool),fun(U_813,bool),collect(U_813),hAPP(U_813,fun(U_813,bool),hAPP(fun(U_813,fun(U_813,bool)),fun(U_813,fun(U_813,bool)),combc(U_813,U_813,bool),fequal(U_813)),U_812)) = hAPP(fun(U_813,bool),fun(U_813,bool),hAPP(U_813,fun(fun(U_813,bool),fun(U_813,bool)),insert(U_813),U_812),bot_bot(fun(U_813,bool))),
    inference(variable_rename,[status(thm)],[f_237_1]) ).

fof(f_237_3,plain,
    ! [U_812,U_813] : hAPP(fun(U_813,bool),fun(U_813,bool),collect(U_813),hAPP(U_813,fun(U_813,bool),hAPP(fun(U_813,fun(U_813,bool)),fun(U_813,fun(U_813,bool)),combc(U_813,U_813,bool),fequal(U_813)),U_812)) = hAPP(fun(U_813,bool),fun(U_813,bool),hAPP(U_813,fun(fun(U_813,bool),fun(U_813,bool)),insert(U_813),U_812),bot_bot(fun(U_813,bool))),
    inference(definitional_conversion,[status(esa)],[f_237_2]) ).

cnf(f_237_4,plain,
    hAPP(fun(U_813,bool),fun(U_813,bool),collect(U_813),hAPP(U_813,fun(U_813,bool),hAPP(fun(U_813,fun(U_813,bool)),fun(U_813,fun(U_813,bool)),combc(U_813,U_813,bool),fequal(U_813)),U_812)) = hAPP(fun(U_813,bool),fun(U_813,bool),hAPP(U_813,fun(fun(U_813,bool),fun(U_813,bool)),insert(U_813),U_812),bot_bot(fun(U_813,bool))),
    inference(clausify,[status(thm)],[f_237_3]) ).

fof(f_238_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_167_singleton__conv2]) ).

fof(f_238_2,plain,
    ! [U_815,U_814] : hAPP(fun(U_815,bool),fun(U_815,bool),collect(U_815),hAPP(U_815,fun(U_815,bool),fequal(U_815),U_814)) = hAPP(fun(U_815,bool),fun(U_815,bool),hAPP(U_815,fun(fun(U_815,bool),fun(U_815,bool)),insert(U_815),U_814),bot_bot(fun(U_815,bool))),
    inference(variable_rename,[status(thm)],[f_238_1]) ).

fof(f_238_3,plain,
    ! [U_814,U_815] : hAPP(fun(U_815,bool),fun(U_815,bool),collect(U_815),hAPP(U_815,fun(U_815,bool),fequal(U_815),U_814)) = hAPP(fun(U_815,bool),fun(U_815,bool),hAPP(U_815,fun(fun(U_815,bool),fun(U_815,bool)),insert(U_815),U_814),bot_bot(fun(U_815,bool))),
    inference(definitional_conversion,[status(esa)],[f_238_2]) ).

cnf(f_238_4,plain,
    hAPP(fun(U_815,bool),fun(U_815,bool),collect(U_815),hAPP(U_815,fun(U_815,bool),fequal(U_815),U_814)) = hAPP(fun(U_815,bool),fun(U_815,bool),hAPP(U_815,fun(fun(U_815,bool),fun(U_815,bool)),insert(U_815),U_814),bot_bot(fun(U_815,bool))),
    inference(clausify,[status(thm)],[f_238_3]) ).

fof(f_239_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_168_card__Suc__Diff1]) ).

fof(f_239_2,plain,
    ! [U_818,U_817,U_816] :
      ( hAPP(nat,nat,suc,hAPP(fun(U_818,bool),nat,finite_card(U_818),hAPP(fun(U_818,bool),fun(U_818,bool),hAPP(fun(U_818,bool),fun(fun(U_818,bool),fun(U_818,bool)),minus_minus(fun(U_818,bool)),U_816),hAPP(fun(U_818,bool),fun(U_818,bool),hAPP(U_818,fun(fun(U_818,bool),fun(U_818,bool)),insert(U_818),U_817),bot_bot(fun(U_818,bool)))))) = hAPP(fun(U_818,bool),nat,finite_card(U_818),U_816)
      | ~ hBOOL(hAPP(fun(U_818,bool),bool,hAPP(U_818,fun(fun(U_818,bool),bool),member(U_818),U_817),U_816))
      | ~ hBOOL(hAPP(fun(U_818,bool),bool,finite_finite(U_818),U_816)) ),
    inference(variable_rename,[status(thm)],[f_239_1]) ).

fof(f_239_3,plain,
    ! [U_817,U_816,U_818] :
      ( hAPP(nat,nat,suc,hAPP(fun(U_818,bool),nat,finite_card(U_818),hAPP(fun(U_818,bool),fun(U_818,bool),hAPP(fun(U_818,bool),fun(fun(U_818,bool),fun(U_818,bool)),minus_minus(fun(U_818,bool)),U_816),hAPP(fun(U_818,bool),fun(U_818,bool),hAPP(U_818,fun(fun(U_818,bool),fun(U_818,bool)),insert(U_818),U_817),bot_bot(fun(U_818,bool)))))) = hAPP(fun(U_818,bool),nat,finite_card(U_818),U_816)
      | ~ hBOOL(hAPP(fun(U_818,bool),bool,hAPP(U_818,fun(fun(U_818,bool),bool),member(U_818),U_817),U_816))
      | ~ hBOOL(hAPP(fun(U_818,bool),bool,finite_finite(U_818),U_816)) ),
    inference(definitional_conversion,[status(esa)],[f_239_2]) ).

cnf(f_239_4,plain,
    ( hAPP(nat,nat,suc,hAPP(fun(U_818,bool),nat,finite_card(U_818),hAPP(fun(U_818,bool),fun(U_818,bool),hAPP(fun(U_818,bool),fun(fun(U_818,bool),fun(U_818,bool)),minus_minus(fun(U_818,bool)),U_816),hAPP(fun(U_818,bool),fun(U_818,bool),hAPP(U_818,fun(fun(U_818,bool),fun(U_818,bool)),insert(U_818),U_817),bot_bot(fun(U_818,bool)))))) = hAPP(fun(U_818,bool),nat,finite_card(U_818),U_816)
    | ~ hBOOL(hAPP(fun(U_818,bool),bool,hAPP(U_818,fun(fun(U_818,bool),bool),member(U_818),U_817),U_816))
    | ~ hBOOL(hAPP(fun(U_818,bool),bool,finite_finite(U_818),U_816)) ),
    inference(clausify,[status(thm)],[f_239_3]) ).

fof(f_240_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_169_card__insert]) ).

fof(f_240_2,plain,
    ! [U_821,U_820,U_819] :
      ( hAPP(fun(U_821,bool),nat,finite_card(U_821),hAPP(fun(U_821,bool),fun(U_821,bool),hAPP(U_821,fun(fun(U_821,bool),fun(U_821,bool)),insert(U_821),U_820),U_819)) = hAPP(nat,nat,suc,hAPP(fun(U_821,bool),nat,finite_card(U_821),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_819),hAPP(fun(U_821,bool),fun(U_821,bool),hAPP(U_821,fun(fun(U_821,bool),fun(U_821,bool)),insert(U_821),U_820),bot_bot(fun(U_821,bool))))))
      | ~ hBOOL(hAPP(fun(U_821,bool),bool,finite_finite(U_821),U_819)) ),
    inference(variable_rename,[status(thm)],[f_240_1]) ).

fof(f_240_3,plain,
    ! [U_820,U_819,U_821] :
      ( hAPP(fun(U_821,bool),nat,finite_card(U_821),hAPP(fun(U_821,bool),fun(U_821,bool),hAPP(U_821,fun(fun(U_821,bool),fun(U_821,bool)),insert(U_821),U_820),U_819)) = hAPP(nat,nat,suc,hAPP(fun(U_821,bool),nat,finite_card(U_821),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_819),hAPP(fun(U_821,bool),fun(U_821,bool),hAPP(U_821,fun(fun(U_821,bool),fun(U_821,bool)),insert(U_821),U_820),bot_bot(fun(U_821,bool))))))
      | ~ hBOOL(hAPP(fun(U_821,bool),bool,finite_finite(U_821),U_819)) ),
    inference(definitional_conversion,[status(esa)],[f_240_2]) ).

cnf(f_240_4,plain,
    ( hAPP(fun(U_821,bool),nat,finite_card(U_821),hAPP(fun(U_821,bool),fun(U_821,bool),hAPP(U_821,fun(fun(U_821,bool),fun(U_821,bool)),insert(U_821),U_820),U_819)) = hAPP(nat,nat,suc,hAPP(fun(U_821,bool),nat,finite_card(U_821),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_819),hAPP(fun(U_821,bool),fun(U_821,bool),hAPP(U_821,fun(fun(U_821,bool),fun(U_821,bool)),insert(U_821),U_820),bot_bot(fun(U_821,bool))))))
    | ~ hBOOL(hAPP(fun(U_821,bool),bool,finite_finite(U_821),U_819)) ),
    inference(clausify,[status(thm)],[f_240_3]) ).

fof(f_241_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_170_card__Diff1__le]) ).

fof(f_241_2,plain,
    ! [U_824,U_823,U_822] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(U_824,bool),nat,finite_card(U_824),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_822),hAPP(fun(U_824,bool),fun(U_824,bool),hAPP(U_824,fun(fun(U_824,bool),fun(U_824,bool)),insert(U_824),U_823),bot_bot(fun(U_824,bool)))))),hAPP(fun(U_824,bool),nat,finite_card(U_824),U_822)))
      | ~ hBOOL(hAPP(fun(U_824,bool),bool,finite_finite(U_824),U_822)) ),
    inference(variable_rename,[status(thm)],[f_241_1]) ).

fof(f_241_3,plain,
    ! [U_824,U_822,U_823] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(U_824,bool),nat,finite_card(U_824),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_822),hAPP(fun(U_824,bool),fun(U_824,bool),hAPP(U_824,fun(fun(U_824,bool),fun(U_824,bool)),insert(U_824),U_823),bot_bot(fun(U_824,bool)))))),hAPP(fun(U_824,bool),nat,finite_card(U_824),U_822)))
      | ~ hBOOL(hAPP(fun(U_824,bool),bool,finite_finite(U_824),U_822)) ),
    inference(definitional_conversion,[status(esa)],[f_241_2]) ).

cnf(f_241_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(U_824,bool),nat,finite_card(U_824),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_822),hAPP(fun(U_824,bool),fun(U_824,bool),hAPP(U_824,fun(fun(U_824,bool),fun(U_824,bool)),insert(U_824),U_823),bot_bot(fun(U_824,bool)))))),hAPP(fun(U_824,bool),nat,finite_card(U_824),U_822)))
    | ~ hBOOL(hAPP(fun(U_824,bool),bool,finite_finite(U_824),U_822)) ),
    inference(clausify,[status(thm)],[f_241_3]) ).

fof(f_242_1,plain,
    ! [X_b,A_3,A_2,B_1] :
      ( ( 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_1))))
        | ~ 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_1))) )
      & ( 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_1)))
        | ~ 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_1)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_171_finite__Diff__insert]) ).

fof(f_242_2,plain,
    ! [U_828,U_827,U_826,U_825] :
      ( ( hBOOL(hAPP(fun(U_828,bool),bool,finite_finite(U_828),hAPP(fun(U_828,bool),fun(U_828,bool),hAPP(fun(U_828,bool),fun(fun(U_828,bool),fun(U_828,bool)),minus_minus(fun(U_828,bool)),U_827),hAPP(fun(U_828,bool),fun(U_828,bool),hAPP(U_828,fun(fun(U_828,bool),fun(U_828,bool)),insert(U_828),U_826),U_825))))
        | ~ hBOOL(hAPP(fun(U_828,bool),bool,finite_finite(U_828),hAPP(fun(U_828,bool),fun(U_828,bool),hAPP(fun(U_828,bool),fun(fun(U_828,bool),fun(U_828,bool)),minus_minus(fun(U_828,bool)),U_827),U_825))) )
      & ( hBOOL(hAPP(fun(U_828,bool),bool,finite_finite(U_828),hAPP(fun(U_828,bool),fun(U_828,bool),hAPP(fun(U_828,bool),fun(fun(U_828,bool),fun(U_828,bool)),minus_minus(fun(U_828,bool)),U_827),U_825)))
        | ~ hBOOL(hAPP(fun(U_828,bool),bool,finite_finite(U_828),hAPP(fun(U_828,bool),fun(U_828,bool),hAPP(fun(U_828,bool),fun(fun(U_828,bool),fun(U_828,bool)),minus_minus(fun(U_828,bool)),U_827),hAPP(fun(U_828,bool),fun(U_828,bool),hAPP(U_828,fun(fun(U_828,bool),fun(U_828,bool)),insert(U_828),U_826),U_825)))) ) ),
    inference(variable_rename,[status(thm)],[f_242_1]) ).

fof(f_242_3,plain,
    ( ! [U_836,U_834,U_832,U_830] :
        ( hBOOL(hAPP(fun(U_836,bool),bool,finite_finite(U_836),hAPP(fun(U_836,bool),fun(U_836,bool),hAPP(fun(U_836,bool),fun(fun(U_836,bool),fun(U_836,bool)),minus_minus(fun(U_836,bool)),U_834),hAPP(fun(U_836,bool),fun(U_836,bool),hAPP(U_836,fun(fun(U_836,bool),fun(U_836,bool)),insert(U_836),U_832),U_830))))
        | ~ hBOOL(hAPP(fun(U_836,bool),bool,finite_finite(U_836),hAPP(fun(U_836,bool),fun(U_836,bool),hAPP(fun(U_836,bool),fun(fun(U_836,bool),fun(U_836,bool)),minus_minus(fun(U_836,bool)),U_834),U_830))) )
    & ! [U_835,U_833,U_831,U_829] :
        ( hBOOL(hAPP(fun(U_835,bool),bool,finite_finite(U_835),hAPP(fun(U_835,bool),fun(U_835,bool),hAPP(fun(U_835,bool),fun(fun(U_835,bool),fun(U_835,bool)),minus_minus(fun(U_835,bool)),U_833),U_829)))
        | ~ hBOOL(hAPP(fun(U_835,bool),bool,finite_finite(U_835),hAPP(fun(U_835,bool),fun(U_835,bool),hAPP(fun(U_835,bool),fun(fun(U_835,bool),fun(U_835,bool)),minus_minus(fun(U_835,bool)),U_833),hAPP(fun(U_835,bool),fun(U_835,bool),hAPP(U_835,fun(fun(U_835,bool),fun(U_835,bool)),insert(U_835),U_831),U_829)))) ) ),
    inference(miniscope,[status(thm)],[f_242_2]) ).

fof(f_242_4,plain,
    ( ! [U_836,U_830,U_832,U_834] :
        ( hBOOL(hAPP(fun(U_836,bool),bool,finite_finite(U_836),hAPP(fun(U_836,bool),fun(U_836,bool),hAPP(fun(U_836,bool),fun(fun(U_836,bool),fun(U_836,bool)),minus_minus(fun(U_836,bool)),U_834),hAPP(fun(U_836,bool),fun(U_836,bool),hAPP(U_836,fun(fun(U_836,bool),fun(U_836,bool)),insert(U_836),U_832),U_830))))
        | ~ hBOOL(hAPP(fun(U_836,bool),bool,finite_finite(U_836),hAPP(fun(U_836,bool),fun(U_836,bool),hAPP(fun(U_836,bool),fun(fun(U_836,bool),fun(U_836,bool)),minus_minus(fun(U_836,bool)),U_834),U_830))) )
    & ! [U_831,U_835,U_829,U_833] :
        ( hBOOL(hAPP(fun(U_835,bool),bool,finite_finite(U_835),hAPP(fun(U_835,bool),fun(U_835,bool),hAPP(fun(U_835,bool),fun(fun(U_835,bool),fun(U_835,bool)),minus_minus(fun(U_835,bool)),U_833),U_829)))
        | ~ hBOOL(hAPP(fun(U_835,bool),bool,finite_finite(U_835),hAPP(fun(U_835,bool),fun(U_835,bool),hAPP(fun(U_835,bool),fun(fun(U_835,bool),fun(U_835,bool)),minus_minus(fun(U_835,bool)),U_833),hAPP(fun(U_835,bool),fun(U_835,bool),hAPP(U_835,fun(fun(U_835,bool),fun(U_835,bool)),insert(U_835),U_831),U_829)))) ) ),
    inference(definitional_conversion,[status(esa)],[f_242_3]) ).

cnf(f_242_5,plain,
    ( hBOOL(hAPP(fun(U_835,bool),bool,finite_finite(U_835),hAPP(fun(U_835,bool),fun(U_835,bool),hAPP(fun(U_835,bool),fun(fun(U_835,bool),fun(U_835,bool)),minus_minus(fun(U_835,bool)),U_833),U_829)))
    | ~ hBOOL(hAPP(fun(U_835,bool),bool,finite_finite(U_835),hAPP(fun(U_835,bool),fun(U_835,bool),hAPP(fun(U_835,bool),fun(fun(U_835,bool),fun(U_835,bool)),minus_minus(fun(U_835,bool)),U_833),hAPP(fun(U_835,bool),fun(U_835,bool),hAPP(U_835,fun(fun(U_835,bool),fun(U_835,bool)),insert(U_835),U_831),U_829)))) ),
    inference(clausify,[status(thm)],[f_242_4]) ).

cnf(f_242_6,plain,
    ( hBOOL(hAPP(fun(U_836,bool),bool,finite_finite(U_836),hAPP(fun(U_836,bool),fun(U_836,bool),hAPP(fun(U_836,bool),fun(fun(U_836,bool),fun(U_836,bool)),minus_minus(fun(U_836,bool)),U_834),hAPP(fun(U_836,bool),fun(U_836,bool),hAPP(U_836,fun(fun(U_836,bool),fun(U_836,bool)),insert(U_836),U_832),U_830))))
    | ~ hBOOL(hAPP(fun(U_836,bool),bool,finite_finite(U_836),hAPP(fun(U_836,bool),fun(U_836,bool),hAPP(fun(U_836,bool),fun(fun(U_836,bool),fun(U_836,bool)),minus_minus(fun(U_836,bool)),U_834),U_830))) ),
    inference(clausify,[status(thm)],[f_242_4]) ).

fof(f_243_1,plain,
    ! [X_b,X_c,F,A_3,B_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)),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_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),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_1)))),
    inference(fof_nnf,[status(thm)],[fact_172_image__diff__subset]) ).

fof(f_243_2,plain,
    ! [U_841,U_840,U_839,U_838,U_837] : hBOOL(hAPP(fun(U_841,bool),bool,hAPP(fun(U_841,bool),fun(fun(U_841,bool),bool),ord_less_eq(fun(U_841,bool)),hAPP(fun(U_841,bool),fun(U_841,bool),hAPP(fun(U_841,bool),fun(fun(U_841,bool),fun(U_841,bool)),minus_minus(fun(U_841,bool)),hAPP(fun(U_840,bool),fun(U_841,bool),hAPP(fun(U_840,U_841),fun(fun(U_840,bool),fun(U_841,bool)),image(U_840,U_841),U_839),U_838)),hAPP(fun(U_840,bool),fun(U_841,bool),hAPP(fun(U_840,U_841),fun(fun(U_840,bool),fun(U_841,bool)),image(U_840,U_841),U_839),U_837))),hAPP(fun(U_840,bool),fun(U_841,bool),hAPP(fun(U_840,U_841),fun(fun(U_840,bool),fun(U_841,bool)),image(U_840,U_841),U_839),hAPP(fun(U_840,bool),fun(U_840,bool),hAPP(fun(U_840,bool),fun(fun(U_840,bool),fun(U_840,bool)),minus_minus(fun(U_840,bool)),U_838),U_837)))),
    inference(variable_rename,[status(thm)],[f_243_1]) ).

fof(f_243_3,plain,
    ! [U_837,U_841,U_839,U_840,U_838] : hBOOL(hAPP(fun(U_841,bool),bool,hAPP(fun(U_841,bool),fun(fun(U_841,bool),bool),ord_less_eq(fun(U_841,bool)),hAPP(fun(U_841,bool),fun(U_841,bool),hAPP(fun(U_841,bool),fun(fun(U_841,bool),fun(U_841,bool)),minus_minus(fun(U_841,bool)),hAPP(fun(U_840,bool),fun(U_841,bool),hAPP(fun(U_840,U_841),fun(fun(U_840,bool),fun(U_841,bool)),image(U_840,U_841),U_839),U_838)),hAPP(fun(U_840,bool),fun(U_841,bool),hAPP(fun(U_840,U_841),fun(fun(U_840,bool),fun(U_841,bool)),image(U_840,U_841),U_839),U_837))),hAPP(fun(U_840,bool),fun(U_841,bool),hAPP(fun(U_840,U_841),fun(fun(U_840,bool),fun(U_841,bool)),image(U_840,U_841),U_839),hAPP(fun(U_840,bool),fun(U_840,bool),hAPP(fun(U_840,bool),fun(fun(U_840,bool),fun(U_840,bool)),minus_minus(fun(U_840,bool)),U_838),U_837)))),
    inference(definitional_conversion,[status(esa)],[f_243_2]) ).

cnf(f_243_4,plain,
    hBOOL(hAPP(fun(U_841,bool),bool,hAPP(fun(U_841,bool),fun(fun(U_841,bool),bool),ord_less_eq(fun(U_841,bool)),hAPP(fun(U_841,bool),fun(U_841,bool),hAPP(fun(U_841,bool),fun(fun(U_841,bool),fun(U_841,bool)),minus_minus(fun(U_841,bool)),hAPP(fun(U_840,bool),fun(U_841,bool),hAPP(fun(U_840,U_841),fun(fun(U_840,bool),fun(U_841,bool)),image(U_840,U_841),U_839),U_838)),hAPP(fun(U_840,bool),fun(U_841,bool),hAPP(fun(U_840,U_841),fun(fun(U_840,bool),fun(U_841,bool)),image(U_840,U_841),U_839),U_837))),hAPP(fun(U_840,bool),fun(U_841,bool),hAPP(fun(U_840,U_841),fun(fun(U_840,bool),fun(U_841,bool)),image(U_840,U_841),U_839),hAPP(fun(U_840,bool),fun(U_840,bool),hAPP(fun(U_840,bool),fun(fun(U_840,bool),fun(U_840,bool)),minus_minus(fun(U_840,bool)),U_838),U_837)))),
    inference(clausify,[status(thm)],[f_243_3]) ).

fof(f_244_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_173_subset__singletonD]) ).

fof(f_244_2,plain,
    ! [U_844,U_843,U_842] :
      ( ti(fun(U_844,bool),U_843) = hAPP(fun(U_844,bool),fun(U_844,bool),hAPP(U_844,fun(fun(U_844,bool),fun(U_844,bool)),insert(U_844),U_842),bot_bot(fun(U_844,bool)))
      | ti(fun(U_844,bool),U_843) = bot_bot(fun(U_844,bool))
      | ~ hBOOL(hAPP(fun(U_844,bool),bool,hAPP(fun(U_844,bool),fun(fun(U_844,bool),bool),ord_less_eq(fun(U_844,bool)),U_843),hAPP(fun(U_844,bool),fun(U_844,bool),hAPP(U_844,fun(fun(U_844,bool),fun(U_844,bool)),insert(U_844),U_842),bot_bot(fun(U_844,bool))))) ),
    inference(variable_rename,[status(thm)],[f_244_1]) ).

fof(f_244_3,plain,
    ! [U_843,U_842,U_844] :
      ( ti(fun(U_844,bool),U_843) = hAPP(fun(U_844,bool),fun(U_844,bool),hAPP(U_844,fun(fun(U_844,bool),fun(U_844,bool)),insert(U_844),U_842),bot_bot(fun(U_844,bool)))
      | ti(fun(U_844,bool),U_843) = bot_bot(fun(U_844,bool))
      | ~ hBOOL(hAPP(fun(U_844,bool),bool,hAPP(fun(U_844,bool),fun(fun(U_844,bool),bool),ord_less_eq(fun(U_844,bool)),U_843),hAPP(fun(U_844,bool),fun(U_844,bool),hAPP(U_844,fun(fun(U_844,bool),fun(U_844,bool)),insert(U_844),U_842),bot_bot(fun(U_844,bool))))) ),
    inference(definitional_conversion,[status(esa)],[f_244_2]) ).

cnf(f_244_4,plain,
    ( ti(fun(U_844,bool),U_843) = hAPP(fun(U_844,bool),fun(U_844,bool),hAPP(U_844,fun(fun(U_844,bool),fun(U_844,bool)),insert(U_844),U_842),bot_bot(fun(U_844,bool)))
    | ti(fun(U_844,bool),U_843) = bot_bot(fun(U_844,bool))
    | ~ hBOOL(hAPP(fun(U_844,bool),bool,hAPP(fun(U_844,bool),fun(fun(U_844,bool),bool),ord_less_eq(fun(U_844,bool)),U_843),hAPP(fun(U_844,bool),fun(U_844,bool),hAPP(U_844,fun(fun(U_844,bool),fun(U_844,bool)),insert(U_844),U_842),bot_bot(fun(U_844,bool))))) ),
    inference(clausify,[status(thm)],[f_244_3]) ).

fof(f_245_1,plain,
    ! [X_b,F1,F2,Nat_3] : 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_3)) = hAPP(nat,X_b,F2,Nat_3),
    inference(fof_nnf,[status(thm)],[fact_174_nat__case__Suc]) ).

fof(f_245_2,plain,
    ! [U_848,U_847,U_846,U_845] : hAPP(nat,U_848,hAPP(fun(nat,U_848),fun(nat,U_848),hAPP(U_848,fun(fun(nat,U_848),fun(nat,U_848)),nat_case(U_848),U_847),U_846),hAPP(nat,nat,suc,U_845)) = hAPP(nat,U_848,U_846,U_845),
    inference(variable_rename,[status(thm)],[f_245_1]) ).

fof(f_245_3,plain,
    ! [U_848,U_846,U_845,U_847] : hAPP(nat,U_848,hAPP(fun(nat,U_848),fun(nat,U_848),hAPP(U_848,fun(fun(nat,U_848),fun(nat,U_848)),nat_case(U_848),U_847),U_846),hAPP(nat,nat,suc,U_845)) = hAPP(nat,U_848,U_846,U_845),
    inference(definitional_conversion,[status(esa)],[f_245_2]) ).

cnf(f_245_4,plain,
    hAPP(nat,U_848,hAPP(fun(nat,U_848),fun(nat,U_848),hAPP(U_848,fun(fun(nat,U_848),fun(nat,U_848)),nat_case(U_848),U_847),U_846),hAPP(nat,nat,suc,U_845)) = hAPP(nat,U_848,U_846,U_845),
    inference(clausify,[status(thm)],[f_245_3]) ).

fof(f_246_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_175_image__constant]) ).

fof(f_246_2,plain,
    ! [U_853,U_852,U_851,U_850,U_849] :
      ( hAPP(fun(U_852,bool),fun(U_853,bool),hAPP(fun(U_852,U_853),fun(fun(U_852,bool),fun(U_853,bool)),image(U_852,U_853),hAPP(U_853,fun(U_852,U_853),combk(U_853,U_852),U_851)),U_849) = hAPP(fun(U_853,bool),fun(U_853,bool),hAPP(U_853,fun(fun(U_853,bool),fun(U_853,bool)),insert(U_853),U_851),bot_bot(fun(U_853,bool)))
      | ~ hBOOL(hAPP(fun(U_852,bool),bool,hAPP(U_852,fun(fun(U_852,bool),bool),member(U_852),U_850),U_849)) ),
    inference(variable_rename,[status(thm)],[f_246_1]) ).

fof(f_246_3,plain,
    ! [U_850,U_852,U_849,U_851,U_853] :
      ( hAPP(fun(U_852,bool),fun(U_853,bool),hAPP(fun(U_852,U_853),fun(fun(U_852,bool),fun(U_853,bool)),image(U_852,U_853),hAPP(U_853,fun(U_852,U_853),combk(U_853,U_852),U_851)),U_849) = hAPP(fun(U_853,bool),fun(U_853,bool),hAPP(U_853,fun(fun(U_853,bool),fun(U_853,bool)),insert(U_853),U_851),bot_bot(fun(U_853,bool)))
      | ~ hBOOL(hAPP(fun(U_852,bool),bool,hAPP(U_852,fun(fun(U_852,bool),bool),member(U_852),U_850),U_849)) ),
    inference(definitional_conversion,[status(esa)],[f_246_2]) ).

cnf(f_246_4,plain,
    ( hAPP(fun(U_852,bool),fun(U_853,bool),hAPP(fun(U_852,U_853),fun(fun(U_852,bool),fun(U_853,bool)),image(U_852,U_853),hAPP(U_853,fun(U_852,U_853),combk(U_853,U_852),U_851)),U_849) = hAPP(fun(U_853,bool),fun(U_853,bool),hAPP(U_853,fun(fun(U_853,bool),fun(U_853,bool)),insert(U_853),U_851),bot_bot(fun(U_853,bool)))
    | ~ hBOOL(hAPP(fun(U_852,bool),bool,hAPP(U_852,fun(fun(U_852,bool),bool),member(U_852),U_850),U_849)) ),
    inference(clausify,[status(thm)],[f_246_3]) ).

fof(f_247_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_176_image__constant__conv]) ).

fof(f_247_2,plain,
    ! [U_857,U_856,U_855,U_854] :
      ( ( hAPP(fun(U_856,bool),fun(U_857,bool),hAPP(fun(U_856,U_857),fun(fun(U_856,bool),fun(U_857,bool)),image(U_856,U_857),hAPP(U_857,fun(U_856,U_857),combk(U_857,U_856),U_855)),U_854) = hAPP(fun(U_857,bool),fun(U_857,bool),hAPP(U_857,fun(fun(U_857,bool),fun(U_857,bool)),insert(U_857),U_855),bot_bot(fun(U_857,bool)))
        | ti(fun(U_856,bool),U_854) = bot_bot(fun(U_856,bool)) )
      & ( hAPP(fun(U_856,bool),fun(U_857,bool),hAPP(fun(U_856,U_857),fun(fun(U_856,bool),fun(U_857,bool)),image(U_856,U_857),hAPP(U_857,fun(U_856,U_857),combk(U_857,U_856),U_855)),U_854) = bot_bot(fun(U_857,bool))
        | ti(fun(U_856,bool),U_854) != bot_bot(fun(U_856,bool)) ) ),
    inference(variable_rename,[status(thm)],[f_247_1]) ).

fof(f_247_3,plain,
    ( ! [U_865,U_863,U_861,U_859] :
        ( hAPP(fun(U_863,bool),fun(U_865,bool),hAPP(fun(U_863,U_865),fun(fun(U_863,bool),fun(U_865,bool)),image(U_863,U_865),hAPP(U_865,fun(U_863,U_865),combk(U_865,U_863),U_861)),U_859) = hAPP(fun(U_865,bool),fun(U_865,bool),hAPP(U_865,fun(fun(U_865,bool),fun(U_865,bool)),insert(U_865),U_861),bot_bot(fun(U_865,bool)))
        | ti(fun(U_863,bool),U_859) = bot_bot(fun(U_863,bool)) )
    & ! [U_864,U_862,U_860,U_858] :
        ( hAPP(fun(U_862,bool),fun(U_864,bool),hAPP(fun(U_862,U_864),fun(fun(U_862,bool),fun(U_864,bool)),image(U_862,U_864),hAPP(U_864,fun(U_862,U_864),combk(U_864,U_862),U_860)),U_858) = bot_bot(fun(U_864,bool))
        | ti(fun(U_862,bool),U_858) != bot_bot(fun(U_862,bool)) ) ),
    inference(miniscope,[status(thm)],[f_247_2]) ).

fof(f_247_4,plain,
    ( ! [U_859,U_861,U_863,U_865] :
        ( hAPP(fun(U_863,bool),fun(U_865,bool),hAPP(fun(U_863,U_865),fun(fun(U_863,bool),fun(U_865,bool)),image(U_863,U_865),hAPP(U_865,fun(U_863,U_865),combk(U_865,U_863),U_861)),U_859) = hAPP(fun(U_865,bool),fun(U_865,bool),hAPP(U_865,fun(fun(U_865,bool),fun(U_865,bool)),insert(U_865),U_861),bot_bot(fun(U_865,bool)))
        | ti(fun(U_863,bool),U_859) = bot_bot(fun(U_863,bool)) )
    & ! [U_860,U_858,U_862,U_864] :
        ( hAPP(fun(U_862,bool),fun(U_864,bool),hAPP(fun(U_862,U_864),fun(fun(U_862,bool),fun(U_864,bool)),image(U_862,U_864),hAPP(U_864,fun(U_862,U_864),combk(U_864,U_862),U_860)),U_858) = bot_bot(fun(U_864,bool))
        | ti(fun(U_862,bool),U_858) != bot_bot(fun(U_862,bool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_247_3]) ).

cnf(f_247_5,plain,
    ( hAPP(fun(U_862,bool),fun(U_864,bool),hAPP(fun(U_862,U_864),fun(fun(U_862,bool),fun(U_864,bool)),image(U_862,U_864),hAPP(U_864,fun(U_862,U_864),combk(U_864,U_862),U_860)),U_858) = bot_bot(fun(U_864,bool))
    | ti(fun(U_862,bool),U_858) != bot_bot(fun(U_862,bool)) ),
    inference(clausify,[status(thm)],[f_247_4]) ).

cnf(f_247_6,plain,
    ( hAPP(fun(U_863,bool),fun(U_865,bool),hAPP(fun(U_863,U_865),fun(fun(U_863,bool),fun(U_865,bool)),image(U_863,U_865),hAPP(U_865,fun(U_863,U_865),combk(U_865,U_863),U_861)),U_859) = hAPP(fun(U_865,bool),fun(U_865,bool),hAPP(U_865,fun(fun(U_865,bool),fun(U_865,bool)),insert(U_865),U_861),bot_bot(fun(U_865,bool)))
    | ti(fun(U_863,bool),U_859) = bot_bot(fun(U_863,bool)) ),
    inference(clausify,[status(thm)],[f_247_4]) ).

fof(f_248_1,plain,
    ! [X_c,X_b,X_1,A_3,F,Z_2,G,F_1] :
      ( 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_1,A_3)) = hAPP(fun(X_c,bool),X_b,F_1,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))),finite908156982e_idem(X_b,X_c),F),Z_2),G),F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_177_folding__image__simple__idem_Oin__idem]) ).

fof(f_248_2,plain,
    ! [U_873,U_872,U_871,U_870,U_869,U_868,U_867,U_866] :
      ( hAPP(U_872,U_872,hAPP(U_872,fun(U_872,U_872),U_869,hAPP(U_873,U_872,U_867,U_871)),hAPP(fun(U_873,bool),U_872,U_866,U_870)) = hAPP(fun(U_873,bool),U_872,U_866,U_870)
      | ~ hBOOL(hAPP(fun(U_873,bool),bool,hAPP(U_873,fun(fun(U_873,bool),bool),member(U_873),U_871),U_870))
      | ~ hBOOL(hAPP(fun(U_873,bool),bool,finite_finite(U_873),U_870))
      | ~ hBOOL(hAPP(fun(fun(U_873,bool),U_872),bool,hAPP(fun(U_873,U_872),fun(fun(fun(U_873,bool),U_872),bool),hAPP(U_872,fun(fun(U_873,U_872),fun(fun(fun(U_873,bool),U_872),bool)),hAPP(fun(U_872,fun(U_872,U_872)),fun(U_872,fun(fun(U_873,U_872),fun(fun(fun(U_873,bool),U_872),bool))),finite908156982e_idem(U_872,U_873),U_869),U_868),U_867),U_866)) ),
    inference(variable_rename,[status(thm)],[f_248_1]) ).

fof(f_248_3,plain,
    ! [U_872,U_866,U_867,U_869,U_868,U_870,U_871,U_873] :
      ( hAPP(U_872,U_872,hAPP(U_872,fun(U_872,U_872),U_869,hAPP(U_873,U_872,U_867,U_871)),hAPP(fun(U_873,bool),U_872,U_866,U_870)) = hAPP(fun(U_873,bool),U_872,U_866,U_870)
      | ~ hBOOL(hAPP(fun(U_873,bool),bool,hAPP(U_873,fun(fun(U_873,bool),bool),member(U_873),U_871),U_870))
      | ~ hBOOL(hAPP(fun(U_873,bool),bool,finite_finite(U_873),U_870))
      | ~ hBOOL(hAPP(fun(fun(U_873,bool),U_872),bool,hAPP(fun(U_873,U_872),fun(fun(fun(U_873,bool),U_872),bool),hAPP(U_872,fun(fun(U_873,U_872),fun(fun(fun(U_873,bool),U_872),bool)),hAPP(fun(U_872,fun(U_872,U_872)),fun(U_872,fun(fun(U_873,U_872),fun(fun(fun(U_873,bool),U_872),bool))),finite908156982e_idem(U_872,U_873),U_869),U_868),U_867),U_866)) ),
    inference(definitional_conversion,[status(esa)],[f_248_2]) ).

cnf(f_248_4,plain,
    ( hAPP(U_872,U_872,hAPP(U_872,fun(U_872,U_872),U_869,hAPP(U_873,U_872,U_867,U_871)),hAPP(fun(U_873,bool),U_872,U_866,U_870)) = hAPP(fun(U_873,bool),U_872,U_866,U_870)
    | ~ hBOOL(hAPP(fun(U_873,bool),bool,hAPP(U_873,fun(fun(U_873,bool),bool),member(U_873),U_871),U_870))
    | ~ hBOOL(hAPP(fun(U_873,bool),bool,finite_finite(U_873),U_870))
    | ~ hBOOL(hAPP(fun(fun(U_873,bool),U_872),bool,hAPP(fun(U_873,U_872),fun(fun(fun(U_873,bool),U_872),bool),hAPP(U_872,fun(fun(U_873,U_872),fun(fun(fun(U_873,bool),U_872),bool)),hAPP(fun(U_872,fun(U_872,U_872)),fun(U_872,fun(fun(U_873,U_872),fun(fun(fun(U_873,bool),U_872),bool))),finite908156982e_idem(U_872,U_873),U_869),U_868),U_867),U_866)) ),
    inference(clausify,[status(thm)],[f_248_3]) ).

fof(f_249_1,plain,
    ! [X_b] :
      ( ! [A_2,B_3,C_1,D_1] :
          ( ( ( ti(X_b,A_2) = ti(X_b,B_3)
              | 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_3) ) )
          | hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3) != 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_178_diff__eq__diff__eq]) ).

fof(f_249_2,plain,
    ! [U_878] :
      ( ! [U_877,U_876,U_875,U_874] :
          ( ( ( ti(U_878,U_877) = ti(U_878,U_876)
              | ti(U_878,U_875) != ti(U_878,U_874) )
            & ( ti(U_878,U_875) = ti(U_878,U_874)
              | ti(U_878,U_877) != ti(U_878,U_876) ) )
          | hAPP(U_878,U_878,hAPP(U_878,fun(U_878,U_878),minus_minus(U_878),U_877),U_876) != hAPP(U_878,U_878,hAPP(U_878,fun(U_878,U_878),minus_minus(U_878),U_875),U_874) )
      | ~ ab_group_add(U_878) ),
    inference(variable_rename,[status(thm)],[f_249_1]) ).

fof(f_249_3,plain,
    ( ! [U_877,U_876,U_875,U_874,U_878] :
        ( ti(U_878,U_877) = ti(U_878,U_876)
        | ti(U_878,U_875) != ti(U_878,U_874)
        | ~ sP37(U_877,U_876,U_875,U_874,U_878) )
    & ! [U_877,U_876,U_875,U_874,U_878] :
        ( ti(U_878,U_875) = ti(U_878,U_874)
        | ti(U_878,U_877) != ti(U_878,U_876)
        | ~ sP37(U_877,U_876,U_875,U_874,U_878) )
    & ! [U_877,U_876,U_875,U_874,U_878] :
        ( sP37(U_877,U_876,U_875,U_874,U_878)
        | hAPP(U_878,U_878,hAPP(U_878,fun(U_878,U_878),minus_minus(U_878),U_877),U_876) != hAPP(U_878,U_878,hAPP(U_878,fun(U_878,U_878),minus_minus(U_878),U_875),U_874)
        | ~ ab_group_add(U_878) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP37])],[f_249_2]) ).

cnf(f_249_4,plain,
    ( sP37(U_877,U_876,U_875,U_874,U_878)
    | hAPP(U_878,U_878,hAPP(U_878,fun(U_878,U_878),minus_minus(U_878),U_877),U_876) != hAPP(U_878,U_878,hAPP(U_878,fun(U_878,U_878),minus_minus(U_878),U_875),U_874)
    | ~ ab_group_add(U_878) ),
    inference(clausify,[status(thm)],[f_249_3]) ).

cnf(f_249_5,plain,
    ( ti(U_878,U_875) = ti(U_878,U_874)
    | ti(U_878,U_877) != ti(U_878,U_876)
    | ~ sP37(U_877,U_876,U_875,U_874,U_878) ),
    inference(clausify,[status(thm)],[f_249_3]) ).

cnf(f_249_6,plain,
    ( ti(U_878,U_877) = ti(U_878,U_876)
    | ti(U_878,U_875) != ti(U_878,U_874)
    | ~ sP37(U_877,U_876,U_875,U_874,U_878) ),
    inference(clausify,[status(thm)],[f_249_3]) ).

fof(f_250_1,plain,
    ! [X_b,A_3,B_1] :
      ( 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_1)) = 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_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)),B_1),A_3))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_1)) ),
    inference(fof_nnf,[status(thm)],[fact_179_card__Diff__subset]) ).

fof(f_250_2,plain,
    ! [U_881,U_880,U_879] :
      ( hAPP(fun(U_881,bool),nat,finite_card(U_881),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),U_879)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(U_881,bool),nat,finite_card(U_881),U_880)),hAPP(fun(U_881,bool),nat,finite_card(U_881),U_879))
      | ~ 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_879),U_880))
      | ~ hBOOL(hAPP(fun(U_881,bool),bool,finite_finite(U_881),U_879)) ),
    inference(variable_rename,[status(thm)],[f_250_1]) ).

fof(f_250_3,plain,
    ! [U_880,U_879,U_881] :
      ( hAPP(fun(U_881,bool),nat,finite_card(U_881),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),U_879)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(U_881,bool),nat,finite_card(U_881),U_880)),hAPP(fun(U_881,bool),nat,finite_card(U_881),U_879))
      | ~ 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_879),U_880))
      | ~ hBOOL(hAPP(fun(U_881,bool),bool,finite_finite(U_881),U_879)) ),
    inference(definitional_conversion,[status(esa)],[f_250_2]) ).

cnf(f_250_4,plain,
    ( hAPP(fun(U_881,bool),nat,finite_card(U_881),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),U_879)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(U_881,bool),nat,finite_card(U_881),U_880)),hAPP(fun(U_881,bool),nat,finite_card(U_881),U_879))
    | ~ 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_879),U_880))
    | ~ hBOOL(hAPP(fun(U_881,bool),bool,finite_finite(U_881),U_879)) ),
    inference(clausify,[status(thm)],[f_250_3]) ).

fof(f_251_1,plain,
    ! [X_b,A_3,B_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),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_1))),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_1))))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_1)) ),
    inference(fof_nnf,[status(thm)],[fact_180_diff__card__le__card__Diff]) ).

fof(f_251_2,plain,
    ! [U_884,U_883,U_882] :
      ( 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_884,bool),nat,finite_card(U_884),U_883)),hAPP(fun(U_884,bool),nat,finite_card(U_884),U_882))),hAPP(fun(U_884,bool),nat,finite_card(U_884),hAPP(fun(U_884,bool),fun(U_884,bool),hAPP(fun(U_884,bool),fun(fun(U_884,bool),fun(U_884,bool)),minus_minus(fun(U_884,bool)),U_883),U_882))))
      | ~ hBOOL(hAPP(fun(U_884,bool),bool,finite_finite(U_884),U_882)) ),
    inference(variable_rename,[status(thm)],[f_251_1]) ).

fof(f_251_3,plain,
    ! [U_882,U_884,U_883] :
      ( 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_884,bool),nat,finite_card(U_884),U_883)),hAPP(fun(U_884,bool),nat,finite_card(U_884),U_882))),hAPP(fun(U_884,bool),nat,finite_card(U_884),hAPP(fun(U_884,bool),fun(U_884,bool),hAPP(fun(U_884,bool),fun(fun(U_884,bool),fun(U_884,bool)),minus_minus(fun(U_884,bool)),U_883),U_882))))
      | ~ hBOOL(hAPP(fun(U_884,bool),bool,finite_finite(U_884),U_882)) ),
    inference(definitional_conversion,[status(esa)],[f_251_2]) ).

cnf(f_251_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_884,bool),nat,finite_card(U_884),U_883)),hAPP(fun(U_884,bool),nat,finite_card(U_884),U_882))),hAPP(fun(U_884,bool),nat,finite_card(U_884),hAPP(fun(U_884,bool),fun(U_884,bool),hAPP(fun(U_884,bool),fun(fun(U_884,bool),fun(U_884,bool)),minus_minus(fun(U_884,bool)),U_883),U_882))))
    | ~ hBOOL(hAPP(fun(U_884,bool),bool,finite_finite(U_884),U_882)) ),
    inference(clausify,[status(thm)],[f_251_3]) ).

fof(f_252_1,plain,
    ! [X_b,Pa,A_3,F_1] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_1))
      | ? [A_4,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_4),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_4),F_3))
          & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_4),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_1),A_3))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_181_finite__subset__induct]) ).

fof(f_252_2,plain,
    ! [U_890,U_889,U_888,U_887] :
      ( hBOOL(hAPP(fun(U_890,bool),bool,U_889,U_887))
      | ? [U_886,U_885] :
          ( ~ hBOOL(hAPP(fun(U_890,bool),bool,U_889,hAPP(fun(U_890,bool),fun(U_890,bool),hAPP(U_890,fun(fun(U_890,bool),fun(U_890,bool)),insert(U_890),U_886),U_885)))
          & hBOOL(hAPP(fun(U_890,bool),bool,U_889,U_885))
          & ~ hBOOL(hAPP(fun(U_890,bool),bool,hAPP(U_890,fun(fun(U_890,bool),bool),member(U_890),U_886),U_885))
          & hBOOL(hAPP(fun(U_890,bool),bool,hAPP(U_890,fun(fun(U_890,bool),bool),member(U_890),U_886),U_888))
          & hBOOL(hAPP(fun(U_890,bool),bool,finite_finite(U_890),U_885)) )
      | ~ hBOOL(hAPP(fun(U_890,bool),bool,U_889,bot_bot(fun(U_890,bool))))
      | ~ hBOOL(hAPP(fun(U_890,bool),bool,hAPP(fun(U_890,bool),fun(fun(U_890,bool),bool),ord_less_eq(fun(U_890,bool)),U_887),U_888))
      | ~ hBOOL(hAPP(fun(U_890,bool),bool,finite_finite(U_890),U_887)) ),
    inference(variable_rename,[status(thm)],[f_252_1]) ).

fof(f_252_3,plain,
    ! [U_890,U_889,U_888,U_887] :
      ( hBOOL(hAPP(fun(U_890,bool),bool,U_889,U_887))
      | ? [U_885] :
          ( ~ hBOOL(hAPP(fun(U_890,bool),bool,U_889,hAPP(fun(U_890,bool),fun(U_890,bool),hAPP(U_890,fun(fun(U_890,bool),fun(U_890,bool)),insert(U_890),sK21(U_890,U_889,U_888,U_887)),U_885)))
          & hBOOL(hAPP(fun(U_890,bool),bool,U_889,U_885))
          & ~ hBOOL(hAPP(fun(U_890,bool),bool,hAPP(U_890,fun(fun(U_890,bool),bool),member(U_890),sK21(U_890,U_889,U_888,U_887)),U_885))
          & hBOOL(hAPP(fun(U_890,bool),bool,hAPP(U_890,fun(fun(U_890,bool),bool),member(U_890),sK21(U_890,U_889,U_888,U_887)),U_888))
          & hBOOL(hAPP(fun(U_890,bool),bool,finite_finite(U_890),U_885)) )
      | ~ hBOOL(hAPP(fun(U_890,bool),bool,U_889,bot_bot(fun(U_890,bool))))
      | ~ hBOOL(hAPP(fun(U_890,bool),bool,hAPP(fun(U_890,bool),fun(fun(U_890,bool),bool),ord_less_eq(fun(U_890,bool)),U_887),U_888))
      | ~ hBOOL(hAPP(fun(U_890,bool),bool,finite_finite(U_890),U_887)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_886,sK21(U_890,U_889,U_888,U_887))],[f_252_2]) ).

fof(f_252_4,plain,
    ! [U_890,U_889,U_888,U_887] :
      ( hBOOL(hAPP(fun(U_890,bool),bool,U_889,U_887))
      | ( ~ hBOOL(hAPP(fun(U_890,bool),bool,U_889,hAPP(fun(U_890,bool),fun(U_890,bool),hAPP(U_890,fun(fun(U_890,bool),fun(U_890,bool)),insert(U_890),sK21(U_890,U_889,U_888,U_887)),sK22(U_890,U_889,U_888,U_887))))
        & hBOOL(hAPP(fun(U_890,bool),bool,U_889,sK22(U_890,U_889,U_888,U_887)))
        & ~ hBOOL(hAPP(fun(U_890,bool),bool,hAPP(U_890,fun(fun(U_890,bool),bool),member(U_890),sK21(U_890,U_889,U_888,U_887)),sK22(U_890,U_889,U_888,U_887)))
        & hBOOL(hAPP(fun(U_890,bool),bool,hAPP(U_890,fun(fun(U_890,bool),bool),member(U_890),sK21(U_890,U_889,U_888,U_887)),U_888))
        & hBOOL(hAPP(fun(U_890,bool),bool,finite_finite(U_890),sK22(U_890,U_889,U_888,U_887))) )
      | ~ hBOOL(hAPP(fun(U_890,bool),bool,U_889,bot_bot(fun(U_890,bool))))
      | ~ hBOOL(hAPP(fun(U_890,bool),bool,hAPP(fun(U_890,bool),fun(fun(U_890,bool),bool),ord_less_eq(fun(U_890,bool)),U_887),U_888))
      | ~ hBOOL(hAPP(fun(U_890,bool),bool,finite_finite(U_890),U_887)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_885,sK22(U_890,U_889,U_888,U_887))],[f_252_3]) ).

fof(f_252_5,plain,
    ( ! [U_889,U_887,U_888,U_890] :
        ( ~ hBOOL(hAPP(fun(U_890,bool),bool,U_889,hAPP(fun(U_890,bool),fun(U_890,bool),hAPP(U_890,fun(fun(U_890,bool),fun(U_890,bool)),insert(U_890),sK21(U_890,U_889,U_888,U_887)),sK22(U_890,U_889,U_888,U_887))))
        | ~ sP38(U_889,U_887,U_888,U_890) )
    & ! [U_889,U_887,U_888,U_890] :
        ( hBOOL(hAPP(fun(U_890,bool),bool,U_889,sK22(U_890,U_889,U_888,U_887)))
        | ~ sP38(U_889,U_887,U_888,U_890) )
    & ! [U_889,U_887,U_888,U_890] :
        ( ~ hBOOL(hAPP(fun(U_890,bool),bool,hAPP(U_890,fun(fun(U_890,bool),bool),member(U_890),sK21(U_890,U_889,U_888,U_887)),sK22(U_890,U_889,U_888,U_887)))
        | ~ sP38(U_889,U_887,U_888,U_890) )
    & ! [U_889,U_887,U_888,U_890] :
        ( hBOOL(hAPP(fun(U_890,bool),bool,hAPP(U_890,fun(fun(U_890,bool),bool),member(U_890),sK21(U_890,U_889,U_888,U_887)),U_888))
        | ~ sP38(U_889,U_887,U_888,U_890) )
    & ! [U_889,U_887,U_888,U_890] :
        ( hBOOL(hAPP(fun(U_890,bool),bool,finite_finite(U_890),sK22(U_890,U_889,U_888,U_887)))
        | ~ sP38(U_889,U_887,U_888,U_890) )
    & ! [U_889,U_887,U_888,U_890] :
        ( hBOOL(hAPP(fun(U_890,bool),bool,U_889,U_887))
        | sP38(U_889,U_887,U_888,U_890)
        | ~ hBOOL(hAPP(fun(U_890,bool),bool,U_889,bot_bot(fun(U_890,bool))))
        | ~ hBOOL(hAPP(fun(U_890,bool),bool,hAPP(fun(U_890,bool),fun(fun(U_890,bool),bool),ord_less_eq(fun(U_890,bool)),U_887),U_888))
        | ~ hBOOL(hAPP(fun(U_890,bool),bool,finite_finite(U_890),U_887)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP38])],[f_252_4]) ).

cnf(f_252_6,plain,
    ( hBOOL(hAPP(fun(U_890,bool),bool,U_889,U_887))
    | sP38(U_889,U_887,U_888,U_890)
    | ~ hBOOL(hAPP(fun(U_890,bool),bool,U_889,bot_bot(fun(U_890,bool))))
    | ~ hBOOL(hAPP(fun(U_890,bool),bool,hAPP(fun(U_890,bool),fun(fun(U_890,bool),bool),ord_less_eq(fun(U_890,bool)),U_887),U_888))
    | ~ hBOOL(hAPP(fun(U_890,bool),bool,finite_finite(U_890),U_887)) ),
    inference(clausify,[status(thm)],[f_252_5]) ).

cnf(f_252_7,plain,
    ( hBOOL(hAPP(fun(U_890,bool),bool,finite_finite(U_890),sK22(U_890,U_889,U_888,U_887)))
    | ~ sP38(U_889,U_887,U_888,U_890) ),
    inference(clausify,[status(thm)],[f_252_5]) ).

cnf(f_252_8,plain,
    ( hBOOL(hAPP(fun(U_890,bool),bool,hAPP(U_890,fun(fun(U_890,bool),bool),member(U_890),sK21(U_890,U_889,U_888,U_887)),U_888))
    | ~ sP38(U_889,U_887,U_888,U_890) ),
    inference(clausify,[status(thm)],[f_252_5]) ).

cnf(f_252_9,plain,
    ( ~ hBOOL(hAPP(fun(U_890,bool),bool,hAPP(U_890,fun(fun(U_890,bool),bool),member(U_890),sK21(U_890,U_889,U_888,U_887)),sK22(U_890,U_889,U_888,U_887)))
    | ~ sP38(U_889,U_887,U_888,U_890) ),
    inference(clausify,[status(thm)],[f_252_5]) ).

cnf(f_252_10,plain,
    ( hBOOL(hAPP(fun(U_890,bool),bool,U_889,sK22(U_890,U_889,U_888,U_887)))
    | ~ sP38(U_889,U_887,U_888,U_890) ),
    inference(clausify,[status(thm)],[f_252_5]) ).

cnf(f_252_11,plain,
    ( ~ hBOOL(hAPP(fun(U_890,bool),bool,U_889,hAPP(fun(U_890,bool),fun(U_890,bool),hAPP(U_890,fun(fun(U_890,bool),fun(U_890,bool)),insert(U_890),sK21(U_890,U_889,U_888,U_887)),sK22(U_890,U_889,U_888,U_887))))
    | ~ sP38(U_889,U_887,U_888,U_890) ),
    inference(clausify,[status(thm)],[f_252_5]) ).

fof(f_253_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_182_assms_I2_J]) ).

fof(f_253_2,plain,
    ! [U_892,U_891] :
      ( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,U_891),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_892)),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_892)),U_891)),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_892)))),bot_bot(fun(x_a,bool))))) ),
    inference(variable_rename,[status(thm)],[f_253_1]) ).

fof(f_253_3,plain,
    ! [U_892,U_891] :
      ( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,U_891),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_892)),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_892)),U_891)),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_892)))),bot_bot(fun(x_a,bool))))) ),
    inference(definitional_conversion,[status(esa)],[f_253_2]) ).

cnf(f_253_4,plain,
    ( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,U_891),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_892)),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_892)),U_891)),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_892)))),bot_bot(fun(x_a,bool))))) ),
    inference(clausify,[status(thm)],[f_253_3]) ).

fof(f_254_1,plain,
    ! [X_b,Pa,A_3] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,Pa,bot_bot(fun(X_b,bool))))
      | ? [A_4,A_5] :
          ( ~ 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_5),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_4),bot_bot(fun(X_b,bool))))))
          & hBOOL(hAPP(fun(X_b,bool),bool,Pa,A_5))
          & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_4),A_5))
          & hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_5)) )
      | ~ 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_183_finite__empty__induct]) ).

fof(f_254_2,plain,
    ! [U_897,U_896,U_895] :
      ( hBOOL(hAPP(fun(U_897,bool),bool,U_896,bot_bot(fun(U_897,bool))))
      | ? [U_894,U_893] :
          ( ~ hBOOL(hAPP(fun(U_897,bool),bool,U_896,hAPP(fun(U_897,bool),fun(U_897,bool),hAPP(fun(U_897,bool),fun(fun(U_897,bool),fun(U_897,bool)),minus_minus(fun(U_897,bool)),U_893),hAPP(fun(U_897,bool),fun(U_897,bool),hAPP(U_897,fun(fun(U_897,bool),fun(U_897,bool)),insert(U_897),U_894),bot_bot(fun(U_897,bool))))))
          & hBOOL(hAPP(fun(U_897,bool),bool,U_896,U_893))
          & hBOOL(hAPP(fun(U_897,bool),bool,hAPP(U_897,fun(fun(U_897,bool),bool),member(U_897),U_894),U_893))
          & hBOOL(hAPP(fun(U_897,bool),bool,finite_finite(U_897),U_893)) )
      | ~ hBOOL(hAPP(fun(U_897,bool),bool,U_896,U_895))
      | ~ hBOOL(hAPP(fun(U_897,bool),bool,finite_finite(U_897),U_895)) ),
    inference(variable_rename,[status(thm)],[f_254_1]) ).

fof(f_254_3,plain,
    ! [U_897,U_896,U_895] :
      ( hBOOL(hAPP(fun(U_897,bool),bool,U_896,bot_bot(fun(U_897,bool))))
      | ? [U_893] :
          ( ~ hBOOL(hAPP(fun(U_897,bool),bool,U_896,hAPP(fun(U_897,bool),fun(U_897,bool),hAPP(fun(U_897,bool),fun(fun(U_897,bool),fun(U_897,bool)),minus_minus(fun(U_897,bool)),U_893),hAPP(fun(U_897,bool),fun(U_897,bool),hAPP(U_897,fun(fun(U_897,bool),fun(U_897,bool)),insert(U_897),sK23(U_897,U_896,U_895)),bot_bot(fun(U_897,bool))))))
          & hBOOL(hAPP(fun(U_897,bool),bool,U_896,U_893))
          & hBOOL(hAPP(fun(U_897,bool),bool,hAPP(U_897,fun(fun(U_897,bool),bool),member(U_897),sK23(U_897,U_896,U_895)),U_893))
          & hBOOL(hAPP(fun(U_897,bool),bool,finite_finite(U_897),U_893)) )
      | ~ hBOOL(hAPP(fun(U_897,bool),bool,U_896,U_895))
      | ~ hBOOL(hAPP(fun(U_897,bool),bool,finite_finite(U_897),U_895)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_894,sK23(U_897,U_896,U_895))],[f_254_2]) ).

fof(f_254_4,plain,
    ! [U_897,U_896,U_895] :
      ( hBOOL(hAPP(fun(U_897,bool),bool,U_896,bot_bot(fun(U_897,bool))))
      | ( ~ hBOOL(hAPP(fun(U_897,bool),bool,U_896,hAPP(fun(U_897,bool),fun(U_897,bool),hAPP(fun(U_897,bool),fun(fun(U_897,bool),fun(U_897,bool)),minus_minus(fun(U_897,bool)),sK24(U_897,U_896,U_895)),hAPP(fun(U_897,bool),fun(U_897,bool),hAPP(U_897,fun(fun(U_897,bool),fun(U_897,bool)),insert(U_897),sK23(U_897,U_896,U_895)),bot_bot(fun(U_897,bool))))))
        & hBOOL(hAPP(fun(U_897,bool),bool,U_896,sK24(U_897,U_896,U_895)))
        & hBOOL(hAPP(fun(U_897,bool),bool,hAPP(U_897,fun(fun(U_897,bool),bool),member(U_897),sK23(U_897,U_896,U_895)),sK24(U_897,U_896,U_895)))
        & hBOOL(hAPP(fun(U_897,bool),bool,finite_finite(U_897),sK24(U_897,U_896,U_895))) )
      | ~ hBOOL(hAPP(fun(U_897,bool),bool,U_896,U_895))
      | ~ hBOOL(hAPP(fun(U_897,bool),bool,finite_finite(U_897),U_895)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_893,sK24(U_897,U_896,U_895))],[f_254_3]) ).

fof(f_254_5,plain,
    ( ! [U_895,U_897,U_896] :
        ( ~ hBOOL(hAPP(fun(U_897,bool),bool,U_896,hAPP(fun(U_897,bool),fun(U_897,bool),hAPP(fun(U_897,bool),fun(fun(U_897,bool),fun(U_897,bool)),minus_minus(fun(U_897,bool)),sK24(U_897,U_896,U_895)),hAPP(fun(U_897,bool),fun(U_897,bool),hAPP(U_897,fun(fun(U_897,bool),fun(U_897,bool)),insert(U_897),sK23(U_897,U_896,U_895)),bot_bot(fun(U_897,bool))))))
        | ~ sP39(U_895,U_897,U_896) )
    & ! [U_895,U_897,U_896] :
        ( hBOOL(hAPP(fun(U_897,bool),bool,U_896,sK24(U_897,U_896,U_895)))
        | ~ sP39(U_895,U_897,U_896) )
    & ! [U_895,U_897,U_896] :
        ( hBOOL(hAPP(fun(U_897,bool),bool,hAPP(U_897,fun(fun(U_897,bool),bool),member(U_897),sK23(U_897,U_896,U_895)),sK24(U_897,U_896,U_895)))
        | ~ sP39(U_895,U_897,U_896) )
    & ! [U_895,U_897,U_896] :
        ( hBOOL(hAPP(fun(U_897,bool),bool,finite_finite(U_897),sK24(U_897,U_896,U_895)))
        | ~ sP39(U_895,U_897,U_896) )
    & ! [U_895,U_897,U_896] :
        ( hBOOL(hAPP(fun(U_897,bool),bool,U_896,bot_bot(fun(U_897,bool))))
        | sP39(U_895,U_897,U_896)
        | ~ hBOOL(hAPP(fun(U_897,bool),bool,U_896,U_895))
        | ~ hBOOL(hAPP(fun(U_897,bool),bool,finite_finite(U_897),U_895)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP39])],[f_254_4]) ).

cnf(f_254_6,plain,
    ( hBOOL(hAPP(fun(U_897,bool),bool,U_896,bot_bot(fun(U_897,bool))))
    | sP39(U_895,U_897,U_896)
    | ~ hBOOL(hAPP(fun(U_897,bool),bool,U_896,U_895))
    | ~ hBOOL(hAPP(fun(U_897,bool),bool,finite_finite(U_897),U_895)) ),
    inference(clausify,[status(thm)],[f_254_5]) ).

cnf(f_254_7,plain,
    ( hBOOL(hAPP(fun(U_897,bool),bool,finite_finite(U_897),sK24(U_897,U_896,U_895)))
    | ~ sP39(U_895,U_897,U_896) ),
    inference(clausify,[status(thm)],[f_254_5]) ).

cnf(f_254_8,plain,
    ( hBOOL(hAPP(fun(U_897,bool),bool,hAPP(U_897,fun(fun(U_897,bool),bool),member(U_897),sK23(U_897,U_896,U_895)),sK24(U_897,U_896,U_895)))
    | ~ sP39(U_895,U_897,U_896) ),
    inference(clausify,[status(thm)],[f_254_5]) ).

cnf(f_254_9,plain,
    ( hBOOL(hAPP(fun(U_897,bool),bool,U_896,sK24(U_897,U_896,U_895)))
    | ~ sP39(U_895,U_897,U_896) ),
    inference(clausify,[status(thm)],[f_254_5]) ).

cnf(f_254_10,plain,
    ( ~ hBOOL(hAPP(fun(U_897,bool),bool,U_896,hAPP(fun(U_897,bool),fun(U_897,bool),hAPP(fun(U_897,bool),fun(fun(U_897,bool),fun(U_897,bool)),minus_minus(fun(U_897,bool)),sK24(U_897,U_896,U_895)),hAPP(fun(U_897,bool),fun(U_897,bool),hAPP(U_897,fun(fun(U_897,bool),fun(U_897,bool)),insert(U_897),sK23(U_897,U_896,U_895)),bot_bot(fun(U_897,bool))))))
    | ~ sP39(U_895,U_897,U_896) ),
    inference(clausify,[status(thm)],[f_254_5]) ).

fof(f_255_1,plain,
    ! [X_b,Pa,F_1] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_1))
      | ? [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_1)) ),
    inference(fof_nnf,[status(thm)],[fact_184_finite__induct]) ).

fof(f_255_2,plain,
    ! [U_902,U_901,U_900] :
      ( hBOOL(hAPP(fun(U_902,bool),bool,U_901,U_900))
      | ? [U_899,U_898] :
          ( ~ hBOOL(hAPP(fun(U_902,bool),bool,U_901,hAPP(fun(U_902,bool),fun(U_902,bool),hAPP(U_902,fun(fun(U_902,bool),fun(U_902,bool)),insert(U_902),U_899),U_898)))
          & hBOOL(hAPP(fun(U_902,bool),bool,U_901,U_898))
          & ~ hBOOL(hAPP(fun(U_902,bool),bool,hAPP(U_902,fun(fun(U_902,bool),bool),member(U_902),U_899),U_898))
          & hBOOL(hAPP(fun(U_902,bool),bool,finite_finite(U_902),U_898)) )
      | ~ hBOOL(hAPP(fun(U_902,bool),bool,U_901,bot_bot(fun(U_902,bool))))
      | ~ hBOOL(hAPP(fun(U_902,bool),bool,finite_finite(U_902),U_900)) ),
    inference(variable_rename,[status(thm)],[f_255_1]) ).

fof(f_255_3,plain,
    ! [U_902,U_901,U_900] :
      ( hBOOL(hAPP(fun(U_902,bool),bool,U_901,U_900))
      | ? [U_898] :
          ( ~ hBOOL(hAPP(fun(U_902,bool),bool,U_901,hAPP(fun(U_902,bool),fun(U_902,bool),hAPP(U_902,fun(fun(U_902,bool),fun(U_902,bool)),insert(U_902),sK25(U_902,U_901,U_900)),U_898)))
          & hBOOL(hAPP(fun(U_902,bool),bool,U_901,U_898))
          & ~ hBOOL(hAPP(fun(U_902,bool),bool,hAPP(U_902,fun(fun(U_902,bool),bool),member(U_902),sK25(U_902,U_901,U_900)),U_898))
          & hBOOL(hAPP(fun(U_902,bool),bool,finite_finite(U_902),U_898)) )
      | ~ hBOOL(hAPP(fun(U_902,bool),bool,U_901,bot_bot(fun(U_902,bool))))
      | ~ hBOOL(hAPP(fun(U_902,bool),bool,finite_finite(U_902),U_900)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_899,sK25(U_902,U_901,U_900))],[f_255_2]) ).

fof(f_255_4,plain,
    ! [U_902,U_901,U_900] :
      ( hBOOL(hAPP(fun(U_902,bool),bool,U_901,U_900))
      | ( ~ hBOOL(hAPP(fun(U_902,bool),bool,U_901,hAPP(fun(U_902,bool),fun(U_902,bool),hAPP(U_902,fun(fun(U_902,bool),fun(U_902,bool)),insert(U_902),sK25(U_902,U_901,U_900)),sK26(U_902,U_901,U_900))))
        & hBOOL(hAPP(fun(U_902,bool),bool,U_901,sK26(U_902,U_901,U_900)))
        & ~ hBOOL(hAPP(fun(U_902,bool),bool,hAPP(U_902,fun(fun(U_902,bool),bool),member(U_902),sK25(U_902,U_901,U_900)),sK26(U_902,U_901,U_900)))
        & hBOOL(hAPP(fun(U_902,bool),bool,finite_finite(U_902),sK26(U_902,U_901,U_900))) )
      | ~ hBOOL(hAPP(fun(U_902,bool),bool,U_901,bot_bot(fun(U_902,bool))))
      | ~ hBOOL(hAPP(fun(U_902,bool),bool,finite_finite(U_902),U_900)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_898,sK26(U_902,U_901,U_900))],[f_255_3]) ).

fof(f_255_5,plain,
    ( ! [U_901,U_902,U_900] :
        ( ~ hBOOL(hAPP(fun(U_902,bool),bool,U_901,hAPP(fun(U_902,bool),fun(U_902,bool),hAPP(U_902,fun(fun(U_902,bool),fun(U_902,bool)),insert(U_902),sK25(U_902,U_901,U_900)),sK26(U_902,U_901,U_900))))
        | ~ sP40(U_901,U_902,U_900) )
    & ! [U_901,U_902,U_900] :
        ( hBOOL(hAPP(fun(U_902,bool),bool,U_901,sK26(U_902,U_901,U_900)))
        | ~ sP40(U_901,U_902,U_900) )
    & ! [U_901,U_902,U_900] :
        ( ~ hBOOL(hAPP(fun(U_902,bool),bool,hAPP(U_902,fun(fun(U_902,bool),bool),member(U_902),sK25(U_902,U_901,U_900)),sK26(U_902,U_901,U_900)))
        | ~ sP40(U_901,U_902,U_900) )
    & ! [U_901,U_902,U_900] :
        ( hBOOL(hAPP(fun(U_902,bool),bool,finite_finite(U_902),sK26(U_902,U_901,U_900)))
        | ~ sP40(U_901,U_902,U_900) )
    & ! [U_901,U_902,U_900] :
        ( hBOOL(hAPP(fun(U_902,bool),bool,U_901,U_900))
        | sP40(U_901,U_902,U_900)
        | ~ hBOOL(hAPP(fun(U_902,bool),bool,U_901,bot_bot(fun(U_902,bool))))
        | ~ hBOOL(hAPP(fun(U_902,bool),bool,finite_finite(U_902),U_900)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP40])],[f_255_4]) ).

cnf(f_255_6,plain,
    ( hBOOL(hAPP(fun(U_902,bool),bool,U_901,U_900))
    | sP40(U_901,U_902,U_900)
    | ~ hBOOL(hAPP(fun(U_902,bool),bool,U_901,bot_bot(fun(U_902,bool))))
    | ~ hBOOL(hAPP(fun(U_902,bool),bool,finite_finite(U_902),U_900)) ),
    inference(clausify,[status(thm)],[f_255_5]) ).

cnf(f_255_7,plain,
    ( hBOOL(hAPP(fun(U_902,bool),bool,finite_finite(U_902),sK26(U_902,U_901,U_900)))
    | ~ sP40(U_901,U_902,U_900) ),
    inference(clausify,[status(thm)],[f_255_5]) ).

cnf(f_255_8,plain,
    ( ~ hBOOL(hAPP(fun(U_902,bool),bool,hAPP(U_902,fun(fun(U_902,bool),bool),member(U_902),sK25(U_902,U_901,U_900)),sK26(U_902,U_901,U_900)))
    | ~ sP40(U_901,U_902,U_900) ),
    inference(clausify,[status(thm)],[f_255_5]) ).

cnf(f_255_9,plain,
    ( hBOOL(hAPP(fun(U_902,bool),bool,U_901,sK26(U_902,U_901,U_900)))
    | ~ sP40(U_901,U_902,U_900) ),
    inference(clausify,[status(thm)],[f_255_5]) ).

cnf(f_255_10,plain,
    ( ~ hBOOL(hAPP(fun(U_902,bool),bool,U_901,hAPP(fun(U_902,bool),fun(U_902,bool),hAPP(U_902,fun(fun(U_902,bool),fun(U_902,bool)),insert(U_902),sK25(U_902,U_901,U_900)),sK26(U_902,U_901,U_900))))
    | ~ sP40(U_901,U_902,U_900) ),
    inference(clausify,[status(thm)],[f_255_5]) ).

fof(f_256_1,plain,
    ! [X_b,A_2] :
      ( ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_2))
        | ( ! [A_5,A_4] :
              ( ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_5))
              | 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_4),A_5) )
          & ti(fun(X_b,bool),A_2) != bot_bot(fun(X_b,bool)) ) )
      & ( ? [A_5,A_4] :
            ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_5))
            & 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_4),A_5) )
        | 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_185_finite_Osimps]) ).

fof(f_256_2,plain,
    ! [U_908,U_907] :
      ( ( hBOOL(hAPP(fun(U_908,bool),bool,finite_finite(U_908),U_907))
        | ( ! [U_906,U_905] :
              ( ~ hBOOL(hAPP(fun(U_908,bool),bool,finite_finite(U_908),U_906))
              | ti(fun(U_908,bool),U_907) != hAPP(fun(U_908,bool),fun(U_908,bool),hAPP(U_908,fun(fun(U_908,bool),fun(U_908,bool)),insert(U_908),U_905),U_906) )
          & ti(fun(U_908,bool),U_907) != bot_bot(fun(U_908,bool)) ) )
      & ( ? [U_904,U_903] :
            ( hBOOL(hAPP(fun(U_908,bool),bool,finite_finite(U_908),U_904))
            & ti(fun(U_908,bool),U_907) = hAPP(fun(U_908,bool),fun(U_908,bool),hAPP(U_908,fun(fun(U_908,bool),fun(U_908,bool)),insert(U_908),U_903),U_904) )
        | ti(fun(U_908,bool),U_907) = bot_bot(fun(U_908,bool))
        | ~ hBOOL(hAPP(fun(U_908,bool),bool,finite_finite(U_908),U_907)) ) ),
    inference(variable_rename,[status(thm)],[f_256_1]) ).

fof(f_256_3,plain,
    ( ! [U_912,U_910] :
        ( hBOOL(hAPP(fun(U_912,bool),bool,finite_finite(U_912),U_910))
        | ( ! [U_906] :
              ( ! [U_905] : ti(fun(U_912,bool),U_910) != hAPP(fun(U_912,bool),fun(U_912,bool),hAPP(U_912,fun(fun(U_912,bool),fun(U_912,bool)),insert(U_912),U_905),U_906)
              | ~ hBOOL(hAPP(fun(U_912,bool),bool,finite_finite(U_912),U_906)) )
          & ti(fun(U_912,bool),U_910) != bot_bot(fun(U_912,bool)) ) )
    & ! [U_911,U_909] :
        ( ? [U_904] :
            ( ? [U_903] : ti(fun(U_911,bool),U_909) = hAPP(fun(U_911,bool),fun(U_911,bool),hAPP(U_911,fun(fun(U_911,bool),fun(U_911,bool)),insert(U_911),U_903),U_904)
            & hBOOL(hAPP(fun(U_911,bool),bool,finite_finite(U_911),U_904)) )
        | ti(fun(U_911,bool),U_909) = bot_bot(fun(U_911,bool))
        | ~ hBOOL(hAPP(fun(U_911,bool),bool,finite_finite(U_911),U_909)) ) ),
    inference(miniscope,[status(thm)],[f_256_2]) ).

fof(f_256_4,plain,
    ( ! [U_912,U_910] :
        ( hBOOL(hAPP(fun(U_912,bool),bool,finite_finite(U_912),U_910))
        | ( ! [U_906] :
              ( ! [U_905] : ti(fun(U_912,bool),U_910) != hAPP(fun(U_912,bool),fun(U_912,bool),hAPP(U_912,fun(fun(U_912,bool),fun(U_912,bool)),insert(U_912),U_905),U_906)
              | ~ hBOOL(hAPP(fun(U_912,bool),bool,finite_finite(U_912),U_906)) )
          & ti(fun(U_912,bool),U_910) != bot_bot(fun(U_912,bool)) ) )
    & ! [U_911,U_909] :
        ( ( ? [U_903] : ti(fun(U_911,bool),U_909) = hAPP(fun(U_911,bool),fun(U_911,bool),hAPP(U_911,fun(fun(U_911,bool),fun(U_911,bool)),insert(U_911),U_903),sK27(U_911,U_909))
          & hBOOL(hAPP(fun(U_911,bool),bool,finite_finite(U_911),sK27(U_911,U_909))) )
        | ti(fun(U_911,bool),U_909) = bot_bot(fun(U_911,bool))
        | ~ hBOOL(hAPP(fun(U_911,bool),bool,finite_finite(U_911),U_909)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_904,sK27(U_911,U_909))],[f_256_3]) ).

fof(f_256_5,plain,
    ( ! [U_912,U_910] :
        ( hBOOL(hAPP(fun(U_912,bool),bool,finite_finite(U_912),U_910))
        | ( ! [U_906] :
              ( ! [U_905] : ti(fun(U_912,bool),U_910) != hAPP(fun(U_912,bool),fun(U_912,bool),hAPP(U_912,fun(fun(U_912,bool),fun(U_912,bool)),insert(U_912),U_905),U_906)
              | ~ hBOOL(hAPP(fun(U_912,bool),bool,finite_finite(U_912),U_906)) )
          & ti(fun(U_912,bool),U_910) != bot_bot(fun(U_912,bool)) ) )
    & ! [U_911,U_909] :
        ( ( ti(fun(U_911,bool),U_909) = hAPP(fun(U_911,bool),fun(U_911,bool),hAPP(U_911,fun(fun(U_911,bool),fun(U_911,bool)),insert(U_911),sK28(U_911,U_909)),sK27(U_911,U_909))
          & hBOOL(hAPP(fun(U_911,bool),bool,finite_finite(U_911),sK27(U_911,U_909))) )
        | ti(fun(U_911,bool),U_909) = bot_bot(fun(U_911,bool))
        | ~ hBOOL(hAPP(fun(U_911,bool),bool,finite_finite(U_911),U_909)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_903,sK28(U_911,U_909))],[f_256_4]) ).

fof(f_256_6,plain,
    ( ! [U_905,U_910,U_906,U_912] :
        ( ti(fun(U_912,bool),U_910) != hAPP(fun(U_912,bool),fun(U_912,bool),hAPP(U_912,fun(fun(U_912,bool),fun(U_912,bool)),insert(U_912),U_905),U_906)
        | ~ hBOOL(hAPP(fun(U_912,bool),bool,finite_finite(U_912),U_906))
        | ~ sP42(U_905,U_910,U_906,U_912) )
    & ! [U_905,U_910,U_906,U_912] :
        ( ti(fun(U_912,bool),U_910) != bot_bot(fun(U_912,bool))
        | ~ sP42(U_905,U_910,U_906,U_912) )
    & ! [U_909,U_911] :
        ( ti(fun(U_911,bool),U_909) = hAPP(fun(U_911,bool),fun(U_911,bool),hAPP(U_911,fun(fun(U_911,bool),fun(U_911,bool)),insert(U_911),sK28(U_911,U_909)),sK27(U_911,U_909))
        | ~ sP41(U_909,U_911) )
    & ! [U_909,U_911] :
        ( hBOOL(hAPP(fun(U_911,bool),bool,finite_finite(U_911),sK27(U_911,U_909)))
        | ~ sP41(U_909,U_911) )
    & ! [U_905,U_910,U_906,U_912] :
        ( hBOOL(hAPP(fun(U_912,bool),bool,finite_finite(U_912),U_910))
        | sP42(U_905,U_910,U_906,U_912) )
    & ! [U_909,U_911] :
        ( sP41(U_909,U_911)
        | ti(fun(U_911,bool),U_909) = bot_bot(fun(U_911,bool))
        | ~ hBOOL(hAPP(fun(U_911,bool),bool,finite_finite(U_911),U_909)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP41,sP42])],[f_256_5]) ).

cnf(f_256_7,plain,
    ( sP41(U_909,U_911)
    | ti(fun(U_911,bool),U_909) = bot_bot(fun(U_911,bool))
    | ~ hBOOL(hAPP(fun(U_911,bool),bool,finite_finite(U_911),U_909)) ),
    inference(clausify,[status(thm)],[f_256_6]) ).

cnf(f_256_8,plain,
    ( hBOOL(hAPP(fun(U_912,bool),bool,finite_finite(U_912),U_910))
    | sP42(U_905,U_910,U_906,U_912) ),
    inference(clausify,[status(thm)],[f_256_6]) ).

cnf(f_256_9,plain,
    ( hBOOL(hAPP(fun(U_911,bool),bool,finite_finite(U_911),sK27(U_911,U_909)))
    | ~ sP41(U_909,U_911) ),
    inference(clausify,[status(thm)],[f_256_6]) ).

cnf(f_256_10,plain,
    ( ti(fun(U_911,bool),U_909) = hAPP(fun(U_911,bool),fun(U_911,bool),hAPP(U_911,fun(fun(U_911,bool),fun(U_911,bool)),insert(U_911),sK28(U_911,U_909)),sK27(U_911,U_909))
    | ~ sP41(U_909,U_911) ),
    inference(clausify,[status(thm)],[f_256_6]) ).

cnf(f_256_11,plain,
    ( ti(fun(U_912,bool),U_910) != bot_bot(fun(U_912,bool))
    | ~ sP42(U_905,U_910,U_906,U_912) ),
    inference(clausify,[status(thm)],[f_256_6]) ).

cnf(f_256_12,plain,
    ( ti(fun(U_912,bool),U_910) != hAPP(fun(U_912,bool),fun(U_912,bool),hAPP(U_912,fun(fun(U_912,bool),fun(U_912,bool)),insert(U_912),U_905),U_906)
    | ~ hBOOL(hAPP(fun(U_912,bool),bool,finite_finite(U_912),U_906))
    | ~ sP42(U_905,U_910,U_906,U_912) ),
    inference(clausify,[status(thm)],[f_256_6]) ).

fof(f_257_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_1] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),hAPP(nat,nat,F,N_1))) ),
    inference(fof_nnf,[status(thm)],[fact_186_finite__less__ub]) ).

fof(f_257_2,plain,
    ! [U_915,U_914] :
      ( 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_914)),U_915))))
      | ? [U_913] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_913),hAPP(nat,nat,U_914,U_913))) ),
    inference(variable_rename,[status(thm)],[f_257_1]) ).

fof(f_257_3,plain,
    ! [U_915,U_914] :
      ( 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_914)),U_915))))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sK29(U_915,U_914)),hAPP(nat,nat,U_914,sK29(U_915,U_914)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_913,sK29(U_915,U_914))],[f_257_2]) ).

fof(f_257_4,plain,
    ! [U_915,U_914] :
      ( 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_914)),U_915))))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sK29(U_915,U_914)),hAPP(nat,nat,U_914,sK29(U_915,U_914)))) ),
    inference(definitional_conversion,[status(esa)],[f_257_3]) ).

cnf(f_257_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_914)),U_915))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sK29(U_915,U_914)),hAPP(nat,nat,U_914,sK29(U_915,U_914)))) ),
    inference(clausify,[status(thm)],[f_257_4]) ).

fof(f_258_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_187_the__elem__eq]) ).

fof(f_258_2,plain,
    ! [U_917,U_916] : hAPP(fun(U_917,bool),U_917,the_elem(U_917),hAPP(fun(U_917,bool),fun(U_917,bool),hAPP(U_917,fun(fun(U_917,bool),fun(U_917,bool)),insert(U_917),U_916),bot_bot(fun(U_917,bool)))) = ti(U_917,U_916),
    inference(variable_rename,[status(thm)],[f_258_1]) ).

fof(f_258_3,plain,
    ! [U_917,U_916] : hAPP(fun(U_917,bool),U_917,the_elem(U_917),hAPP(fun(U_917,bool),fun(U_917,bool),hAPP(U_917,fun(fun(U_917,bool),fun(U_917,bool)),insert(U_917),U_916),bot_bot(fun(U_917,bool)))) = ti(U_917,U_916),
    inference(definitional_conversion,[status(esa)],[f_258_2]) ).

cnf(f_258_4,plain,
    hAPP(fun(U_917,bool),U_917,the_elem(U_917),hAPP(fun(U_917,bool),fun(U_917,bool),hAPP(U_917,fun(fun(U_917,bool),fun(U_917,bool)),insert(U_917),U_916),bot_bot(fun(U_917,bool)))) = ti(U_917,U_916),
    inference(clausify,[status(thm)],[f_258_3]) ).

fof(f_259_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_188_nonempty__iff]) ).

fof(f_259_2,plain,
    ! [U_923,U_922] :
      ( ( ti(fun(U_923,bool),U_922) != bot_bot(fun(U_923,bool))
        | ! [U_921,U_920] :
            ( hBOOL(hAPP(fun(U_923,bool),bool,hAPP(U_923,fun(fun(U_923,bool),bool),member(U_923),U_921),U_920))
            | ti(fun(U_923,bool),U_922) != hAPP(fun(U_923,bool),fun(U_923,bool),hAPP(U_923,fun(fun(U_923,bool),fun(U_923,bool)),insert(U_923),U_921),U_920) ) )
      & ( ? [U_919,U_918] :
            ( ~ hBOOL(hAPP(fun(U_923,bool),bool,hAPP(U_923,fun(fun(U_923,bool),bool),member(U_923),U_919),U_918))
            & ti(fun(U_923,bool),U_922) = hAPP(fun(U_923,bool),fun(U_923,bool),hAPP(U_923,fun(fun(U_923,bool),fun(U_923,bool)),insert(U_923),U_919),U_918) )
        | ti(fun(U_923,bool),U_922) = bot_bot(fun(U_923,bool)) ) ),
    inference(variable_rename,[status(thm)],[f_259_1]) ).

fof(f_259_3,plain,
    ( ! [U_927,U_925] :
        ( ti(fun(U_927,bool),U_925) != bot_bot(fun(U_927,bool))
        | ! [U_921,U_920] :
            ( hBOOL(hAPP(fun(U_927,bool),bool,hAPP(U_927,fun(fun(U_927,bool),bool),member(U_927),U_921),U_920))
            | ti(fun(U_927,bool),U_925) != hAPP(fun(U_927,bool),fun(U_927,bool),hAPP(U_927,fun(fun(U_927,bool),fun(U_927,bool)),insert(U_927),U_921),U_920) ) )
    & ! [U_926,U_924] :
        ( ? [U_919,U_918] :
            ( ~ hBOOL(hAPP(fun(U_926,bool),bool,hAPP(U_926,fun(fun(U_926,bool),bool),member(U_926),U_919),U_918))
            & ti(fun(U_926,bool),U_924) = 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_919),U_918) )
        | ti(fun(U_926,bool),U_924) = bot_bot(fun(U_926,bool)) ) ),
    inference(miniscope,[status(thm)],[f_259_2]) ).

fof(f_259_4,plain,
    ( ! [U_927,U_925] :
        ( ti(fun(U_927,bool),U_925) != bot_bot(fun(U_927,bool))
        | ! [U_921,U_920] :
            ( hBOOL(hAPP(fun(U_927,bool),bool,hAPP(U_927,fun(fun(U_927,bool),bool),member(U_927),U_921),U_920))
            | ti(fun(U_927,bool),U_925) != hAPP(fun(U_927,bool),fun(U_927,bool),hAPP(U_927,fun(fun(U_927,bool),fun(U_927,bool)),insert(U_927),U_921),U_920) ) )
    & ! [U_926,U_924] :
        ( ? [U_918] :
            ( ~ hBOOL(hAPP(fun(U_926,bool),bool,hAPP(U_926,fun(fun(U_926,bool),bool),member(U_926),sK30(U_926,U_924)),U_918))
            & ti(fun(U_926,bool),U_924) = hAPP(fun(U_926,bool),fun(U_926,bool),hAPP(U_926,fun(fun(U_926,bool),fun(U_926,bool)),insert(U_926),sK30(U_926,U_924)),U_918) )
        | ti(fun(U_926,bool),U_924) = bot_bot(fun(U_926,bool)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_919,sK30(U_926,U_924))],[f_259_3]) ).

fof(f_259_5,plain,
    ( ! [U_927,U_925] :
        ( ti(fun(U_927,bool),U_925) != bot_bot(fun(U_927,bool))
        | ! [U_921,U_920] :
            ( hBOOL(hAPP(fun(U_927,bool),bool,hAPP(U_927,fun(fun(U_927,bool),bool),member(U_927),U_921),U_920))
            | ti(fun(U_927,bool),U_925) != hAPP(fun(U_927,bool),fun(U_927,bool),hAPP(U_927,fun(fun(U_927,bool),fun(U_927,bool)),insert(U_927),U_921),U_920) ) )
    & ! [U_926,U_924] :
        ( ( ~ hBOOL(hAPP(fun(U_926,bool),bool,hAPP(U_926,fun(fun(U_926,bool),bool),member(U_926),sK30(U_926,U_924)),sK31(U_926,U_924)))
          & ti(fun(U_926,bool),U_924) = hAPP(fun(U_926,bool),fun(U_926,bool),hAPP(U_926,fun(fun(U_926,bool),fun(U_926,bool)),insert(U_926),sK30(U_926,U_924)),sK31(U_926,U_924)) )
        | ti(fun(U_926,bool),U_924) = bot_bot(fun(U_926,bool)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(U_918,sK31(U_926,U_924))],[f_259_4]) ).

fof(f_259_6,plain,
    ( ! [U_924,U_926] :
        ( ~ hBOOL(hAPP(fun(U_926,bool),bool,hAPP(U_926,fun(fun(U_926,bool),bool),member(U_926),sK30(U_926,U_924)),sK31(U_926,U_924)))
        | ~ sP43(U_924,U_926) )
    & ! [U_924,U_926] :
        ( ti(fun(U_926,bool),U_924) = hAPP(fun(U_926,bool),fun(U_926,bool),hAPP(U_926,fun(fun(U_926,bool),fun(U_926,bool)),insert(U_926),sK30(U_926,U_924)),sK31(U_926,U_924))
        | ~ sP43(U_924,U_926) )
    & ! [U_920,U_921,U_925,U_927] :
        ( ti(fun(U_927,bool),U_925) != bot_bot(fun(U_927,bool))
        | hBOOL(hAPP(fun(U_927,bool),bool,hAPP(U_927,fun(fun(U_927,bool),bool),member(U_927),U_921),U_920))
        | ti(fun(U_927,bool),U_925) != hAPP(fun(U_927,bool),fun(U_927,bool),hAPP(U_927,fun(fun(U_927,bool),fun(U_927,bool)),insert(U_927),U_921),U_920) )
    & ! [U_924,U_926] :
        ( sP43(U_924,U_926)
        | ti(fun(U_926,bool),U_924) = bot_bot(fun(U_926,bool)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP43])],[f_259_5]) ).

cnf(f_259_7,plain,
    ( sP43(U_924,U_926)
    | ti(fun(U_926,bool),U_924) = bot_bot(fun(U_926,bool)) ),
    inference(clausify,[status(thm)],[f_259_6]) ).

cnf(f_259_8,plain,
    ( ti(fun(U_927,bool),U_925) != bot_bot(fun(U_927,bool))
    | hBOOL(hAPP(fun(U_927,bool),bool,hAPP(U_927,fun(fun(U_927,bool),bool),member(U_927),U_921),U_920))
    | ti(fun(U_927,bool),U_925) != hAPP(fun(U_927,bool),fun(U_927,bool),hAPP(U_927,fun(fun(U_927,bool),fun(U_927,bool)),insert(U_927),U_921),U_920) ),
    inference(clausify,[status(thm)],[f_259_6]) ).

cnf(f_259_9,plain,
    ( ti(fun(U_926,bool),U_924) = hAPP(fun(U_926,bool),fun(U_926,bool),hAPP(U_926,fun(fun(U_926,bool),fun(U_926,bool)),insert(U_926),sK30(U_926,U_924)),sK31(U_926,U_924))
    | ~ sP43(U_924,U_926) ),
    inference(clausify,[status(thm)],[f_259_6]) ).

cnf(f_259_10,plain,
    ( ~ hBOOL(hAPP(fun(U_926,bool),bool,hAPP(U_926,fun(fun(U_926,bool),bool),member(U_926),sK30(U_926,U_924)),sK31(U_926,U_924)))
    | ~ sP43(U_924,U_926) ),
    inference(clausify,[status(thm)],[f_259_6]) ).

fof(f_260_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_189_assms_I4_J]) ).

fof(f_260_2,plain,
    ! [U_928] :
      ( hBOOL(hAPP(com,bool,wt,hAPP(option(com),com,the_1(com),hAPP(pname,option(com),body,U_928))))
      | ~ hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),U_928),u)) ),
    inference(variable_rename,[status(thm)],[f_260_1]) ).

fof(f_260_3,plain,
    ! [U_928] :
      ( hBOOL(hAPP(com,bool,wt,hAPP(option(com),com,the_1(com),hAPP(pname,option(com),body,U_928))))
      | ~ hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),U_928),u)) ),
    inference(definitional_conversion,[status(esa)],[f_260_2]) ).

cnf(f_260_4,plain,
    ( hBOOL(hAPP(com,bool,wt,hAPP(option(com),com,the_1(com),hAPP(pname,option(com),body,U_928))))
    | ~ hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),U_928),u)) ),
    inference(clausify,[status(thm)],[f_260_3]) ).

fof(f_261_1,plain,
    ! [X_b,C_1,A_3,B_1] :
      ( ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_1))
        & 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_1))) ),
    inference(fof_nnf,[status(thm)],[fact_190_DiffE]) ).

fof(f_261_2,plain,
    ! [U_932,U_931,U_930,U_929] :
      ( ( ~ hBOOL(hAPP(fun(U_932,bool),bool,hAPP(U_932,fun(fun(U_932,bool),bool),member(U_932),U_931),U_929))
        & hBOOL(hAPP(fun(U_932,bool),bool,hAPP(U_932,fun(fun(U_932,bool),bool),member(U_932),U_931),U_930)) )
      | ~ hBOOL(hAPP(fun(U_932,bool),bool,hAPP(U_932,fun(fun(U_932,bool),bool),member(U_932),U_931),hAPP(fun(U_932,bool),fun(U_932,bool),hAPP(fun(U_932,bool),fun(fun(U_932,bool),fun(U_932,bool)),minus_minus(fun(U_932,bool)),U_930),U_929))) ),
    inference(variable_rename,[status(thm)],[f_261_1]) ).

fof(f_261_3,plain,
    ( ! [U_931,U_932,U_929,U_930] :
        ( ~ hBOOL(hAPP(fun(U_932,bool),bool,hAPP(U_932,fun(fun(U_932,bool),bool),member(U_932),U_931),U_929))
        | ~ sP44(U_931,U_932,U_929,U_930) )
    & ! [U_931,U_932,U_929,U_930] :
        ( hBOOL(hAPP(fun(U_932,bool),bool,hAPP(U_932,fun(fun(U_932,bool),bool),member(U_932),U_931),U_930))
        | ~ sP44(U_931,U_932,U_929,U_930) )
    & ! [U_931,U_932,U_929,U_930] :
        ( sP44(U_931,U_932,U_929,U_930)
        | ~ hBOOL(hAPP(fun(U_932,bool),bool,hAPP(U_932,fun(fun(U_932,bool),bool),member(U_932),U_931),hAPP(fun(U_932,bool),fun(U_932,bool),hAPP(fun(U_932,bool),fun(fun(U_932,bool),fun(U_932,bool)),minus_minus(fun(U_932,bool)),U_930),U_929))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP44])],[f_261_2]) ).

cnf(f_261_4,plain,
    ( sP44(U_931,U_932,U_929,U_930)
    | ~ hBOOL(hAPP(fun(U_932,bool),bool,hAPP(U_932,fun(fun(U_932,bool),bool),member(U_932),U_931),hAPP(fun(U_932,bool),fun(U_932,bool),hAPP(fun(U_932,bool),fun(fun(U_932,bool),fun(U_932,bool)),minus_minus(fun(U_932,bool)),U_930),U_929))) ),
    inference(clausify,[status(thm)],[f_261_3]) ).

cnf(f_261_5,plain,
    ( hBOOL(hAPP(fun(U_932,bool),bool,hAPP(U_932,fun(fun(U_932,bool),bool),member(U_932),U_931),U_930))
    | ~ sP44(U_931,U_932,U_929,U_930) ),
    inference(clausify,[status(thm)],[f_261_3]) ).

cnf(f_261_6,plain,
    ( ~ hBOOL(hAPP(fun(U_932,bool),bool,hAPP(U_932,fun(fun(U_932,bool),bool),member(U_932),U_931),U_929))
    | ~ sP44(U_931,U_932,U_929,U_930) ),
    inference(clausify,[status(thm)],[f_261_3]) ).

fof(f_262_1,plain,
    ! [X_b,B_1,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_1)))
      | hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_1))
      | ~ 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_191_DiffI]) ).

fof(f_262_2,plain,
    ! [U_936,U_935,U_934,U_933] :
      ( hBOOL(hAPP(fun(U_936,bool),bool,hAPP(U_936,fun(fun(U_936,bool),bool),member(U_936),U_934),hAPP(fun(U_936,bool),fun(U_936,bool),hAPP(fun(U_936,bool),fun(fun(U_936,bool),fun(U_936,bool)),minus_minus(fun(U_936,bool)),U_933),U_935)))
      | hBOOL(hAPP(fun(U_936,bool),bool,hAPP(U_936,fun(fun(U_936,bool),bool),member(U_936),U_934),U_935))
      | ~ hBOOL(hAPP(fun(U_936,bool),bool,hAPP(U_936,fun(fun(U_936,bool),bool),member(U_936),U_934),U_933)) ),
    inference(variable_rename,[status(thm)],[f_262_1]) ).

fof(f_262_3,plain,
    ! [U_934,U_936,U_935,U_933] :
      ( hBOOL(hAPP(fun(U_936,bool),bool,hAPP(U_936,fun(fun(U_936,bool),bool),member(U_936),U_934),hAPP(fun(U_936,bool),fun(U_936,bool),hAPP(fun(U_936,bool),fun(fun(U_936,bool),fun(U_936,bool)),minus_minus(fun(U_936,bool)),U_933),U_935)))
      | hBOOL(hAPP(fun(U_936,bool),bool,hAPP(U_936,fun(fun(U_936,bool),bool),member(U_936),U_934),U_935))
      | ~ hBOOL(hAPP(fun(U_936,bool),bool,hAPP(U_936,fun(fun(U_936,bool),bool),member(U_936),U_934),U_933)) ),
    inference(definitional_conversion,[status(esa)],[f_262_2]) ).

cnf(f_262_4,plain,
    ( hBOOL(hAPP(fun(U_936,bool),bool,hAPP(U_936,fun(fun(U_936,bool),bool),member(U_936),U_934),hAPP(fun(U_936,bool),fun(U_936,bool),hAPP(fun(U_936,bool),fun(fun(U_936,bool),fun(U_936,bool)),minus_minus(fun(U_936,bool)),U_933),U_935)))
    | hBOOL(hAPP(fun(U_936,bool),bool,hAPP(U_936,fun(fun(U_936,bool),bool),member(U_936),U_934),U_935))
    | ~ hBOOL(hAPP(fun(U_936,bool),bool,hAPP(U_936,fun(fun(U_936,bool),bool),member(U_936),U_934),U_933)) ),
    inference(clausify,[status(thm)],[f_262_3]) ).

fof(f_263_1,plain,
    ! [X_b,C_1,A_3,B_1] :
      ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_1))
      | ~ 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_1))) ),
    inference(fof_nnf,[status(thm)],[fact_192_DiffD2]) ).

fof(f_263_2,plain,
    ! [U_940,U_939,U_938,U_937] :
      ( ~ hBOOL(hAPP(fun(U_940,bool),bool,hAPP(U_940,fun(fun(U_940,bool),bool),member(U_940),U_939),U_937))
      | ~ hBOOL(hAPP(fun(U_940,bool),bool,hAPP(U_940,fun(fun(U_940,bool),bool),member(U_940),U_939),hAPP(fun(U_940,bool),fun(U_940,bool),hAPP(fun(U_940,bool),fun(fun(U_940,bool),fun(U_940,bool)),minus_minus(fun(U_940,bool)),U_938),U_937))) ),
    inference(variable_rename,[status(thm)],[f_263_1]) ).

fof(f_263_3,plain,
    ! [U_938,U_937,U_939,U_940] :
      ( ~ hBOOL(hAPP(fun(U_940,bool),bool,hAPP(U_940,fun(fun(U_940,bool),bool),member(U_940),U_939),U_937))
      | ~ hBOOL(hAPP(fun(U_940,bool),bool,hAPP(U_940,fun(fun(U_940,bool),bool),member(U_940),U_939),hAPP(fun(U_940,bool),fun(U_940,bool),hAPP(fun(U_940,bool),fun(fun(U_940,bool),fun(U_940,bool)),minus_minus(fun(U_940,bool)),U_938),U_937))) ),
    inference(definitional_conversion,[status(esa)],[f_263_2]) ).

cnf(f_263_4,plain,
    ( ~ hBOOL(hAPP(fun(U_940,bool),bool,hAPP(U_940,fun(fun(U_940,bool),bool),member(U_940),U_939),U_937))
    | ~ hBOOL(hAPP(fun(U_940,bool),bool,hAPP(U_940,fun(fun(U_940,bool),bool),member(U_940),U_939),hAPP(fun(U_940,bool),fun(U_940,bool),hAPP(fun(U_940,bool),fun(fun(U_940,bool),fun(U_940,bool)),minus_minus(fun(U_940,bool)),U_938),U_937))) ),
    inference(clausify,[status(thm)],[f_263_3]) ).

fof(f_264_1,plain,
    ! [X_b,C_1,A_3,B_1] :
      ( 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_1))) ),
    inference(fof_nnf,[status(thm)],[fact_193_DiffD1]) ).

fof(f_264_2,plain,
    ! [U_944,U_943,U_942,U_941] :
      ( hBOOL(hAPP(fun(U_944,bool),bool,hAPP(U_944,fun(fun(U_944,bool),bool),member(U_944),U_943),U_942))
      | ~ hBOOL(hAPP(fun(U_944,bool),bool,hAPP(U_944,fun(fun(U_944,bool),bool),member(U_944),U_943),hAPP(fun(U_944,bool),fun(U_944,bool),hAPP(fun(U_944,bool),fun(fun(U_944,bool),fun(U_944,bool)),minus_minus(fun(U_944,bool)),U_942),U_941))) ),
    inference(variable_rename,[status(thm)],[f_264_1]) ).

fof(f_264_3,plain,
    ! [U_944,U_943,U_942] :
      ( ! [U_941] : ~ hBOOL(hAPP(fun(U_944,bool),bool,hAPP(U_944,fun(fun(U_944,bool),bool),member(U_944),U_943),hAPP(fun(U_944,bool),fun(U_944,bool),hAPP(fun(U_944,bool),fun(fun(U_944,bool),fun(U_944,bool)),minus_minus(fun(U_944,bool)),U_942),U_941)))
      | hBOOL(hAPP(fun(U_944,bool),bool,hAPP(U_944,fun(fun(U_944,bool),bool),member(U_944),U_943),U_942)) ),
    inference(miniscope,[status(thm)],[f_264_2]) ).

fof(f_264_4,plain,
    ! [U_941,U_943,U_944,U_942] :
      ( ~ hBOOL(hAPP(fun(U_944,bool),bool,hAPP(U_944,fun(fun(U_944,bool),bool),member(U_944),U_943),hAPP(fun(U_944,bool),fun(U_944,bool),hAPP(fun(U_944,bool),fun(fun(U_944,bool),fun(U_944,bool)),minus_minus(fun(U_944,bool)),U_942),U_941)))
      | hBOOL(hAPP(fun(U_944,bool),bool,hAPP(U_944,fun(fun(U_944,bool),bool),member(U_944),U_943),U_942)) ),
    inference(definitional_conversion,[status(esa)],[f_264_3]) ).

cnf(f_264_5,plain,
    ( ~ hBOOL(hAPP(fun(U_944,bool),bool,hAPP(U_944,fun(fun(U_944,bool),bool),member(U_944),U_943),hAPP(fun(U_944,bool),fun(U_944,bool),hAPP(fun(U_944,bool),fun(fun(U_944,bool),fun(U_944,bool)),minus_minus(fun(U_944,bool)),U_942),U_941)))
    | hBOOL(hAPP(fun(U_944,bool),bool,hAPP(U_944,fun(fun(U_944,bool),bool),member(U_944),U_943),U_942)) ),
    inference(clausify,[status(thm)],[f_264_4]) ).

fof(f_265_1,plain,
    ! [X_b,A_3,B_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)),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_1)),B_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_1),
    inference(fof_nnf,[status(thm)],[fact_194_Diff__idemp]) ).

fof(f_265_2,plain,
    ! [U_947,U_946,U_945] : 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)),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_946),U_945)),U_945) = 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_946),U_945),
    inference(variable_rename,[status(thm)],[f_265_1]) ).

fof(f_265_3,plain,
    ! [U_947,U_945,U_946] : 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)),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_946),U_945)),U_945) = 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_946),U_945),
    inference(definitional_conversion,[status(esa)],[f_265_2]) ).

cnf(f_265_4,plain,
    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)),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_946),U_945)),U_945) = 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_946),U_945),
    inference(clausify,[status(thm)],[f_265_3]) ).

fof(f_266_1,plain,
    ! [X_b,C_1,A_3,B_1] :
      ( ( 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_1)))
        | hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_1))
        | ~ 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_1))
          & 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_1))) ) ),
    inference(fof_nnf,[status(thm)],[fact_195_Diff__iff]) ).

fof(f_266_2,plain,
    ! [U_951,U_950,U_949,U_948] :
      ( ( hBOOL(hAPP(fun(U_951,bool),bool,hAPP(U_951,fun(fun(U_951,bool),bool),member(U_951),U_950),hAPP(fun(U_951,bool),fun(U_951,bool),hAPP(fun(U_951,bool),fun(fun(U_951,bool),fun(U_951,bool)),minus_minus(fun(U_951,bool)),U_949),U_948)))
        | hBOOL(hAPP(fun(U_951,bool),bool,hAPP(U_951,fun(fun(U_951,bool),bool),member(U_951),U_950),U_948))
        | ~ hBOOL(hAPP(fun(U_951,bool),bool,hAPP(U_951,fun(fun(U_951,bool),bool),member(U_951),U_950),U_949)) )
      & ( ( ~ hBOOL(hAPP(fun(U_951,bool),bool,hAPP(U_951,fun(fun(U_951,bool),bool),member(U_951),U_950),U_948))
          & hBOOL(hAPP(fun(U_951,bool),bool,hAPP(U_951,fun(fun(U_951,bool),bool),member(U_951),U_950),U_949)) )
        | ~ hBOOL(hAPP(fun(U_951,bool),bool,hAPP(U_951,fun(fun(U_951,bool),bool),member(U_951),U_950),hAPP(fun(U_951,bool),fun(U_951,bool),hAPP(fun(U_951,bool),fun(fun(U_951,bool),fun(U_951,bool)),minus_minus(fun(U_951,bool)),U_949),U_948))) ) ),
    inference(variable_rename,[status(thm)],[f_266_1]) ).

fof(f_266_3,plain,
    ( ! [U_959,U_957,U_955,U_953] :
        ( hBOOL(hAPP(fun(U_959,bool),bool,hAPP(U_959,fun(fun(U_959,bool),bool),member(U_959),U_957),hAPP(fun(U_959,bool),fun(U_959,bool),hAPP(fun(U_959,bool),fun(fun(U_959,bool),fun(U_959,bool)),minus_minus(fun(U_959,bool)),U_955),U_953)))
        | hBOOL(hAPP(fun(U_959,bool),bool,hAPP(U_959,fun(fun(U_959,bool),bool),member(U_959),U_957),U_953))
        | ~ hBOOL(hAPP(fun(U_959,bool),bool,hAPP(U_959,fun(fun(U_959,bool),bool),member(U_959),U_957),U_955)) )
    & ! [U_958,U_956,U_954,U_952] :
        ( ( ~ hBOOL(hAPP(fun(U_958,bool),bool,hAPP(U_958,fun(fun(U_958,bool),bool),member(U_958),U_956),U_952))
          & hBOOL(hAPP(fun(U_958,bool),bool,hAPP(U_958,fun(fun(U_958,bool),bool),member(U_958),U_956),U_954)) )
        | ~ hBOOL(hAPP(fun(U_958,bool),bool,hAPP(U_958,fun(fun(U_958,bool),bool),member(U_958),U_956),hAPP(fun(U_958,bool),fun(U_958,bool),hAPP(fun(U_958,bool),fun(fun(U_958,bool),fun(U_958,bool)),minus_minus(fun(U_958,bool)),U_954),U_952))) ) ),
    inference(miniscope,[status(thm)],[f_266_2]) ).

fof(f_266_4,plain,
    ( ! [U_954,U_958,U_952,U_956] :
        ( ~ hBOOL(hAPP(fun(U_958,bool),bool,hAPP(U_958,fun(fun(U_958,bool),bool),member(U_958),U_956),U_952))
        | ~ sP45(U_954,U_958,U_952,U_956) )
    & ! [U_954,U_958,U_952,U_956] :
        ( hBOOL(hAPP(fun(U_958,bool),bool,hAPP(U_958,fun(fun(U_958,bool),bool),member(U_958),U_956),U_954))
        | ~ sP45(U_954,U_958,U_952,U_956) )
    & ! [U_957,U_953,U_955,U_959] :
        ( hBOOL(hAPP(fun(U_959,bool),bool,hAPP(U_959,fun(fun(U_959,bool),bool),member(U_959),U_957),hAPP(fun(U_959,bool),fun(U_959,bool),hAPP(fun(U_959,bool),fun(fun(U_959,bool),fun(U_959,bool)),minus_minus(fun(U_959,bool)),U_955),U_953)))
        | hBOOL(hAPP(fun(U_959,bool),bool,hAPP(U_959,fun(fun(U_959,bool),bool),member(U_959),U_957),U_953))
        | ~ hBOOL(hAPP(fun(U_959,bool),bool,hAPP(U_959,fun(fun(U_959,bool),bool),member(U_959),U_957),U_955)) )
    & ! [U_954,U_958,U_952,U_956] :
        ( sP45(U_954,U_958,U_952,U_956)
        | ~ hBOOL(hAPP(fun(U_958,bool),bool,hAPP(U_958,fun(fun(U_958,bool),bool),member(U_958),U_956),hAPP(fun(U_958,bool),fun(U_958,bool),hAPP(fun(U_958,bool),fun(fun(U_958,bool),fun(U_958,bool)),minus_minus(fun(U_958,bool)),U_954),U_952))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP45])],[f_266_3]) ).

cnf(f_266_5,plain,
    ( sP45(U_954,U_958,U_952,U_956)
    | ~ hBOOL(hAPP(fun(U_958,bool),bool,hAPP(U_958,fun(fun(U_958,bool),bool),member(U_958),U_956),hAPP(fun(U_958,bool),fun(U_958,bool),hAPP(fun(U_958,bool),fun(fun(U_958,bool),fun(U_958,bool)),minus_minus(fun(U_958,bool)),U_954),U_952))) ),
    inference(clausify,[status(thm)],[f_266_4]) ).

cnf(f_266_6,plain,
    ( hBOOL(hAPP(fun(U_959,bool),bool,hAPP(U_959,fun(fun(U_959,bool),bool),member(U_959),U_957),hAPP(fun(U_959,bool),fun(U_959,bool),hAPP(fun(U_959,bool),fun(fun(U_959,bool),fun(U_959,bool)),minus_minus(fun(U_959,bool)),U_955),U_953)))
    | hBOOL(hAPP(fun(U_959,bool),bool,hAPP(U_959,fun(fun(U_959,bool),bool),member(U_959),U_957),U_953))
    | ~ hBOOL(hAPP(fun(U_959,bool),bool,hAPP(U_959,fun(fun(U_959,bool),bool),member(U_959),U_957),U_955)) ),
    inference(clausify,[status(thm)],[f_266_4]) ).

cnf(f_266_7,plain,
    ( hBOOL(hAPP(fun(U_958,bool),bool,hAPP(U_958,fun(fun(U_958,bool),bool),member(U_958),U_956),U_954))
    | ~ sP45(U_954,U_958,U_952,U_956) ),
    inference(clausify,[status(thm)],[f_266_4]) ).

cnf(f_266_8,plain,
    ( ~ hBOOL(hAPP(fun(U_958,bool),bool,hAPP(U_958,fun(fun(U_958,bool),bool),member(U_958),U_956),U_952))
    | ~ sP45(U_954,U_958,U_952,U_956) ),
    inference(clausify,[status(thm)],[f_266_4]) ).

fof(f_267_1,plain,
    ! [X_b,A_3,B_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_1) = 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_1)))),
    inference(fof_nnf,[status(thm)],[fact_196_set__diff__eq]) ).

fof(f_267_2,plain,
    ! [U_962,U_961,U_960] : hAPP(fun(U_962,bool),fun(U_962,bool),hAPP(fun(U_962,bool),fun(fun(U_962,bool),fun(U_962,bool)),minus_minus(fun(U_962,bool)),U_961),U_960) = hAPP(fun(U_962,bool),fun(U_962,bool),collect(U_962),hAPP(fun(U_962,bool),fun(U_962,bool),hAPP(fun(U_962,fun(bool,bool)),fun(fun(U_962,bool),fun(U_962,bool)),combs(U_962,bool,bool),hAPP(fun(U_962,bool),fun(U_962,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_962,bool),fun(U_962,fun(bool,bool))),combb(bool,fun(bool,bool),U_962),fconj),hAPP(fun(U_962,bool),fun(U_962,bool),hAPP(fun(U_962,fun(fun(U_962,bool),bool)),fun(fun(U_962,bool),fun(U_962,bool)),combc(U_962,fun(U_962,bool),bool),member(U_962)),U_961))),hAPP(fun(U_962,bool),fun(U_962,bool),hAPP(fun(bool,bool),fun(fun(U_962,bool),fun(U_962,bool)),combb(bool,bool,U_962),fNot),hAPP(fun(U_962,bool),fun(U_962,bool),hAPP(fun(U_962,fun(fun(U_962,bool),bool)),fun(fun(U_962,bool),fun(U_962,bool)),combc(U_962,fun(U_962,bool),bool),member(U_962)),U_960)))),
    inference(variable_rename,[status(thm)],[f_267_1]) ).

fof(f_267_3,plain,
    ! [U_962,U_960,U_961] : hAPP(fun(U_962,bool),fun(U_962,bool),hAPP(fun(U_962,bool),fun(fun(U_962,bool),fun(U_962,bool)),minus_minus(fun(U_962,bool)),U_961),U_960) = hAPP(fun(U_962,bool),fun(U_962,bool),collect(U_962),hAPP(fun(U_962,bool),fun(U_962,bool),hAPP(fun(U_962,fun(bool,bool)),fun(fun(U_962,bool),fun(U_962,bool)),combs(U_962,bool,bool),hAPP(fun(U_962,bool),fun(U_962,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_962,bool),fun(U_962,fun(bool,bool))),combb(bool,fun(bool,bool),U_962),fconj),hAPP(fun(U_962,bool),fun(U_962,bool),hAPP(fun(U_962,fun(fun(U_962,bool),bool)),fun(fun(U_962,bool),fun(U_962,bool)),combc(U_962,fun(U_962,bool),bool),member(U_962)),U_961))),hAPP(fun(U_962,bool),fun(U_962,bool),hAPP(fun(bool,bool),fun(fun(U_962,bool),fun(U_962,bool)),combb(bool,bool,U_962),fNot),hAPP(fun(U_962,bool),fun(U_962,bool),hAPP(fun(U_962,fun(fun(U_962,bool),bool)),fun(fun(U_962,bool),fun(U_962,bool)),combc(U_962,fun(U_962,bool),bool),member(U_962)),U_960)))),
    inference(definitional_conversion,[status(esa)],[f_267_2]) ).

cnf(f_267_4,plain,
    hAPP(fun(U_962,bool),fun(U_962,bool),hAPP(fun(U_962,bool),fun(fun(U_962,bool),fun(U_962,bool)),minus_minus(fun(U_962,bool)),U_961),U_960) = hAPP(fun(U_962,bool),fun(U_962,bool),collect(U_962),hAPP(fun(U_962,bool),fun(U_962,bool),hAPP(fun(U_962,fun(bool,bool)),fun(fun(U_962,bool),fun(U_962,bool)),combs(U_962,bool,bool),hAPP(fun(U_962,bool),fun(U_962,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_962,bool),fun(U_962,fun(bool,bool))),combb(bool,fun(bool,bool),U_962),fconj),hAPP(fun(U_962,bool),fun(U_962,bool),hAPP(fun(U_962,fun(fun(U_962,bool),bool)),fun(fun(U_962,bool),fun(U_962,bool)),combc(U_962,fun(U_962,bool),bool),member(U_962)),U_961))),hAPP(fun(U_962,bool),fun(U_962,bool),hAPP(fun(bool,bool),fun(fun(U_962,bool),fun(U_962,bool)),combb(bool,bool,U_962),fNot),hAPP(fun(U_962,bool),fun(U_962,bool),hAPP(fun(U_962,fun(fun(U_962,bool),bool)),fun(fun(U_962,bool),fun(U_962,bool)),combc(U_962,fun(U_962,bool),bool),member(U_962)),U_960)))),
    inference(clausify,[status(thm)],[f_267_3]) ).

fof(f_268_1,plain,
    ! [X_b,X_1,A_3,F,F_1] :
      ( ( ( hAPP(fun(X_b,bool),X_b,F_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(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),hAPP(fun(X_b,bool),X_b,F_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))))))
          | 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_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)) = 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_1)) ),
    inference(fof_nnf,[status(thm)],[fact_197_folding__one_Oinsert__remove]) ).

fof(f_268_2,plain,
    ! [U_967,U_966,U_965,U_964,U_963] :
      ( ( ( hAPP(fun(U_967,bool),U_967,U_963,hAPP(fun(U_967,bool),fun(U_967,bool),hAPP(U_967,fun(fun(U_967,bool),fun(U_967,bool)),insert(U_967),U_966),U_965)) = hAPP(U_967,U_967,hAPP(U_967,fun(U_967,U_967),U_964,U_966),hAPP(fun(U_967,bool),U_967,U_963,hAPP(fun(U_967,bool),fun(U_967,bool),hAPP(fun(U_967,bool),fun(fun(U_967,bool),fun(U_967,bool)),minus_minus(fun(U_967,bool)),U_965),hAPP(fun(U_967,bool),fun(U_967,bool),hAPP(U_967,fun(fun(U_967,bool),fun(U_967,bool)),insert(U_967),U_966),bot_bot(fun(U_967,bool))))))
          | hAPP(fun(U_967,bool),fun(U_967,bool),hAPP(fun(U_967,bool),fun(fun(U_967,bool),fun(U_967,bool)),minus_minus(fun(U_967,bool)),U_965),hAPP(fun(U_967,bool),fun(U_967,bool),hAPP(U_967,fun(fun(U_967,bool),fun(U_967,bool)),insert(U_967),U_966),bot_bot(fun(U_967,bool)))) = bot_bot(fun(U_967,bool)) )
        & ( hAPP(fun(U_967,bool),U_967,U_963,hAPP(fun(U_967,bool),fun(U_967,bool),hAPP(U_967,fun(fun(U_967,bool),fun(U_967,bool)),insert(U_967),U_966),U_965)) = ti(U_967,U_966)
          | hAPP(fun(U_967,bool),fun(U_967,bool),hAPP(fun(U_967,bool),fun(fun(U_967,bool),fun(U_967,bool)),minus_minus(fun(U_967,bool)),U_965),hAPP(fun(U_967,bool),fun(U_967,bool),hAPP(U_967,fun(fun(U_967,bool),fun(U_967,bool)),insert(U_967),U_966),bot_bot(fun(U_967,bool)))) != bot_bot(fun(U_967,bool)) ) )
      | ~ hBOOL(hAPP(fun(U_967,bool),bool,finite_finite(U_967),U_965))
      | ~ hBOOL(hAPP(fun(fun(U_967,bool),U_967),bool,hAPP(fun(U_967,fun(U_967,U_967)),fun(fun(fun(U_967,bool),U_967),bool),finite_folding_one(U_967),U_964),U_963)) ),
    inference(variable_rename,[status(thm)],[f_268_1]) ).

fof(f_268_3,plain,
    ( ! [U_963,U_964,U_965,U_967,U_966] :
        ( hAPP(fun(U_967,bool),U_967,U_963,hAPP(fun(U_967,bool),fun(U_967,bool),hAPP(U_967,fun(fun(U_967,bool),fun(U_967,bool)),insert(U_967),U_966),U_965)) = hAPP(U_967,U_967,hAPP(U_967,fun(U_967,U_967),U_964,U_966),hAPP(fun(U_967,bool),U_967,U_963,hAPP(fun(U_967,bool),fun(U_967,bool),hAPP(fun(U_967,bool),fun(fun(U_967,bool),fun(U_967,bool)),minus_minus(fun(U_967,bool)),U_965),hAPP(fun(U_967,bool),fun(U_967,bool),hAPP(U_967,fun(fun(U_967,bool),fun(U_967,bool)),insert(U_967),U_966),bot_bot(fun(U_967,bool))))))
        | hAPP(fun(U_967,bool),fun(U_967,bool),hAPP(fun(U_967,bool),fun(fun(U_967,bool),fun(U_967,bool)),minus_minus(fun(U_967,bool)),U_965),hAPP(fun(U_967,bool),fun(U_967,bool),hAPP(U_967,fun(fun(U_967,bool),fun(U_967,bool)),insert(U_967),U_966),bot_bot(fun(U_967,bool)))) = bot_bot(fun(U_967,bool))
        | ~ sP46(U_963,U_964,U_965,U_967,U_966) )
    & ! [U_963,U_964,U_965,U_967,U_966] :
        ( hAPP(fun(U_967,bool),U_967,U_963,hAPP(fun(U_967,bool),fun(U_967,bool),hAPP(U_967,fun(fun(U_967,bool),fun(U_967,bool)),insert(U_967),U_966),U_965)) = ti(U_967,U_966)
        | hAPP(fun(U_967,bool),fun(U_967,bool),hAPP(fun(U_967,bool),fun(fun(U_967,bool),fun(U_967,bool)),minus_minus(fun(U_967,bool)),U_965),hAPP(fun(U_967,bool),fun(U_967,bool),hAPP(U_967,fun(fun(U_967,bool),fun(U_967,bool)),insert(U_967),U_966),bot_bot(fun(U_967,bool)))) != bot_bot(fun(U_967,bool))
        | ~ sP46(U_963,U_964,U_965,U_967,U_966) )
    & ! [U_963,U_964,U_965,U_967,U_966] :
        ( sP46(U_963,U_964,U_965,U_967,U_966)
        | ~ hBOOL(hAPP(fun(U_967,bool),bool,finite_finite(U_967),U_965))
        | ~ hBOOL(hAPP(fun(fun(U_967,bool),U_967),bool,hAPP(fun(U_967,fun(U_967,U_967)),fun(fun(fun(U_967,bool),U_967),bool),finite_folding_one(U_967),U_964),U_963)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP46])],[f_268_2]) ).

cnf(f_268_4,plain,
    ( sP46(U_963,U_964,U_965,U_967,U_966)
    | ~ hBOOL(hAPP(fun(U_967,bool),bool,finite_finite(U_967),U_965))
    | ~ hBOOL(hAPP(fun(fun(U_967,bool),U_967),bool,hAPP(fun(U_967,fun(U_967,U_967)),fun(fun(fun(U_967,bool),U_967),bool),finite_folding_one(U_967),U_964),U_963)) ),
    inference(clausify,[status(thm)],[f_268_3]) ).

cnf(f_268_5,plain,
    ( hAPP(fun(U_967,bool),U_967,U_963,hAPP(fun(U_967,bool),fun(U_967,bool),hAPP(U_967,fun(fun(U_967,bool),fun(U_967,bool)),insert(U_967),U_966),U_965)) = ti(U_967,U_966)
    | hAPP(fun(U_967,bool),fun(U_967,bool),hAPP(fun(U_967,bool),fun(fun(U_967,bool),fun(U_967,bool)),minus_minus(fun(U_967,bool)),U_965),hAPP(fun(U_967,bool),fun(U_967,bool),hAPP(U_967,fun(fun(U_967,bool),fun(U_967,bool)),insert(U_967),U_966),bot_bot(fun(U_967,bool)))) != bot_bot(fun(U_967,bool))
    | ~ sP46(U_963,U_964,U_965,U_967,U_966) ),
    inference(clausify,[status(thm)],[f_268_3]) ).

cnf(f_268_6,plain,
    ( hAPP(fun(U_967,bool),U_967,U_963,hAPP(fun(U_967,bool),fun(U_967,bool),hAPP(U_967,fun(fun(U_967,bool),fun(U_967,bool)),insert(U_967),U_966),U_965)) = hAPP(U_967,U_967,hAPP(U_967,fun(U_967,U_967),U_964,U_966),hAPP(fun(U_967,bool),U_967,U_963,hAPP(fun(U_967,bool),fun(U_967,bool),hAPP(fun(U_967,bool),fun(fun(U_967,bool),fun(U_967,bool)),minus_minus(fun(U_967,bool)),U_965),hAPP(fun(U_967,bool),fun(U_967,bool),hAPP(U_967,fun(fun(U_967,bool),fun(U_967,bool)),insert(U_967),U_966),bot_bot(fun(U_967,bool))))))
    | hAPP(fun(U_967,bool),fun(U_967,bool),hAPP(fun(U_967,bool),fun(fun(U_967,bool),fun(U_967,bool)),minus_minus(fun(U_967,bool)),U_965),hAPP(fun(U_967,bool),fun(U_967,bool),hAPP(U_967,fun(fun(U_967,bool),fun(U_967,bool)),insert(U_967),U_966),bot_bot(fun(U_967,bool)))) = bot_bot(fun(U_967,bool))
    | ~ sP46(U_963,U_964,U_965,U_967,U_966) ),
    inference(clausify,[status(thm)],[f_268_3]) ).

fof(f_269_1,plain,
    ! [X_b,X_1,A_3,F,F_1] :
      ( ( ( hAPP(fun(X_b,bool),X_b,F_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_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))))))
          | 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_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,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_1)) ),
    inference(fof_nnf,[status(thm)],[fact_198_folding__one_Oremove]) ).

fof(f_269_2,plain,
    ! [U_972,U_971,U_970,U_969,U_968] :
      ( ( ( hAPP(fun(U_972,bool),U_972,U_968,U_970) = hAPP(U_972,U_972,hAPP(U_972,fun(U_972,U_972),U_969,U_971),hAPP(fun(U_972,bool),U_972,U_968,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),hAPP(fun(U_972,bool),fun(U_972,bool),hAPP(U_972,fun(fun(U_972,bool),fun(U_972,bool)),insert(U_972),U_971),bot_bot(fun(U_972,bool))))))
          | 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),hAPP(fun(U_972,bool),fun(U_972,bool),hAPP(U_972,fun(fun(U_972,bool),fun(U_972,bool)),insert(U_972),U_971),bot_bot(fun(U_972,bool)))) = bot_bot(fun(U_972,bool)) )
        & ( hAPP(fun(U_972,bool),U_972,U_968,U_970) = ti(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),hAPP(fun(U_972,bool),fun(U_972,bool),hAPP(U_972,fun(fun(U_972,bool),fun(U_972,bool)),insert(U_972),U_971),bot_bot(fun(U_972,bool)))) != bot_bot(fun(U_972,bool)) ) )
      | ~ 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,finite_finite(U_972),U_970))
      | ~ hBOOL(hAPP(fun(fun(U_972,bool),U_972),bool,hAPP(fun(U_972,fun(U_972,U_972)),fun(fun(fun(U_972,bool),U_972),bool),finite_folding_one(U_972),U_969),U_968)) ),
    inference(variable_rename,[status(thm)],[f_269_1]) ).

fof(f_269_3,plain,
    ( ! [U_970,U_972,U_968,U_969,U_971] :
        ( hAPP(fun(U_972,bool),U_972,U_968,U_970) = hAPP(U_972,U_972,hAPP(U_972,fun(U_972,U_972),U_969,U_971),hAPP(fun(U_972,bool),U_972,U_968,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),hAPP(fun(U_972,bool),fun(U_972,bool),hAPP(U_972,fun(fun(U_972,bool),fun(U_972,bool)),insert(U_972),U_971),bot_bot(fun(U_972,bool))))))
        | 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),hAPP(fun(U_972,bool),fun(U_972,bool),hAPP(U_972,fun(fun(U_972,bool),fun(U_972,bool)),insert(U_972),U_971),bot_bot(fun(U_972,bool)))) = bot_bot(fun(U_972,bool))
        | ~ sP47(U_970,U_972,U_968,U_969,U_971) )
    & ! [U_970,U_972,U_968,U_969,U_971] :
        ( hAPP(fun(U_972,bool),U_972,U_968,U_970) = ti(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),hAPP(fun(U_972,bool),fun(U_972,bool),hAPP(U_972,fun(fun(U_972,bool),fun(U_972,bool)),insert(U_972),U_971),bot_bot(fun(U_972,bool)))) != bot_bot(fun(U_972,bool))
        | ~ sP47(U_970,U_972,U_968,U_969,U_971) )
    & ! [U_970,U_972,U_968,U_969,U_971] :
        ( sP47(U_970,U_972,U_968,U_969,U_971)
        | ~ 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,finite_finite(U_972),U_970))
        | ~ hBOOL(hAPP(fun(fun(U_972,bool),U_972),bool,hAPP(fun(U_972,fun(U_972,U_972)),fun(fun(fun(U_972,bool),U_972),bool),finite_folding_one(U_972),U_969),U_968)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP47])],[f_269_2]) ).

cnf(f_269_4,plain,
    ( sP47(U_970,U_972,U_968,U_969,U_971)
    | ~ 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,finite_finite(U_972),U_970))
    | ~ hBOOL(hAPP(fun(fun(U_972,bool),U_972),bool,hAPP(fun(U_972,fun(U_972,U_972)),fun(fun(fun(U_972,bool),U_972),bool),finite_folding_one(U_972),U_969),U_968)) ),
    inference(clausify,[status(thm)],[f_269_3]) ).

cnf(f_269_5,plain,
    ( hAPP(fun(U_972,bool),U_972,U_968,U_970) = ti(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),hAPP(fun(U_972,bool),fun(U_972,bool),hAPP(U_972,fun(fun(U_972,bool),fun(U_972,bool)),insert(U_972),U_971),bot_bot(fun(U_972,bool)))) != bot_bot(fun(U_972,bool))
    | ~ sP47(U_970,U_972,U_968,U_969,U_971) ),
    inference(clausify,[status(thm)],[f_269_3]) ).

cnf(f_269_6,plain,
    ( hAPP(fun(U_972,bool),U_972,U_968,U_970) = hAPP(U_972,U_972,hAPP(U_972,fun(U_972,U_972),U_969,U_971),hAPP(fun(U_972,bool),U_972,U_968,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),hAPP(fun(U_972,bool),fun(U_972,bool),hAPP(U_972,fun(fun(U_972,bool),fun(U_972,bool)),insert(U_972),U_971),bot_bot(fun(U_972,bool))))))
    | 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),hAPP(fun(U_972,bool),fun(U_972,bool),hAPP(U_972,fun(fun(U_972,bool),fun(U_972,bool)),insert(U_972),U_971),bot_bot(fun(U_972,bool)))) = bot_bot(fun(U_972,bool))
    | ~ sP47(U_970,U_972,U_968,U_969,U_971) ),
    inference(clausify,[status(thm)],[f_269_3]) ).

fof(f_270_1,plain,
    ! [X_c,X_b,X_1,A_3,F,Z_2,G,F_1] :
      ( hAPP(fun(X_c,bool),X_b,F_1,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_1,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_2),G),F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_199_folding__image__simple_Oinsert__remove]) ).

fof(f_270_2,plain,
    ! [U_980,U_979,U_978,U_977,U_976,U_975,U_974,U_973] :
      ( hAPP(fun(U_980,bool),U_979,U_973,hAPP(fun(U_980,bool),fun(U_980,bool),hAPP(U_980,fun(fun(U_980,bool),fun(U_980,bool)),insert(U_980),U_978),U_977)) = hAPP(U_979,U_979,hAPP(U_979,fun(U_979,U_979),U_976,hAPP(U_980,U_979,U_974,U_978)),hAPP(fun(U_980,bool),U_979,U_973,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_977),hAPP(fun(U_980,bool),fun(U_980,bool),hAPP(U_980,fun(fun(U_980,bool),fun(U_980,bool)),insert(U_980),U_978),bot_bot(fun(U_980,bool))))))
      | ~ hBOOL(hAPP(fun(U_980,bool),bool,finite_finite(U_980),U_977))
      | ~ hBOOL(hAPP(fun(fun(U_980,bool),U_979),bool,hAPP(fun(U_980,U_979),fun(fun(fun(U_980,bool),U_979),bool),hAPP(U_979,fun(fun(U_980,U_979),fun(fun(fun(U_980,bool),U_979),bool)),hAPP(fun(U_979,fun(U_979,U_979)),fun(U_979,fun(fun(U_980,U_979),fun(fun(fun(U_980,bool),U_979),bool))),finite1357897459simple(U_979,U_980),U_976),U_975),U_974),U_973)) ),
    inference(variable_rename,[status(thm)],[f_270_1]) ).

fof(f_270_3,plain,
    ! [U_974,U_978,U_973,U_980,U_979,U_975,U_976,U_977] :
      ( hAPP(fun(U_980,bool),U_979,U_973,hAPP(fun(U_980,bool),fun(U_980,bool),hAPP(U_980,fun(fun(U_980,bool),fun(U_980,bool)),insert(U_980),U_978),U_977)) = hAPP(U_979,U_979,hAPP(U_979,fun(U_979,U_979),U_976,hAPP(U_980,U_979,U_974,U_978)),hAPP(fun(U_980,bool),U_979,U_973,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_977),hAPP(fun(U_980,bool),fun(U_980,bool),hAPP(U_980,fun(fun(U_980,bool),fun(U_980,bool)),insert(U_980),U_978),bot_bot(fun(U_980,bool))))))
      | ~ hBOOL(hAPP(fun(U_980,bool),bool,finite_finite(U_980),U_977))
      | ~ hBOOL(hAPP(fun(fun(U_980,bool),U_979),bool,hAPP(fun(U_980,U_979),fun(fun(fun(U_980,bool),U_979),bool),hAPP(U_979,fun(fun(U_980,U_979),fun(fun(fun(U_980,bool),U_979),bool)),hAPP(fun(U_979,fun(U_979,U_979)),fun(U_979,fun(fun(U_980,U_979),fun(fun(fun(U_980,bool),U_979),bool))),finite1357897459simple(U_979,U_980),U_976),U_975),U_974),U_973)) ),
    inference(definitional_conversion,[status(esa)],[f_270_2]) ).

cnf(f_270_4,plain,
    ( hAPP(fun(U_980,bool),U_979,U_973,hAPP(fun(U_980,bool),fun(U_980,bool),hAPP(U_980,fun(fun(U_980,bool),fun(U_980,bool)),insert(U_980),U_978),U_977)) = hAPP(U_979,U_979,hAPP(U_979,fun(U_979,U_979),U_976,hAPP(U_980,U_979,U_974,U_978)),hAPP(fun(U_980,bool),U_979,U_973,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_977),hAPP(fun(U_980,bool),fun(U_980,bool),hAPP(U_980,fun(fun(U_980,bool),fun(U_980,bool)),insert(U_980),U_978),bot_bot(fun(U_980,bool))))))
    | ~ hBOOL(hAPP(fun(U_980,bool),bool,finite_finite(U_980),U_977))
    | ~ hBOOL(hAPP(fun(fun(U_980,bool),U_979),bool,hAPP(fun(U_980,U_979),fun(fun(fun(U_980,bool),U_979),bool),hAPP(U_979,fun(fun(U_980,U_979),fun(fun(fun(U_980,bool),U_979),bool)),hAPP(fun(U_979,fun(U_979,U_979)),fun(U_979,fun(fun(U_980,U_979),fun(fun(fun(U_980,bool),U_979),bool))),finite1357897459simple(U_979,U_980),U_976),U_975),U_974),U_973)) ),
    inference(clausify,[status(thm)],[f_270_3]) ).

fof(f_271_1,plain,
    ! [X_c,X_b,X_1,A_3,F,Z_2,G,F_1] :
      ( hAPP(fun(X_c,bool),X_b,F_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_1,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_2),G),F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_200_folding__image__simple_Oremove]) ).

fof(f_271_2,plain,
    ! [U_988,U_987,U_986,U_985,U_984,U_983,U_982,U_981] :
      ( hAPP(fun(U_988,bool),U_987,U_981,U_985) = hAPP(U_987,U_987,hAPP(U_987,fun(U_987,U_987),U_984,hAPP(U_988,U_987,U_982,U_986)),hAPP(fun(U_988,bool),U_987,U_981,hAPP(fun(U_988,bool),fun(U_988,bool),hAPP(fun(U_988,bool),fun(fun(U_988,bool),fun(U_988,bool)),minus_minus(fun(U_988,bool)),U_985),hAPP(fun(U_988,bool),fun(U_988,bool),hAPP(U_988,fun(fun(U_988,bool),fun(U_988,bool)),insert(U_988),U_986),bot_bot(fun(U_988,bool))))))
      | ~ hBOOL(hAPP(fun(U_988,bool),bool,hAPP(U_988,fun(fun(U_988,bool),bool),member(U_988),U_986),U_985))
      | ~ hBOOL(hAPP(fun(U_988,bool),bool,finite_finite(U_988),U_985))
      | ~ hBOOL(hAPP(fun(fun(U_988,bool),U_987),bool,hAPP(fun(U_988,U_987),fun(fun(fun(U_988,bool),U_987),bool),hAPP(U_987,fun(fun(U_988,U_987),fun(fun(fun(U_988,bool),U_987),bool)),hAPP(fun(U_987,fun(U_987,U_987)),fun(U_987,fun(fun(U_988,U_987),fun(fun(fun(U_988,bool),U_987),bool))),finite1357897459simple(U_987,U_988),U_984),U_983),U_982),U_981)) ),
    inference(variable_rename,[status(thm)],[f_271_1]) ).

fof(f_271_3,plain,
    ! [U_988,U_985,U_982,U_981,U_987,U_983,U_984,U_986] :
      ( hAPP(fun(U_988,bool),U_987,U_981,U_985) = hAPP(U_987,U_987,hAPP(U_987,fun(U_987,U_987),U_984,hAPP(U_988,U_987,U_982,U_986)),hAPP(fun(U_988,bool),U_987,U_981,hAPP(fun(U_988,bool),fun(U_988,bool),hAPP(fun(U_988,bool),fun(fun(U_988,bool),fun(U_988,bool)),minus_minus(fun(U_988,bool)),U_985),hAPP(fun(U_988,bool),fun(U_988,bool),hAPP(U_988,fun(fun(U_988,bool),fun(U_988,bool)),insert(U_988),U_986),bot_bot(fun(U_988,bool))))))
      | ~ hBOOL(hAPP(fun(U_988,bool),bool,hAPP(U_988,fun(fun(U_988,bool),bool),member(U_988),U_986),U_985))
      | ~ hBOOL(hAPP(fun(U_988,bool),bool,finite_finite(U_988),U_985))
      | ~ hBOOL(hAPP(fun(fun(U_988,bool),U_987),bool,hAPP(fun(U_988,U_987),fun(fun(fun(U_988,bool),U_987),bool),hAPP(U_987,fun(fun(U_988,U_987),fun(fun(fun(U_988,bool),U_987),bool)),hAPP(fun(U_987,fun(U_987,U_987)),fun(U_987,fun(fun(U_988,U_987),fun(fun(fun(U_988,bool),U_987),bool))),finite1357897459simple(U_987,U_988),U_984),U_983),U_982),U_981)) ),
    inference(definitional_conversion,[status(esa)],[f_271_2]) ).

cnf(f_271_4,plain,
    ( hAPP(fun(U_988,bool),U_987,U_981,U_985) = hAPP(U_987,U_987,hAPP(U_987,fun(U_987,U_987),U_984,hAPP(U_988,U_987,U_982,U_986)),hAPP(fun(U_988,bool),U_987,U_981,hAPP(fun(U_988,bool),fun(U_988,bool),hAPP(fun(U_988,bool),fun(fun(U_988,bool),fun(U_988,bool)),minus_minus(fun(U_988,bool)),U_985),hAPP(fun(U_988,bool),fun(U_988,bool),hAPP(U_988,fun(fun(U_988,bool),fun(U_988,bool)),insert(U_988),U_986),bot_bot(fun(U_988,bool))))))
    | ~ hBOOL(hAPP(fun(U_988,bool),bool,hAPP(U_988,fun(fun(U_988,bool),bool),member(U_988),U_986),U_985))
    | ~ hBOOL(hAPP(fun(U_988,bool),bool,finite_finite(U_988),U_985))
    | ~ hBOOL(hAPP(fun(fun(U_988,bool),U_987),bool,hAPP(fun(U_988,U_987),fun(fun(fun(U_988,bool),U_987),bool),hAPP(U_987,fun(fun(U_988,U_987),fun(fun(fun(U_988,bool),U_987),bool)),hAPP(fun(U_987,fun(U_987,U_987)),fun(U_987,fun(fun(U_988,U_987),fun(fun(fun(U_988,bool),U_987),bool))),finite1357897459simple(U_987,U_988),U_984),U_983),U_982),U_981)) ),
    inference(clausify,[status(thm)],[f_271_3]) ).

fof(f_272_1,plain,
    ! [X_b,X_c] :
      ( ! [A_3,B_1,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_1),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_1,X_2))
      | ~ minus(X_c) ),
    inference(fof_nnf,[status(thm)],[fact_201_fun__diff__def]) ).

fof(f_272_2,plain,
    ! [U_993,U_992] :
      ( ! [U_991,U_990,U_989] : hAPP(U_993,U_992,hAPP(fun(U_993,U_992),fun(U_993,U_992),hAPP(fun(U_993,U_992),fun(fun(U_993,U_992),fun(U_993,U_992)),minus_minus(fun(U_993,U_992)),U_991),U_990),U_989) = hAPP(U_992,U_992,hAPP(U_992,fun(U_992,U_992),minus_minus(U_992),hAPP(U_993,U_992,U_991,U_989)),hAPP(U_993,U_992,U_990,U_989))
      | ~ minus(U_992) ),
    inference(variable_rename,[status(thm)],[f_272_1]) ).

fof(f_272_3,plain,
    ! [U_993,U_990,U_989,U_992,U_991] :
      ( hAPP(U_993,U_992,hAPP(fun(U_993,U_992),fun(U_993,U_992),hAPP(fun(U_993,U_992),fun(fun(U_993,U_992),fun(U_993,U_992)),minus_minus(fun(U_993,U_992)),U_991),U_990),U_989) = hAPP(U_992,U_992,hAPP(U_992,fun(U_992,U_992),minus_minus(U_992),hAPP(U_993,U_992,U_991,U_989)),hAPP(U_993,U_992,U_990,U_989))
      | ~ minus(U_992) ),
    inference(definitional_conversion,[status(esa)],[f_272_2]) ).

cnf(f_272_4,plain,
    ( hAPP(U_993,U_992,hAPP(fun(U_993,U_992),fun(U_993,U_992),hAPP(fun(U_993,U_992),fun(fun(U_993,U_992),fun(U_993,U_992)),minus_minus(fun(U_993,U_992)),U_991),U_990),U_989) = hAPP(U_992,U_992,hAPP(U_992,fun(U_992,U_992),minus_minus(U_992),hAPP(U_993,U_992,U_991,U_989)),hAPP(U_993,U_992,U_990,U_989))
    | ~ minus(U_992) ),
    inference(clausify,[status(thm)],[f_272_3]) ).

fof(f_273_1,plain,
    ! [X_c,X_b] :
      ( ! [A_3,B_1,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_1),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_1,X_1))
      | ~ minus(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_202_minus__apply]) ).

fof(f_273_2,plain,
    ! [U_998,U_997] :
      ( ! [U_996,U_995,U_994] : hAPP(U_998,U_997,hAPP(fun(U_998,U_997),fun(U_998,U_997),hAPP(fun(U_998,U_997),fun(fun(U_998,U_997),fun(U_998,U_997)),minus_minus(fun(U_998,U_997)),U_996),U_995),U_994) = hAPP(U_997,U_997,hAPP(U_997,fun(U_997,U_997),minus_minus(U_997),hAPP(U_998,U_997,U_996,U_994)),hAPP(U_998,U_997,U_995,U_994))
      | ~ minus(U_997) ),
    inference(variable_rename,[status(thm)],[f_273_1]) ).

fof(f_273_3,plain,
    ! [U_995,U_994,U_997,U_996,U_998] :
      ( hAPP(U_998,U_997,hAPP(fun(U_998,U_997),fun(U_998,U_997),hAPP(fun(U_998,U_997),fun(fun(U_998,U_997),fun(U_998,U_997)),minus_minus(fun(U_998,U_997)),U_996),U_995),U_994) = hAPP(U_997,U_997,hAPP(U_997,fun(U_997,U_997),minus_minus(U_997),hAPP(U_998,U_997,U_996,U_994)),hAPP(U_998,U_997,U_995,U_994))
      | ~ minus(U_997) ),
    inference(definitional_conversion,[status(esa)],[f_273_2]) ).

cnf(f_273_4,plain,
    ( hAPP(U_998,U_997,hAPP(fun(U_998,U_997),fun(U_998,U_997),hAPP(fun(U_998,U_997),fun(fun(U_998,U_997),fun(U_998,U_997)),minus_minus(fun(U_998,U_997)),U_996),U_995),U_994) = hAPP(U_997,U_997,hAPP(U_997,fun(U_997,U_997),minus_minus(U_997),hAPP(U_998,U_997,U_996,U_994)),hAPP(U_998,U_997,U_995,U_994))
    | ~ minus(U_997) ),
    inference(clausify,[status(thm)],[f_273_3]) ).

fof(f_274_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_203_card__Diff__singleton__if]) ).

fof(f_274_2,plain,
    ! [U_1001,U_1000,U_999] :
      ( ( ( hAPP(fun(U_1001,bool),nat,finite_card(U_1001),hAPP(fun(U_1001,bool),fun(U_1001,bool),hAPP(fun(U_1001,bool),fun(fun(U_1001,bool),fun(U_1001,bool)),minus_minus(fun(U_1001,bool)),U_999),hAPP(fun(U_1001,bool),fun(U_1001,bool),hAPP(U_1001,fun(fun(U_1001,bool),fun(U_1001,bool)),insert(U_1001),U_1000),bot_bot(fun(U_1001,bool))))) = hAPP(fun(U_1001,bool),nat,finite_card(U_1001),U_999)
          | hBOOL(hAPP(fun(U_1001,bool),bool,hAPP(U_1001,fun(fun(U_1001,bool),bool),member(U_1001),U_1000),U_999)) )
        & ( hAPP(fun(U_1001,bool),nat,finite_card(U_1001),hAPP(fun(U_1001,bool),fun(U_1001,bool),hAPP(fun(U_1001,bool),fun(fun(U_1001,bool),fun(U_1001,bool)),minus_minus(fun(U_1001,bool)),U_999),hAPP(fun(U_1001,bool),fun(U_1001,bool),hAPP(U_1001,fun(fun(U_1001,bool),fun(U_1001,bool)),insert(U_1001),U_1000),bot_bot(fun(U_1001,bool))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(U_1001,bool),nat,finite_card(U_1001),U_999)),one_one(nat))
          | ~ hBOOL(hAPP(fun(U_1001,bool),bool,hAPP(U_1001,fun(fun(U_1001,bool),bool),member(U_1001),U_1000),U_999)) ) )
      | ~ hBOOL(hAPP(fun(U_1001,bool),bool,finite_finite(U_1001),U_999)) ),
    inference(variable_rename,[status(thm)],[f_274_1]) ).

fof(f_274_3,plain,
    ( ! [U_1001,U_1000,U_999] :
        ( hAPP(fun(U_1001,bool),nat,finite_card(U_1001),hAPP(fun(U_1001,bool),fun(U_1001,bool),hAPP(fun(U_1001,bool),fun(fun(U_1001,bool),fun(U_1001,bool)),minus_minus(fun(U_1001,bool)),U_999),hAPP(fun(U_1001,bool),fun(U_1001,bool),hAPP(U_1001,fun(fun(U_1001,bool),fun(U_1001,bool)),insert(U_1001),U_1000),bot_bot(fun(U_1001,bool))))) = hAPP(fun(U_1001,bool),nat,finite_card(U_1001),U_999)
        | hBOOL(hAPP(fun(U_1001,bool),bool,hAPP(U_1001,fun(fun(U_1001,bool),bool),member(U_1001),U_1000),U_999))
        | ~ sP48(U_1001,U_1000,U_999) )
    & ! [U_1001,U_1000,U_999] :
        ( hAPP(fun(U_1001,bool),nat,finite_card(U_1001),hAPP(fun(U_1001,bool),fun(U_1001,bool),hAPP(fun(U_1001,bool),fun(fun(U_1001,bool),fun(U_1001,bool)),minus_minus(fun(U_1001,bool)),U_999),hAPP(fun(U_1001,bool),fun(U_1001,bool),hAPP(U_1001,fun(fun(U_1001,bool),fun(U_1001,bool)),insert(U_1001),U_1000),bot_bot(fun(U_1001,bool))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(U_1001,bool),nat,finite_card(U_1001),U_999)),one_one(nat))
        | ~ hBOOL(hAPP(fun(U_1001,bool),bool,hAPP(U_1001,fun(fun(U_1001,bool),bool),member(U_1001),U_1000),U_999))
        | ~ sP48(U_1001,U_1000,U_999) )
    & ! [U_1001,U_1000,U_999] :
        ( sP48(U_1001,U_1000,U_999)
        | ~ hBOOL(hAPP(fun(U_1001,bool),bool,finite_finite(U_1001),U_999)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP48])],[f_274_2]) ).

cnf(f_274_4,plain,
    ( sP48(U_1001,U_1000,U_999)
    | ~ hBOOL(hAPP(fun(U_1001,bool),bool,finite_finite(U_1001),U_999)) ),
    inference(clausify,[status(thm)],[f_274_3]) ).

cnf(f_274_5,plain,
    ( hAPP(fun(U_1001,bool),nat,finite_card(U_1001),hAPP(fun(U_1001,bool),fun(U_1001,bool),hAPP(fun(U_1001,bool),fun(fun(U_1001,bool),fun(U_1001,bool)),minus_minus(fun(U_1001,bool)),U_999),hAPP(fun(U_1001,bool),fun(U_1001,bool),hAPP(U_1001,fun(fun(U_1001,bool),fun(U_1001,bool)),insert(U_1001),U_1000),bot_bot(fun(U_1001,bool))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(U_1001,bool),nat,finite_card(U_1001),U_999)),one_one(nat))
    | ~ hBOOL(hAPP(fun(U_1001,bool),bool,hAPP(U_1001,fun(fun(U_1001,bool),bool),member(U_1001),U_1000),U_999))
    | ~ sP48(U_1001,U_1000,U_999) ),
    inference(clausify,[status(thm)],[f_274_3]) ).

cnf(f_274_6,plain,
    ( hAPP(fun(U_1001,bool),nat,finite_card(U_1001),hAPP(fun(U_1001,bool),fun(U_1001,bool),hAPP(fun(U_1001,bool),fun(fun(U_1001,bool),fun(U_1001,bool)),minus_minus(fun(U_1001,bool)),U_999),hAPP(fun(U_1001,bool),fun(U_1001,bool),hAPP(U_1001,fun(fun(U_1001,bool),fun(U_1001,bool)),insert(U_1001),U_1000),bot_bot(fun(U_1001,bool))))) = hAPP(fun(U_1001,bool),nat,finite_card(U_1001),U_999)
    | hBOOL(hAPP(fun(U_1001,bool),bool,hAPP(U_1001,fun(fun(U_1001,bool),bool),member(U_1001),U_1000),U_999))
    | ~ sP48(U_1001,U_1000,U_999) ),
    inference(clausify,[status(thm)],[f_274_3]) ).

fof(f_275_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_204_card__Diff__singleton]) ).

fof(f_275_2,plain,
    ! [U_1004,U_1003,U_1002] :
      ( hAPP(fun(U_1004,bool),nat,finite_card(U_1004),hAPP(fun(U_1004,bool),fun(U_1004,bool),hAPP(fun(U_1004,bool),fun(fun(U_1004,bool),fun(U_1004,bool)),minus_minus(fun(U_1004,bool)),U_1002),hAPP(fun(U_1004,bool),fun(U_1004,bool),hAPP(U_1004,fun(fun(U_1004,bool),fun(U_1004,bool)),insert(U_1004),U_1003),bot_bot(fun(U_1004,bool))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(U_1004,bool),nat,finite_card(U_1004),U_1002)),one_one(nat))
      | ~ hBOOL(hAPP(fun(U_1004,bool),bool,hAPP(U_1004,fun(fun(U_1004,bool),bool),member(U_1004),U_1003),U_1002))
      | ~ hBOOL(hAPP(fun(U_1004,bool),bool,finite_finite(U_1004),U_1002)) ),
    inference(variable_rename,[status(thm)],[f_275_1]) ).

fof(f_275_3,plain,
    ! [U_1002,U_1003,U_1004] :
      ( hAPP(fun(U_1004,bool),nat,finite_card(U_1004),hAPP(fun(U_1004,bool),fun(U_1004,bool),hAPP(fun(U_1004,bool),fun(fun(U_1004,bool),fun(U_1004,bool)),minus_minus(fun(U_1004,bool)),U_1002),hAPP(fun(U_1004,bool),fun(U_1004,bool),hAPP(U_1004,fun(fun(U_1004,bool),fun(U_1004,bool)),insert(U_1004),U_1003),bot_bot(fun(U_1004,bool))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(U_1004,bool),nat,finite_card(U_1004),U_1002)),one_one(nat))
      | ~ hBOOL(hAPP(fun(U_1004,bool),bool,hAPP(U_1004,fun(fun(U_1004,bool),bool),member(U_1004),U_1003),U_1002))
      | ~ hBOOL(hAPP(fun(U_1004,bool),bool,finite_finite(U_1004),U_1002)) ),
    inference(definitional_conversion,[status(esa)],[f_275_2]) ).

cnf(f_275_4,plain,
    ( hAPP(fun(U_1004,bool),nat,finite_card(U_1004),hAPP(fun(U_1004,bool),fun(U_1004,bool),hAPP(fun(U_1004,bool),fun(fun(U_1004,bool),fun(U_1004,bool)),minus_minus(fun(U_1004,bool)),U_1002),hAPP(fun(U_1004,bool),fun(U_1004,bool),hAPP(U_1004,fun(fun(U_1004,bool),fun(U_1004,bool)),insert(U_1004),U_1003),bot_bot(fun(U_1004,bool))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(U_1004,bool),nat,finite_card(U_1004),U_1002)),one_one(nat))
    | ~ hBOOL(hAPP(fun(U_1004,bool),bool,hAPP(U_1004,fun(fun(U_1004,bool),bool),member(U_1004),U_1003),U_1002))
    | ~ hBOOL(hAPP(fun(U_1004,bool),bool,finite_finite(U_1004),U_1002)) ),
    inference(clausify,[status(thm)],[f_275_3]) ).

fof(f_276_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_205_one__reorient]) ).

fof(f_276_2,plain,
    ! [U_1006] :
      ( ! [U_1005] :
          ( ( one_one(U_1006) = ti(U_1006,U_1005)
            | ti(U_1006,U_1005) != one_one(U_1006) )
          & ( ti(U_1006,U_1005) = one_one(U_1006)
            | one_one(U_1006) != ti(U_1006,U_1005) ) )
      | ~ one(U_1006) ),
    inference(variable_rename,[status(thm)],[f_276_1]) ).

fof(f_276_3,plain,
    ! [U_1006] :
      ( ( ! [U_1008] :
            ( one_one(U_1006) = ti(U_1006,U_1008)
            | ti(U_1006,U_1008) != one_one(U_1006) )
        & ! [U_1007] :
            ( ti(U_1006,U_1007) = one_one(U_1006)
            | one_one(U_1006) != ti(U_1006,U_1007) ) )
      | ~ one(U_1006) ),
    inference(miniscope,[status(thm)],[f_276_2]) ).

fof(f_276_4,plain,
    ( ! [U_1006,U_1008,U_1007] :
        ( one_one(U_1006) = ti(U_1006,U_1008)
        | ti(U_1006,U_1008) != one_one(U_1006)
        | ~ sP49(U_1006,U_1008,U_1007) )
    & ! [U_1006,U_1008,U_1007] :
        ( ti(U_1006,U_1007) = one_one(U_1006)
        | one_one(U_1006) != ti(U_1006,U_1007)
        | ~ sP49(U_1006,U_1008,U_1007) )
    & ! [U_1006,U_1008,U_1007] :
        ( sP49(U_1006,U_1008,U_1007)
        | ~ one(U_1006) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP49])],[f_276_3]) ).

cnf(f_276_5,plain,
    ( sP49(U_1006,U_1008,U_1007)
    | ~ one(U_1006) ),
    inference(clausify,[status(thm)],[f_276_4]) ).

cnf(f_276_6,plain,
    ( ti(U_1006,U_1007) = one_one(U_1006)
    | one_one(U_1006) != ti(U_1006,U_1007)
    | ~ sP49(U_1006,U_1008,U_1007) ),
    inference(clausify,[status(thm)],[f_276_4]) ).

cnf(f_276_7,plain,
    ( one_one(U_1006) = ti(U_1006,U_1008)
    | ti(U_1006,U_1008) != one_one(U_1006)
    | ~ sP49(U_1006,U_1008,U_1007) ),
    inference(clausify,[status(thm)],[f_276_4]) ).

fof(f_277_1,plain,
    ! [X_c,X_b,F,Z_2,G,F_1] :
      ( hAPP(fun(X_c,bool),X_b,F_1,bot_bot(fun(X_c,bool))) = ti(X_b,Z_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_2),G),F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_206_folding__image__simple_Oempty]) ).

fof(f_277_2,plain,
    ! [U_1014,U_1013,U_1012,U_1011,U_1010,U_1009] :
      ( hAPP(fun(U_1014,bool),U_1013,U_1009,bot_bot(fun(U_1014,bool))) = ti(U_1013,U_1011)
      | ~ hBOOL(hAPP(fun(fun(U_1014,bool),U_1013),bool,hAPP(fun(U_1014,U_1013),fun(fun(fun(U_1014,bool),U_1013),bool),hAPP(U_1013,fun(fun(U_1014,U_1013),fun(fun(fun(U_1014,bool),U_1013),bool)),hAPP(fun(U_1013,fun(U_1013,U_1013)),fun(U_1013,fun(fun(U_1014,U_1013),fun(fun(fun(U_1014,bool),U_1013),bool))),finite1357897459simple(U_1013,U_1014),U_1012),U_1011),U_1010),U_1009)) ),
    inference(variable_rename,[status(thm)],[f_277_1]) ).

fof(f_277_3,plain,
    ! [U_1009,U_1013,U_1011,U_1010,U_1012,U_1014] :
      ( hAPP(fun(U_1014,bool),U_1013,U_1009,bot_bot(fun(U_1014,bool))) = ti(U_1013,U_1011)
      | ~ hBOOL(hAPP(fun(fun(U_1014,bool),U_1013),bool,hAPP(fun(U_1014,U_1013),fun(fun(fun(U_1014,bool),U_1013),bool),hAPP(U_1013,fun(fun(U_1014,U_1013),fun(fun(fun(U_1014,bool),U_1013),bool)),hAPP(fun(U_1013,fun(U_1013,U_1013)),fun(U_1013,fun(fun(U_1014,U_1013),fun(fun(fun(U_1014,bool),U_1013),bool))),finite1357897459simple(U_1013,U_1014),U_1012),U_1011),U_1010),U_1009)) ),
    inference(definitional_conversion,[status(esa)],[f_277_2]) ).

cnf(f_277_4,plain,
    ( hAPP(fun(U_1014,bool),U_1013,U_1009,bot_bot(fun(U_1014,bool))) = ti(U_1013,U_1011)
    | ~ hBOOL(hAPP(fun(fun(U_1014,bool),U_1013),bool,hAPP(fun(U_1014,U_1013),fun(fun(fun(U_1014,bool),U_1013),bool),hAPP(U_1013,fun(fun(U_1014,U_1013),fun(fun(fun(U_1014,bool),U_1013),bool)),hAPP(fun(U_1013,fun(U_1013,U_1013)),fun(U_1013,fun(fun(U_1014,U_1013),fun(fun(fun(U_1014,bool),U_1013),bool))),finite1357897459simple(U_1013,U_1014),U_1012),U_1011),U_1010),U_1009)) ),
    inference(clausify,[status(thm)],[f_277_3]) ).

fof(f_278_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_207_diff__Suc__1]) ).

fof(f_278_2,plain,
    ! [U_1015] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,U_1015)),one_one(nat)) = U_1015,
    inference(variable_rename,[status(thm)],[f_278_1]) ).

fof(f_278_3,plain,
    ! [U_1015] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,U_1015)),one_one(nat)) = U_1015,
    inference(definitional_conversion,[status(esa)],[f_278_2]) ).

cnf(f_278_4,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,U_1015)),one_one(nat)) = U_1015,
    inference(clausify,[status(thm)],[f_278_3]) ).

fof(f_279_1,plain,
    ! [M_1,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),hAPP(nat,nat,suc,N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),one_one(nat))),N),
    inference(fof_nnf,[status(thm)],[fact_208_diff__Suc__eq__diff__pred]) ).

fof(f_279_2,plain,
    ! [U_1017,U_1016] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1017),hAPP(nat,nat,suc,U_1016)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1017),one_one(nat))),U_1016),
    inference(variable_rename,[status(thm)],[f_279_1]) ).

fof(f_279_3,plain,
    ! [U_1017,U_1016] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1017),hAPP(nat,nat,suc,U_1016)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1017),one_one(nat))),U_1016),
    inference(definitional_conversion,[status(esa)],[f_279_2]) ).

cnf(f_279_4,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1017),hAPP(nat,nat,suc,U_1016)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1017),one_one(nat))),U_1016),
    inference(clausify,[status(thm)],[f_279_3]) ).

fof(f_280_1,plain,
    ! [X_b,X_1,F,F_1] :
      ( hAPP(fun(X_b,bool),X_b,F_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),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_1)) ),
    inference(fof_nnf,[status(thm)],[fact_209_folding__one_Osingleton]) ).

fof(f_280_2,plain,
    ! [U_1021,U_1020,U_1019,U_1018] :
      ( hAPP(fun(U_1021,bool),U_1021,U_1018,hAPP(fun(U_1021,bool),fun(U_1021,bool),hAPP(U_1021,fun(fun(U_1021,bool),fun(U_1021,bool)),insert(U_1021),U_1020),bot_bot(fun(U_1021,bool)))) = ti(U_1021,U_1020)
      | ~ hBOOL(hAPP(fun(fun(U_1021,bool),U_1021),bool,hAPP(fun(U_1021,fun(U_1021,U_1021)),fun(fun(fun(U_1021,bool),U_1021),bool),finite_folding_one(U_1021),U_1019),U_1018)) ),
    inference(variable_rename,[status(thm)],[f_280_1]) ).

fof(f_280_3,plain,
    ! [U_1019,U_1018,U_1021,U_1020] :
      ( hAPP(fun(U_1021,bool),U_1021,U_1018,hAPP(fun(U_1021,bool),fun(U_1021,bool),hAPP(U_1021,fun(fun(U_1021,bool),fun(U_1021,bool)),insert(U_1021),U_1020),bot_bot(fun(U_1021,bool)))) = ti(U_1021,U_1020)
      | ~ hBOOL(hAPP(fun(fun(U_1021,bool),U_1021),bool,hAPP(fun(U_1021,fun(U_1021,U_1021)),fun(fun(fun(U_1021,bool),U_1021),bool),finite_folding_one(U_1021),U_1019),U_1018)) ),
    inference(definitional_conversion,[status(esa)],[f_280_2]) ).

cnf(f_280_4,plain,
    ( hAPP(fun(U_1021,bool),U_1021,U_1018,hAPP(fun(U_1021,bool),fun(U_1021,bool),hAPP(U_1021,fun(fun(U_1021,bool),fun(U_1021,bool)),insert(U_1021),U_1020),bot_bot(fun(U_1021,bool)))) = ti(U_1021,U_1020)
    | ~ hBOOL(hAPP(fun(fun(U_1021,bool),U_1021),bool,hAPP(fun(U_1021,fun(U_1021,U_1021)),fun(fun(fun(U_1021,bool),U_1021),bool),finite_folding_one(U_1021),U_1019),U_1018)) ),
    inference(clausify,[status(thm)],[f_280_3]) ).

fof(f_281_1,plain,
    ! [X_c,X_b,X_1,A_3,F,Z_2,G,F_1] :
      ( hAPP(fun(X_c,bool),X_b,F_1,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_1,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_2),G),F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_210_folding__image__simple_Oinsert]) ).

fof(f_281_2,plain,
    ! [U_1029,U_1028,U_1027,U_1026,U_1025,U_1024,U_1023,U_1022] :
      ( hAPP(fun(U_1029,bool),U_1028,U_1022,hAPP(fun(U_1029,bool),fun(U_1029,bool),hAPP(U_1029,fun(fun(U_1029,bool),fun(U_1029,bool)),insert(U_1029),U_1027),U_1026)) = hAPP(U_1028,U_1028,hAPP(U_1028,fun(U_1028,U_1028),U_1025,hAPP(U_1029,U_1028,U_1023,U_1027)),hAPP(fun(U_1029,bool),U_1028,U_1022,U_1026))
      | hBOOL(hAPP(fun(U_1029,bool),bool,hAPP(U_1029,fun(fun(U_1029,bool),bool),member(U_1029),U_1027),U_1026))
      | ~ hBOOL(hAPP(fun(U_1029,bool),bool,finite_finite(U_1029),U_1026))
      | ~ hBOOL(hAPP(fun(fun(U_1029,bool),U_1028),bool,hAPP(fun(U_1029,U_1028),fun(fun(fun(U_1029,bool),U_1028),bool),hAPP(U_1028,fun(fun(U_1029,U_1028),fun(fun(fun(U_1029,bool),U_1028),bool)),hAPP(fun(U_1028,fun(U_1028,U_1028)),fun(U_1028,fun(fun(U_1029,U_1028),fun(fun(fun(U_1029,bool),U_1028),bool))),finite1357897459simple(U_1028,U_1029),U_1025),U_1024),U_1023),U_1022)) ),
    inference(variable_rename,[status(thm)],[f_281_1]) ).

fof(f_281_3,plain,
    ! [U_1023,U_1022,U_1028,U_1024,U_1025,U_1026,U_1027,U_1029] :
      ( hAPP(fun(U_1029,bool),U_1028,U_1022,hAPP(fun(U_1029,bool),fun(U_1029,bool),hAPP(U_1029,fun(fun(U_1029,bool),fun(U_1029,bool)),insert(U_1029),U_1027),U_1026)) = hAPP(U_1028,U_1028,hAPP(U_1028,fun(U_1028,U_1028),U_1025,hAPP(U_1029,U_1028,U_1023,U_1027)),hAPP(fun(U_1029,bool),U_1028,U_1022,U_1026))
      | hBOOL(hAPP(fun(U_1029,bool),bool,hAPP(U_1029,fun(fun(U_1029,bool),bool),member(U_1029),U_1027),U_1026))
      | ~ hBOOL(hAPP(fun(U_1029,bool),bool,finite_finite(U_1029),U_1026))
      | ~ hBOOL(hAPP(fun(fun(U_1029,bool),U_1028),bool,hAPP(fun(U_1029,U_1028),fun(fun(fun(U_1029,bool),U_1028),bool),hAPP(U_1028,fun(fun(U_1029,U_1028),fun(fun(fun(U_1029,bool),U_1028),bool)),hAPP(fun(U_1028,fun(U_1028,U_1028)),fun(U_1028,fun(fun(U_1029,U_1028),fun(fun(fun(U_1029,bool),U_1028),bool))),finite1357897459simple(U_1028,U_1029),U_1025),U_1024),U_1023),U_1022)) ),
    inference(definitional_conversion,[status(esa)],[f_281_2]) ).

cnf(f_281_4,plain,
    ( hAPP(fun(U_1029,bool),U_1028,U_1022,hAPP(fun(U_1029,bool),fun(U_1029,bool),hAPP(U_1029,fun(fun(U_1029,bool),fun(U_1029,bool)),insert(U_1029),U_1027),U_1026)) = hAPP(U_1028,U_1028,hAPP(U_1028,fun(U_1028,U_1028),U_1025,hAPP(U_1029,U_1028,U_1023,U_1027)),hAPP(fun(U_1029,bool),U_1028,U_1022,U_1026))
    | hBOOL(hAPP(fun(U_1029,bool),bool,hAPP(U_1029,fun(fun(U_1029,bool),bool),member(U_1029),U_1027),U_1026))
    | ~ hBOOL(hAPP(fun(U_1029,bool),bool,finite_finite(U_1029),U_1026))
    | ~ hBOOL(hAPP(fun(fun(U_1029,bool),U_1028),bool,hAPP(fun(U_1029,U_1028),fun(fun(fun(U_1029,bool),U_1028),bool),hAPP(U_1028,fun(fun(U_1029,U_1028),fun(fun(fun(U_1029,bool),U_1028),bool)),hAPP(fun(U_1028,fun(U_1028,U_1028)),fun(U_1028,fun(fun(U_1029,U_1028),fun(fun(fun(U_1029,bool),U_1028),bool))),finite1357897459simple(U_1028,U_1029),U_1025),U_1024),U_1023),U_1022)) ),
    inference(clausify,[status(thm)],[f_281_3]) ).

fof(f_282_1,plain,
    ! [X_b,B_1,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_1))) = 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_1))),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_1))
      | ~ 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_211_card__Diff__insert]) ).

fof(f_282_2,plain,
    ! [U_1033,U_1032,U_1031,U_1030] :
      ( hAPP(fun(U_1033,bool),nat,finite_card(U_1033),hAPP(fun(U_1033,bool),fun(U_1033,bool),hAPP(fun(U_1033,bool),fun(fun(U_1033,bool),fun(U_1033,bool)),minus_minus(fun(U_1033,bool)),U_1030),hAPP(fun(U_1033,bool),fun(U_1033,bool),hAPP(U_1033,fun(fun(U_1033,bool),fun(U_1033,bool)),insert(U_1033),U_1031),U_1032))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(U_1033,bool),nat,finite_card(U_1033),hAPP(fun(U_1033,bool),fun(U_1033,bool),hAPP(fun(U_1033,bool),fun(fun(U_1033,bool),fun(U_1033,bool)),minus_minus(fun(U_1033,bool)),U_1030),U_1032))),one_one(nat))
      | hBOOL(hAPP(fun(U_1033,bool),bool,hAPP(U_1033,fun(fun(U_1033,bool),bool),member(U_1033),U_1031),U_1032))
      | ~ hBOOL(hAPP(fun(U_1033,bool),bool,hAPP(U_1033,fun(fun(U_1033,bool),bool),member(U_1033),U_1031),U_1030))
      | ~ hBOOL(hAPP(fun(U_1033,bool),bool,finite_finite(U_1033),U_1030)) ),
    inference(variable_rename,[status(thm)],[f_282_1]) ).

fof(f_282_3,plain,
    ! [U_1031,U_1032,U_1033,U_1030] :
      ( hAPP(fun(U_1033,bool),nat,finite_card(U_1033),hAPP(fun(U_1033,bool),fun(U_1033,bool),hAPP(fun(U_1033,bool),fun(fun(U_1033,bool),fun(U_1033,bool)),minus_minus(fun(U_1033,bool)),U_1030),hAPP(fun(U_1033,bool),fun(U_1033,bool),hAPP(U_1033,fun(fun(U_1033,bool),fun(U_1033,bool)),insert(U_1033),U_1031),U_1032))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(U_1033,bool),nat,finite_card(U_1033),hAPP(fun(U_1033,bool),fun(U_1033,bool),hAPP(fun(U_1033,bool),fun(fun(U_1033,bool),fun(U_1033,bool)),minus_minus(fun(U_1033,bool)),U_1030),U_1032))),one_one(nat))
      | hBOOL(hAPP(fun(U_1033,bool),bool,hAPP(U_1033,fun(fun(U_1033,bool),bool),member(U_1033),U_1031),U_1032))
      | ~ hBOOL(hAPP(fun(U_1033,bool),bool,hAPP(U_1033,fun(fun(U_1033,bool),bool),member(U_1033),U_1031),U_1030))
      | ~ hBOOL(hAPP(fun(U_1033,bool),bool,finite_finite(U_1033),U_1030)) ),
    inference(definitional_conversion,[status(esa)],[f_282_2]) ).

cnf(f_282_4,plain,
    ( hAPP(fun(U_1033,bool),nat,finite_card(U_1033),hAPP(fun(U_1033,bool),fun(U_1033,bool),hAPP(fun(U_1033,bool),fun(fun(U_1033,bool),fun(U_1033,bool)),minus_minus(fun(U_1033,bool)),U_1030),hAPP(fun(U_1033,bool),fun(U_1033,bool),hAPP(U_1033,fun(fun(U_1033,bool),fun(U_1033,bool)),insert(U_1033),U_1031),U_1032))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(U_1033,bool),nat,finite_card(U_1033),hAPP(fun(U_1033,bool),fun(U_1033,bool),hAPP(fun(U_1033,bool),fun(fun(U_1033,bool),fun(U_1033,bool)),minus_minus(fun(U_1033,bool)),U_1030),U_1032))),one_one(nat))
    | hBOOL(hAPP(fun(U_1033,bool),bool,hAPP(U_1033,fun(fun(U_1033,bool),bool),member(U_1033),U_1031),U_1032))
    | ~ hBOOL(hAPP(fun(U_1033,bool),bool,hAPP(U_1033,fun(fun(U_1033,bool),bool),member(U_1033),U_1031),U_1030))
    | ~ hBOOL(hAPP(fun(U_1033,bool),bool,finite_finite(U_1033),U_1030)) ),
    inference(clausify,[status(thm)],[f_282_3]) ).

fof(f_283_1,plain,
    ! [X_b,X_1,A_3,F,F_1] :
      ( hAPP(fun(X_b,bool),X_b,F_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(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),hAPP(fun(X_b,bool),X_b,F_1,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_1)) ),
    inference(fof_nnf,[status(thm)],[fact_212_folding__one_Oinsert]) ).

fof(f_283_2,plain,
    ! [U_1038,U_1037,U_1036,U_1035,U_1034] :
      ( hAPP(fun(U_1038,bool),U_1038,U_1034,hAPP(fun(U_1038,bool),fun(U_1038,bool),hAPP(U_1038,fun(fun(U_1038,bool),fun(U_1038,bool)),insert(U_1038),U_1037),U_1036)) = hAPP(U_1038,U_1038,hAPP(U_1038,fun(U_1038,U_1038),U_1035,U_1037),hAPP(fun(U_1038,bool),U_1038,U_1034,U_1036))
      | ti(fun(U_1038,bool),U_1036) = bot_bot(fun(U_1038,bool))
      | hBOOL(hAPP(fun(U_1038,bool),bool,hAPP(U_1038,fun(fun(U_1038,bool),bool),member(U_1038),U_1037),U_1036))
      | ~ hBOOL(hAPP(fun(U_1038,bool),bool,finite_finite(U_1038),U_1036))
      | ~ hBOOL(hAPP(fun(fun(U_1038,bool),U_1038),bool,hAPP(fun(U_1038,fun(U_1038,U_1038)),fun(fun(fun(U_1038,bool),U_1038),bool),finite_folding_one(U_1038),U_1035),U_1034)) ),
    inference(variable_rename,[status(thm)],[f_283_1]) ).

fof(f_283_3,plain,
    ! [U_1034,U_1035,U_1036,U_1038,U_1037] :
      ( hAPP(fun(U_1038,bool),U_1038,U_1034,hAPP(fun(U_1038,bool),fun(U_1038,bool),hAPP(U_1038,fun(fun(U_1038,bool),fun(U_1038,bool)),insert(U_1038),U_1037),U_1036)) = hAPP(U_1038,U_1038,hAPP(U_1038,fun(U_1038,U_1038),U_1035,U_1037),hAPP(fun(U_1038,bool),U_1038,U_1034,U_1036))
      | ti(fun(U_1038,bool),U_1036) = bot_bot(fun(U_1038,bool))
      | hBOOL(hAPP(fun(U_1038,bool),bool,hAPP(U_1038,fun(fun(U_1038,bool),bool),member(U_1038),U_1037),U_1036))
      | ~ hBOOL(hAPP(fun(U_1038,bool),bool,finite_finite(U_1038),U_1036))
      | ~ hBOOL(hAPP(fun(fun(U_1038,bool),U_1038),bool,hAPP(fun(U_1038,fun(U_1038,U_1038)),fun(fun(fun(U_1038,bool),U_1038),bool),finite_folding_one(U_1038),U_1035),U_1034)) ),
    inference(definitional_conversion,[status(esa)],[f_283_2]) ).

cnf(f_283_4,plain,
    ( hAPP(fun(U_1038,bool),U_1038,U_1034,hAPP(fun(U_1038,bool),fun(U_1038,bool),hAPP(U_1038,fun(fun(U_1038,bool),fun(U_1038,bool)),insert(U_1038),U_1037),U_1036)) = hAPP(U_1038,U_1038,hAPP(U_1038,fun(U_1038,U_1038),U_1035,U_1037),hAPP(fun(U_1038,bool),U_1038,U_1034,U_1036))
    | ti(fun(U_1038,bool),U_1036) = bot_bot(fun(U_1038,bool))
    | hBOOL(hAPP(fun(U_1038,bool),bool,hAPP(U_1038,fun(fun(U_1038,bool),bool),member(U_1038),U_1037),U_1036))
    | ~ hBOOL(hAPP(fun(U_1038,bool),bool,finite_finite(U_1038),U_1036))
    | ~ hBOOL(hAPP(fun(fun(U_1038,bool),U_1038),bool,hAPP(fun(U_1038,fun(U_1038,U_1038)),fun(fun(fun(U_1038,bool),U_1038),bool),finite_folding_one(U_1038),U_1035),U_1034)) ),
    inference(clausify,[status(thm)],[f_283_3]) ).

fof(f_284_1,plain,
    ! [X_b,A_3,F,F_1] :
      ( 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_1,A_3)),A_3))
      | ? [X_2,Y_1] : ~ 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_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_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_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,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_1)) ),
    inference(fof_nnf,[status(thm)],[fact_213_folding__one_Oclosed]) ).

fof(f_284_2,plain,
    ! [U_1044,U_1043,U_1042,U_1041] :
      ( hBOOL(hAPP(fun(U_1044,bool),bool,hAPP(U_1044,fun(fun(U_1044,bool),bool),member(U_1044),hAPP(fun(U_1044,bool),U_1044,U_1041,U_1043)),U_1043))
      | ? [U_1040,U_1039] : ~ hBOOL(hAPP(fun(U_1044,bool),bool,hAPP(U_1044,fun(fun(U_1044,bool),bool),member(U_1044),hAPP(U_1044,U_1044,hAPP(U_1044,fun(U_1044,U_1044),U_1042,U_1040),U_1039)),hAPP(fun(U_1044,bool),fun(U_1044,bool),hAPP(U_1044,fun(fun(U_1044,bool),fun(U_1044,bool)),insert(U_1044),U_1040),hAPP(fun(U_1044,bool),fun(U_1044,bool),hAPP(U_1044,fun(fun(U_1044,bool),fun(U_1044,bool)),insert(U_1044),U_1039),bot_bot(fun(U_1044,bool))))))
      | ti(fun(U_1044,bool),U_1043) = bot_bot(fun(U_1044,bool))
      | ~ hBOOL(hAPP(fun(U_1044,bool),bool,finite_finite(U_1044),U_1043))
      | ~ hBOOL(hAPP(fun(fun(U_1044,bool),U_1044),bool,hAPP(fun(U_1044,fun(U_1044,U_1044)),fun(fun(fun(U_1044,bool),U_1044),bool),finite_folding_one(U_1044),U_1042),U_1041)) ),
    inference(variable_rename,[status(thm)],[f_284_1]) ).

fof(f_284_3,plain,
    ! [U_1044,U_1043,U_1042,U_1041] :
      ( hBOOL(hAPP(fun(U_1044,bool),bool,hAPP(U_1044,fun(fun(U_1044,bool),bool),member(U_1044),hAPP(fun(U_1044,bool),U_1044,U_1041,U_1043)),U_1043))
      | ? [U_1039] : ~ hBOOL(hAPP(fun(U_1044,bool),bool,hAPP(U_1044,fun(fun(U_1044,bool),bool),member(U_1044),hAPP(U_1044,U_1044,hAPP(U_1044,fun(U_1044,U_1044),U_1042,sK32(U_1044,U_1043,U_1042,U_1041)),U_1039)),hAPP(fun(U_1044,bool),fun(U_1044,bool),hAPP(U_1044,fun(fun(U_1044,bool),fun(U_1044,bool)),insert(U_1044),sK32(U_1044,U_1043,U_1042,U_1041)),hAPP(fun(U_1044,bool),fun(U_1044,bool),hAPP(U_1044,fun(fun(U_1044,bool),fun(U_1044,bool)),insert(U_1044),U_1039),bot_bot(fun(U_1044,bool))))))
      | ti(fun(U_1044,bool),U_1043) = bot_bot(fun(U_1044,bool))
      | ~ hBOOL(hAPP(fun(U_1044,bool),bool,finite_finite(U_1044),U_1043))
      | ~ hBOOL(hAPP(fun(fun(U_1044,bool),U_1044),bool,hAPP(fun(U_1044,fun(U_1044,U_1044)),fun(fun(fun(U_1044,bool),U_1044),bool),finite_folding_one(U_1044),U_1042),U_1041)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(U_1040,sK32(U_1044,U_1043,U_1042,U_1041))],[f_284_2]) ).

fof(f_284_4,plain,
    ! [U_1044,U_1043,U_1042,U_1041] :
      ( hBOOL(hAPP(fun(U_1044,bool),bool,hAPP(U_1044,fun(fun(U_1044,bool),bool),member(U_1044),hAPP(fun(U_1044,bool),U_1044,U_1041,U_1043)),U_1043))
      | ~ hBOOL(hAPP(fun(U_1044,bool),bool,hAPP(U_1044,fun(fun(U_1044,bool),bool),member(U_1044),hAPP(U_1044,U_1044,hAPP(U_1044,fun(U_1044,U_1044),U_1042,sK32(U_1044,U_1043,U_1042,U_1041)),sK33(U_1044,U_1043,U_1042,U_1041))),hAPP(fun(U_1044,bool),fun(U_1044,bool),hAPP(U_1044,fun(fun(U_1044,bool),fun(U_1044,bool)),insert(U_1044),sK32(U_1044,U_1043,U_1042,U_1041)),hAPP(fun(U_1044,bool),fun(U_1044,bool),hAPP(U_1044,fun(fun(U_1044,bool),fun(U_1044,bool)),insert(U_1044),sK33(U_1044,U_1043,U_1042,U_1041)),bot_bot(fun(U_1044,bool))))))
      | ti(fun(U_1044,bool),U_1043) = bot_bot(fun(U_1044,bool))
      | ~ hBOOL(hAPP(fun(U_1044,bool),bool,finite_finite(U_1044),U_1043))
      | ~ hBOOL(hAPP(fun(fun(U_1044,bool),U_1044),bool,hAPP(fun(U_1044,fun(U_1044,U_1044)),fun(fun(fun(U_1044,bool),U_1044),bool),finite_folding_one(U_1044),U_1042),U_1041)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(U_1039,sK33(U_1044,U_1043,U_1042,U_1041))],[f_284_3]) ).

fof(f_284_5,plain,
    ! [U_1041,U_1042,U_1043,U_1044] :
      ( hBOOL(hAPP(fun(U_1044,bool),bool,hAPP(U_1044,fun(fun(U_1044,bool),bool),member(U_1044),hAPP(fun(U_1044,bool),U_1044,U_1041,U_1043)),U_1043))
      | ~ hBOOL(hAPP(fun(U_1044,bool),bool,hAPP(U_1044,fun(fun(U_1044,bool),bool),member(U_1044),hAPP(U_1044,U_1044,hAPP(U_1044,fun(U_1044,U_1044),U_1042,sK32(U_1044,U_1043,U_1042,U_1041)),sK33(U_1044,U_1043,U_1042,U_1041))),hAPP(fun(U_1044,bool),fun(U_1044,bool),hAPP(U_1044,fun(fun(U_1044,bool),fun(U_1044,bool)),insert(U_1044),sK32(U_1044,U_1043,U_1042,U_1041)),hAPP(fun(U_1044,bool),fun(U_1044,bool),hAPP(U_1044,fun(fun(U_1044,bool),fun(U_1044,bool)),insert(U_1044),sK33(U_1044,U_1043,U_1042,U_1041)),bot_bot(fun(U_1044,bool))))))
      | ti(fun(U_1044,bool),U_1043) = bot_bot(fun(U_1044,bool))
      | ~ hBOOL(hAPP(fun(U_1044,bool),bool,finite_finite(U_1044),U_1043))
      | ~ hBOOL(hAPP(fun(fun(U_1044,bool),U_1044),bool,hAPP(fun(U_1044,fun(U_1044,U_1044)),fun(fun(fun(U_1044,bool),U_1044),bool),finite_folding_one(U_1044),U_1042),U_1041)) ),
    inference(definitional_conversion,[status(esa)],[f_284_4]) ).

cnf(f_284_6,plain,
    ( hBOOL(hAPP(fun(U_1044,bool),bool,hAPP(U_1044,fun(fun(U_1044,bool),bool),member(U_1044),hAPP(fun(U_1044,bool),U_1044,U_1041,U_1043)),U_1043))
    | ~ hBOOL(hAPP(fun(U_1044,bool),bool,hAPP(U_1044,fun(fun(U_1044,bool),bool),member(U_1044),hAPP(U_1044,U_1044,hAPP(U_1044,fun(U_1044,U_1044),U_1042,sK32(U_1044,U_1043,U_1042,U_1041)),sK33(U_1044,U_1043,U_1042,U_1041))),hAPP(fun(U_1044,bool),fun(U_1044,bool),hAPP(U_1044,fun(fun(U_1044,bool),fun(U_1044,bool)),insert(U_1044),sK32(U_1044,U_1043,U_1042,U_1041)),hAPP(fun(U_1044,bool),fun(U_1044,bool),hAPP(U_1044,fun(fun(U_1044,bool),fun(U_1044,bool)),insert(U_1044),sK33(U_1044,U_1043,U_1042,U_1041)),bot_bot(fun(U_1044,bool))))))
    | ti(fun(U_1044,bool),U_1043) = bot_bot(fun(U_1044,bool))
    | ~ hBOOL(hAPP(fun(U_1044,bool),bool,finite_finite(U_1044),U_1043))
    | ~ hBOOL(hAPP(fun(fun(U_1044,bool),U_1044),bool,hAPP(fun(U_1044,fun(U_1044,U_1044)),fun(fun(fun(U_1044,bool),U_1044),bool),finite_folding_one(U_1044),U_1042),U_1041)) ),
    inference(clausify,[status(thm)],[f_284_5]) ).

fof(f_285_1,plain,
    ! [X_c,X_b,A_3,F,Z_2,G,F_1] :
      ( hAPP(fun(X_c,bool),X_b,F_1,A_3) = ti(X_b,Z_2)
      | ? [X_2] :
          ( hAPP(X_c,X_b,G,X_2) != ti(X_b,Z_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_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_2),G),F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_214_folding__image__simple_Oneutral]) ).

fof(f_285_2,plain,
    ! [U_1052,U_1051,U_1050,U_1049,U_1048,U_1047,U_1046] :
      ( hAPP(fun(U_1052,bool),U_1051,U_1046,U_1050) = ti(U_1051,U_1048)
      | ? [U_1045] :
          ( hAPP(U_1052,U_1051,U_1047,U_1045) != ti(U_1051,U_1048)
          & hBOOL(hAPP(fun(U_1052,bool),bool,hAPP(U_1052,fun(fun(U_1052,bool),bool),member(U_1052),U_1045),U_1050)) )
      | ~ hBOOL(hAPP(fun(U_1052,bool),bool,finite_finite(U_1052),U_1050))
      | ~ hBOOL(hAPP(fun(fun(U_1052,bool),U_1051),bool,hAPP(fun(U_1052,U_1051),fun(fun(fun(U_1052,bool),U_1051),bool),hAPP(U_1051,fun(fun(U_1052,U_1051),fun(fun(fun(U_1052,bool),U_1051),bool)),hAPP(fun(U_1051,fun(U_1051,U_1051)),fun(U_1051,fun(fun(U_1052,U_1051),fun(fun(fun(U_1052,bool),U_1051),bool))),finite1357897459simple(U_1051,U_1052),U_1049),U_1048),U_1047),U_1046)) ),
    inference(variable_rename,[status(thm)],[f_285_1]) ).

fof(f_285_3,plain,
    ! [U_1052,U_1051,U_1050,U_1049,U_1048,U_1047,U_1046] :
      ( hAPP(fun(U_1052,bool),U_1051,U_1046,U_1050) = ti(U_1051,U_1048)
      | ( hAPP(U_1052,U_1051,U_1047,sK34(U_1052,U_1051,U_1050,U_1049,U_1048,U_1047,U_1046)) != ti(U_1051,U_1048)
        & hBOOL(hAPP(fun(U_1052,bool),bool,hAPP(U_1052,fun(fun(U_1052,bool),bool),member(U_1052),sK34(U_1052,U_1051,U_1050,U_1049,U_1048,U_1047,U_1046)),U_1050)) )
      | ~ hBOOL(hAPP(fun(U_1052,bool),bool,finite_finite(U_1052),U_1050))
      | ~ hBOOL(hAPP(fun(fun(U_1052,bool),U_1051),bool,hAPP(fun(U_1052,U_1051),fun(fun(fun(U_1052,bool),U_1051),bool),hAPP(U_1051,fun(fun(U_1052,U_1051),fun(fun(fun(U_1052,bool),U_1051),bool)),hAPP(fun(U_1051,fun(U_1051,U_1051)),fun(U_1051,fun(fun(U_1052,U_1051),fun(fun(fun(U_1052,bool),U_1051),bool))),finite1357897459simple(U_1051,U_1052),U_1049),U_1048),U_1047),U_1046)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(U_1045,sK34(U_1052,U_1051,U_1050,U_1049,U_1048,U_1047,U_1046))],[f_285_2]) ).

fof(f_285_4,plain,
    ( ! [U_1050,U_1046,U_1047,U_1048,U_1051,U_1049,U_1052] :
        ( hAPP(U_1052,U_1051,U_1047,sK34(U_1052,U_1051,U_1050,U_1049,U_1048,U_1047,U_1046)) != ti(U_1051,U_1048)
        | ~ sP50(U_1050,U_1046,U_1047,U_1048,U_1051,U_1049,U_1052) )
    & ! [U_1050,U_1046,U_1047,U_1048,U_1051,U_1049,U_1052] :
        ( hBOOL(hAPP(fun(U_1052,bool),bool,hAPP(U_1052,fun(fun(U_1052,bool),bool),member(U_1052),sK34(U_1052,U_1051,U_1050,U_1049,U_1048,U_1047,U_1046)),U_1050))
        | ~ sP50(U_1050,U_1046,U_1047,U_1048,U_1051,U_1049,U_1052) )
    & ! [U_1050,U_1046,U_1047,U_1048,U_1051,U_1049,U_1052] :
        ( hAPP(fun(U_1052,bool),U_1051,U_1046,U_1050) = ti(U_1051,U_1048)
        | sP50(U_1050,U_1046,U_1047,U_1048,U_1051,U_1049,U_1052)
        | ~ hBOOL(hAPP(fun(U_1052,bool),bool,finite_finite(U_1052),U_1050))
        | ~ hBOOL(hAPP(fun(fun(U_1052,bool),U_1051),bool,hAPP(fun(U_1052,U_1051),fun(fun(fun(U_1052,bool),U_1051),bool),hAPP(U_1051,fun(fun(U_1052,U_1051),fun(fun(fun(U_1052,bool),U_1051),bool)),hAPP(fun(U_1051,fun(U_1051,U_1051)),fun(U_1051,fun(fun(U_1052,U_1051),fun(fun(fun(U_1052,bool),U_1051),bool))),finite1357897459simple(U_1051,U_1052),U_1049),U_1048),U_1047),U_1046)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP50])],[f_285_3]) ).

cnf(f_285_5,plain,
    ( hAPP(fun(U_1052,bool),U_1051,U_1046,U_1050) = ti(U_1051,U_1048)
    | sP50(U_1050,U_1046,U_1047,U_1048,U_1051,U_1049,U_1052)
    | ~ hBOOL(hAPP(fun(U_1052,bool),bool,finite_finite(U_1052),U_1050))
    | ~ hBOOL(hAPP(fun(fun(U_1052,bool),U_1051),bool,hAPP(fun(U_1052,U_1051),fun(fun(fun(U_1052,bool),U_1051),bool),hAPP(U_1051,fun(fun(U_1052,U_1051),fun(fun(fun(U_1052,bool),U_1051),bool)),hAPP(fun(U_1051,fun(U_1051,U_1051)),fun(U_1051,fun(fun(U_1052,U_1051),fun(fun(fun(U_1052,bool),U_1051),bool))),finite1357897459simple(U_1051,U_1052),U_1049),U_1048),U_1047),U_1046)) ),
    inference(clausify,[status(thm)],[f_285_4]) ).

cnf(f_285_6,plain,
    ( hBOOL(hAPP(fun(U_1052,bool),bool,hAPP(U_1052,fun(fun(U_1052,bool),bool),member(U_1052),sK34(U_1052,U_1051,U_1050,U_1049,U_1048,U_1047,U_1046)),U_1050))
    | ~ sP50(U_1050,U_1046,U_1047,U_1048,U_1051,U_1049,U_1052) ),
    inference(clausify,[status(thm)],[f_285_4]) ).

cnf(f_285_7,plain,
    ( hAPP(U_1052,U_1051,U_1047,sK34(U_1052,U_1051,U_1050,U_1049,U_1048,U_1047,U_1046)) != ti(U_1051,U_1048)
    | ~ sP50(U_1050,U_1046,U_1047,U_1048,U_1051,U_1049,U_1052) ),
    inference(clausify,[status(thm)],[f_285_4]) ).

fof(f_286_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_215_card_Oremove]) ).

fof(f_286_2,plain,
    ! [U_1055,U_1054,U_1053] :
      ( hAPP(fun(U_1055,bool),nat,finite_card(U_1055),U_1053) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(fun(U_1055,bool),nat,finite_card(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_1054),bot_bot(fun(U_1055,bool))))))
      | ~ hBOOL(hAPP(fun(U_1055,bool),bool,hAPP(U_1055,fun(fun(U_1055,bool),bool),member(U_1055),U_1054),U_1053))
      | ~ hBOOL(hAPP(fun(U_1055,bool),bool,finite_finite(U_1055),U_1053)) ),
    inference(variable_rename,[status(thm)],[f_286_1]) ).

fof(f_286_3,plain,
    ! [U_1054,U_1053,U_1055] :
      ( hAPP(fun(U_1055,bool),nat,finite_card(U_1055),U_1053) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(fun(U_1055,bool),nat,finite_card(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_1054),bot_bot(fun(U_1055,bool))))))
      | ~ hBOOL(hAPP(fun(U_1055,bool),bool,hAPP(U_1055,fun(fun(U_1055,bool),bool),member(U_1055),U_1054),U_1053))
      | ~ hBOOL(hAPP(fun(U_1055,bool),bool,finite_finite(U_1055),U_1053)) ),
    inference(definitional_conversion,[status(esa)],[f_286_2]) ).

cnf(f_286_4,plain,
    ( hAPP(fun(U_1055,bool),nat,finite_card(U_1055),U_1053) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(fun(U_1055,bool),nat,finite_card(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_1054),bot_bot(fun(U_1055,bool))))))
    | ~ hBOOL(hAPP(fun(U_1055,bool),bool,hAPP(U_1055,fun(fun(U_1055,bool),bool),member(U_1055),U_1054),U_1053))
    | ~ hBOOL(hAPP(fun(U_1055,bool),bool,finite_finite(U_1055),U_1053)) ),
    inference(clausify,[status(thm)],[f_286_3]) ).

fof(f_287_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_216_card_Oinsert__remove]) ).

fof(f_287_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(U_1058,fun(fun(U_1058,bool),fun(U_1058,bool)),insert(U_1058),U_1057),U_1056)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),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))))))
      | ~ hBOOL(hAPP(fun(U_1058,bool),bool,finite_finite(U_1058),U_1056)) ),
    inference(variable_rename,[status(thm)],[f_287_1]) ).

fof(f_287_3,plain,
    ! [U_1057,U_1058,U_1056] :
      ( hAPP(fun(U_1058,bool),nat,finite_card(U_1058),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),U_1056)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),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))))))
      | ~ hBOOL(hAPP(fun(U_1058,bool),bool,finite_finite(U_1058),U_1056)) ),
    inference(definitional_conversion,[status(esa)],[f_287_2]) ).

cnf(f_287_4,plain,
    ( hAPP(fun(U_1058,bool),nat,finite_card(U_1058),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),U_1056)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),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))))))
    | ~ hBOOL(hAPP(fun(U_1058,bool),bool,finite_finite(U_1058),U_1056)) ),
    inference(clausify,[status(thm)],[f_287_3]) ).

fof(f_288_1,plain,
    ! [X_b,B_1,A_3,F,F_1] :
      ( hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(fun(X_b,bool),X_b,F_1,B_1)),hAPP(fun(X_b,bool),X_b,F_1,A_3)) = hAPP(fun(X_b,bool),X_b,F_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)),B_1),A_3))
      | ti(fun(X_b,bool),B_1) = 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_1)) ),
    inference(fof_nnf,[status(thm)],[fact_217_folding__one__idem_Osubset__idem]) ).

fof(f_288_2,plain,
    ! [U_1063,U_1062,U_1061,U_1060,U_1059] :
      ( hAPP(U_1063,U_1063,hAPP(U_1063,fun(U_1063,U_1063),U_1060,hAPP(fun(U_1063,bool),U_1063,U_1059,U_1062)),hAPP(fun(U_1063,bool),U_1063,U_1059,U_1061)) = hAPP(fun(U_1063,bool),U_1063,U_1059,U_1061)
      | ~ hBOOL(hAPP(fun(U_1063,bool),bool,hAPP(fun(U_1063,bool),fun(fun(U_1063,bool),bool),ord_less_eq(fun(U_1063,bool)),U_1062),U_1061))
      | ti(fun(U_1063,bool),U_1062) = bot_bot(fun(U_1063,bool))
      | ~ hBOOL(hAPP(fun(U_1063,bool),bool,finite_finite(U_1063),U_1061))
      | ~ hBOOL(hAPP(fun(fun(U_1063,bool),U_1063),bool,hAPP(fun(U_1063,fun(U_1063,U_1063)),fun(fun(fun(U_1063,bool),U_1063),bool),finite2073411215e_idem(U_1063),U_1060),U_1059)) ),
    inference(variable_rename,[status(thm)],[f_288_1]) ).

fof(f_288_3,plain,
    ! [U_1059,U_1060,U_1062,U_1061,U_1063] :
      ( hAPP(U_1063,U_1063,hAPP(U_1063,fun(U_1063,U_1063),U_1060,hAPP(fun(U_1063,bool),U_1063,U_1059,U_1062)),hAPP(fun(U_1063,bool),U_1063,U_1059,U_1061)) = hAPP(fun(U_1063,bool),U_1063,U_1059,U_1061)
      | ~ hBOOL(hAPP(fun(U_1063,bool),bool,hAPP(fun(U_1063,bool),fun(fun(U_1063,bool),bool),ord_less_eq(fun(U_1063,bool)),U_1062),U_1061))
      | ti(fun(U_1063,bool),U_1062) = bot_bot(fun(U_1063,bool))
      | ~ hBOOL(hAPP(fun(U_1063,bool),bool,finite_finite(U_1063),U_1061))
      | ~ hBOOL(hAPP(fun(fun(U_1063,bool),U_1063),bool,hAPP(fun(U_1063,fun(U_1063,U_1063)),fun(fun(fun(U_1063,bool),U_1063),bool),finite2073411215e_idem(U_1063),U_1060),U_1059)) ),
    inference(definitional_conversion,[status(esa)],[f_288_2]) ).

cnf(f_288_4,plain,
    ( hAPP(U_1063,U_1063,hAPP(U_1063,fun(U_1063,U_1063),U_1060,hAPP(fun(U_1063,bool),U_1063,U_1059,U_1062)),hAPP(fun(U_1063,bool),U_1063,U_1059,U_1061)) = hAPP(fun(U_1063,bool),U_1063,U_1059,U_1061)
    | ~ hBOOL(hAPP(fun(U_1063,bool),bool,hAPP(fun(U_1063,bool),fun(fun(U_1063,bool),bool),ord_less_eq(fun(U_1063,bool)),U_1062),U_1061))
    | ti(fun(U_1063,bool),U_1062) = bot_bot(fun(U_1063,bool))
    | ~ hBOOL(hAPP(fun(U_1063,bool),bool,finite_finite(U_1063),U_1061))
    | ~ hBOOL(hAPP(fun(fun(U_1063,bool),U_1063),bool,hAPP(fun(U_1063,fun(U_1063,U_1063)),fun(fun(fun(U_1063,bool),U_1063),bool),finite2073411215e_idem(U_1063),U_1060),U_1059)) ),
    inference(clausify,[status(thm)],[f_288_3]) ).

fof(f_289_1,plain,
    ! [X_b,X_1,A_3,F,F_1] :
      ( hAPP(fun(X_b,bool),X_b,F_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(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),hAPP(fun(X_b,bool),X_b,F_1,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_1)) ),
    inference(fof_nnf,[status(thm)],[fact_218_folding__one__idem_Oinsert__idem]) ).

fof(f_289_2,plain,
    ! [U_1068,U_1067,U_1066,U_1065,U_1064] :
      ( hAPP(fun(U_1068,bool),U_1068,U_1064,hAPP(fun(U_1068,bool),fun(U_1068,bool),hAPP(U_1068,fun(fun(U_1068,bool),fun(U_1068,bool)),insert(U_1068),U_1067),U_1066)) = hAPP(U_1068,U_1068,hAPP(U_1068,fun(U_1068,U_1068),U_1065,U_1067),hAPP(fun(U_1068,bool),U_1068,U_1064,U_1066))
      | ti(fun(U_1068,bool),U_1066) = bot_bot(fun(U_1068,bool))
      | ~ hBOOL(hAPP(fun(U_1068,bool),bool,finite_finite(U_1068),U_1066))
      | ~ hBOOL(hAPP(fun(fun(U_1068,bool),U_1068),bool,hAPP(fun(U_1068,fun(U_1068,U_1068)),fun(fun(fun(U_1068,bool),U_1068),bool),finite2073411215e_idem(U_1068),U_1065),U_1064)) ),
    inference(variable_rename,[status(thm)],[f_289_1]) ).

fof(f_289_3,plain,
    ! [U_1068,U_1065,U_1067,U_1064,U_1066] :
      ( hAPP(fun(U_1068,bool),U_1068,U_1064,hAPP(fun(U_1068,bool),fun(U_1068,bool),hAPP(U_1068,fun(fun(U_1068,bool),fun(U_1068,bool)),insert(U_1068),U_1067),U_1066)) = hAPP(U_1068,U_1068,hAPP(U_1068,fun(U_1068,U_1068),U_1065,U_1067),hAPP(fun(U_1068,bool),U_1068,U_1064,U_1066))
      | ti(fun(U_1068,bool),U_1066) = bot_bot(fun(U_1068,bool))
      | ~ hBOOL(hAPP(fun(U_1068,bool),bool,finite_finite(U_1068),U_1066))
      | ~ hBOOL(hAPP(fun(fun(U_1068,bool),U_1068),bool,hAPP(fun(U_1068,fun(U_1068,U_1068)),fun(fun(fun(U_1068,bool),U_1068),bool),finite2073411215e_idem(U_1068),U_1065),U_1064)) ),
    inference(definitional_conversion,[status(esa)],[f_289_2]) ).

cnf(f_289_4,plain,
    ( hAPP(fun(U_1068,bool),U_1068,U_1064,hAPP(fun(U_1068,bool),fun(U_1068,bool),hAPP(U_1068,fun(fun(U_1068,bool),fun(U_1068,bool)),insert(U_1068),U_1067),U_1066)) = hAPP(U_1068,U_1068,hAPP(U_1068,fun(U_1068,U_1068),U_1065,U_1067),hAPP(fun(U_1068,bool),U_1068,U_1064,U_1066))
    | ti(fun(U_1068,bool),U_1066) = bot_bot(fun(U_1068,bool))
    | ~ hBOOL(hAPP(fun(U_1068,bool),bool,finite_finite(U_1068),U_1066))
    | ~ hBOOL(hAPP(fun(fun(U_1068,bool),U_1068),bool,hAPP(fun(U_1068,fun(U_1068,U_1068)),fun(fun(fun(U_1068,bool),U_1068),bool),finite2073411215e_idem(U_1068),U_1065),U_1064)) ),
    inference(clausify,[status(thm)],[f_289_3]) ).

fof(f_290_1,plain,
    ! [X_b,Pa,F_1] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_1))
      | ? [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_1) = bot_bot(fun(X_b,bool))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_219_finite__ne__induct]) ).

fof(f_290_2,plain,
    ! [U_1074,U_1073,U_1072] :
      ( hBOOL(hAPP(fun(U_1074,bool),bool,U_1073,U_1072))
      | ? [U_1071,U_1070] :
          ( ~ hBOOL(hAPP(fun(U_1074,bool),bool,U_1073,hAPP(fun(U_1074,bool),fun(U_1074,bool),hAPP(U_1074,fun(fun(U_1074,bool),fun(U_1074,bool)),insert(U_1074),U_1071),U_1070)))
          & hBOOL(hAPP(fun(U_1074,bool),bool,U_1073,U_1070))
          & ~ hBOOL(hAPP(fun(U_1074,bool),bool,hAPP(U_1074,fun(fun(U_1074,bool),bool),member(U_1074),U_1071),U_1070))
          & ti(fun(U_1074,bool),U_1070) != bot_bot(fun(U_1074,bool))
          & hBOOL(hAPP(fun(U_1074,bool),bool,finite_finite(U_1074),U_1070)) )
      | ? [U_1069] : ~ hBOOL(hAPP(fun(U_1074,bool),bool,U_1073,hAPP(fun(U_1074,bool),fun(U_1074,bool),hAPP(U_1074,fun(fun(U_1074,bool),fun(U_1074,bool)),insert(U_1074),U_1069),bot_bot(fun(U_1074,bool)))))
      | ti(fun(U_1074,bool),U_1072) = bot_bot(fun(U_1074,bool))
      | ~ hBOOL(hAPP(fun(U_1074,bool),bool,finite_finite(U_1074),U_1072)) ),
    inference(variable_rename,[status(thm)],[f_290_1]) ).

fof(f_290_3,plain,
    ! [U_1074,U_1073,U_1072] :
      ( hBOOL(hAPP(fun(U_1074,bool),bool,U_1073,U_1072))
      | ? [U_1071,U_1070] :
          ( ~ hBOOL(hAPP(fun(U_1074,bool),bool,U_1073,hAPP(fun(U_1074,bool),fun(U_1074,bool),hAPP(U_1074,fun(fun(U_1074,bool),fun(U_1074,bool)),insert(U_1074),U_1071),U_1070)))
          & hBOOL(hAPP(fun(U_1074,bool),bool,U_1073,U_1070))
          & ~ hBOOL(hAPP(fun(U_1074,bool),bool,hAPP(U_1074,fun(fun(U_1074,bool),bool),member(U_1074),U_1071),U_1070))
          & ti(fun(U_1074,bool),U_1070) != bot_bot(fun(U_1074,bool))
          & hBOOL(hAPP(fun(U_1074,bool),bool,finite_finite(U_1074),U_1070)) )
      | ~ hBOOL(hAPP(fun(U_1074,bool),bool,U_1073,hAPP(fun(U_1074,bool),fun(U_1074,bool),hAPP(U_1074,fun(fun(U_1074,bool),fun(U_1074,bool)),insert(U_1074),sK35(U_1074,U_1073,U_1072)),bot_bot(fun(U_1074,bool)))))
      | ti(fun(U_1074,bool),U_1072) = bot_bot(fun(U_1074,bool))
      | ~ hBOOL(hAPP(fun(U_1074,bool),bool,finite_finite(U_1074),U_1072)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(U_1069,sK35(U_1074,U_1073,U_1072))],[f_290_2]) ).

fof(f_290_4,plain,
    ! [U_1074,U_1073,U_1072] :
      ( hBOOL(hAPP(fun(U_1074,bool),bool,U_1073,U_1072))
      | ? [U_1070] :
          ( ~ hBOOL(hAPP(fun(U_1074,bool),bool,U_1073,hAPP(fun(U_1074,bool),fun(U_1074,bool),hAPP(U_1074,fun(fun(U_1074,bool),fun(U_1074,bool)),insert(U_1074),sK36(U_1074,U_1073,U_1072)),U_1070)))
          & hBOOL(hAPP(fun(U_1074,bool),bool,U_1073,U_1070))
          & ~ hBOOL(hAPP(fun(U_1074,bool),bool,hAPP(U_1074,fun(fun(U_1074,bool),bool),member(U_1074),sK36(U_1074,U_1073,U_1072)),U_1070))
          & ti(fun(U_1074,bool),U_1070) != bot_bot(fun(U_1074,bool))
          & hBOOL(hAPP(fun(U_1074,bool),bool,finite_finite(U_1074),U_1070)) )
      | ~ hBOOL(hAPP(fun(U_1074,bool),bool,U_1073,hAPP(fun(U_1074,bool),fun(U_1074,bool),hAPP(U_1074,fun(fun(U_1074,bool),fun(U_1074,bool)),insert(U_1074),sK35(U_1074,U_1073,U_1072)),bot_bot(fun(U_1074,bool)))))
      | ti(fun(U_1074,bool),U_1072) = bot_bot(fun(U_1074,bool))
      | ~ hBOOL(hAPP(fun(U_1074,bool),bool,finite_finite(U_1074),U_1072)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK36]),skolemize(U_1071,sK36(U_1074,U_1073,U_1072))],[f_290_3]) ).

fof(f_290_5,plain,
    ! [U_1074,U_1073,U_1072] :
      ( hBOOL(hAPP(fun(U_1074,bool),bool,U_1073,U_1072))
      | ( ~ hBOOL(hAPP(fun(U_1074,bool),bool,U_1073,hAPP(fun(U_1074,bool),fun(U_1074,bool),hAPP(U_1074,fun(fun(U_1074,bool),fun(U_1074,bool)),insert(U_1074),sK36(U_1074,U_1073,U_1072)),sK37(U_1074,U_1073,U_1072))))
        & hBOOL(hAPP(fun(U_1074,bool),bool,U_1073,sK37(U_1074,U_1073,U_1072)))
        & ~ hBOOL(hAPP(fun(U_1074,bool),bool,hAPP(U_1074,fun(fun(U_1074,bool),bool),member(U_1074),sK36(U_1074,U_1073,U_1072)),sK37(U_1074,U_1073,U_1072)))
        & ti(fun(U_1074,bool),sK37(U_1074,U_1073,U_1072)) != bot_bot(fun(U_1074,bool))
        & hBOOL(hAPP(fun(U_1074,bool),bool,finite_finite(U_1074),sK37(U_1074,U_1073,U_1072))) )
      | ~ hBOOL(hAPP(fun(U_1074,bool),bool,U_1073,hAPP(fun(U_1074,bool),fun(U_1074,bool),hAPP(U_1074,fun(fun(U_1074,bool),fun(U_1074,bool)),insert(U_1074),sK35(U_1074,U_1073,U_1072)),bot_bot(fun(U_1074,bool)))))
      | ti(fun(U_1074,bool),U_1072) = bot_bot(fun(U_1074,bool))
      | ~ hBOOL(hAPP(fun(U_1074,bool),bool,finite_finite(U_1074),U_1072)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK37]),skolemize(U_1070,sK37(U_1074,U_1073,U_1072))],[f_290_4]) ).

fof(f_290_6,plain,
    ( ! [U_1072,U_1073,U_1074] :
        ( ~ hBOOL(hAPP(fun(U_1074,bool),bool,U_1073,hAPP(fun(U_1074,bool),fun(U_1074,bool),hAPP(U_1074,fun(fun(U_1074,bool),fun(U_1074,bool)),insert(U_1074),sK36(U_1074,U_1073,U_1072)),sK37(U_1074,U_1073,U_1072))))
        | ~ sP51(U_1072,U_1073,U_1074) )
    & ! [U_1072,U_1073,U_1074] :
        ( hBOOL(hAPP(fun(U_1074,bool),bool,U_1073,sK37(U_1074,U_1073,U_1072)))
        | ~ sP51(U_1072,U_1073,U_1074) )
    & ! [U_1072,U_1073,U_1074] :
        ( ~ hBOOL(hAPP(fun(U_1074,bool),bool,hAPP(U_1074,fun(fun(U_1074,bool),bool),member(U_1074),sK36(U_1074,U_1073,U_1072)),sK37(U_1074,U_1073,U_1072)))
        | ~ sP51(U_1072,U_1073,U_1074) )
    & ! [U_1072,U_1073,U_1074] :
        ( ti(fun(U_1074,bool),sK37(U_1074,U_1073,U_1072)) != bot_bot(fun(U_1074,bool))
        | ~ sP51(U_1072,U_1073,U_1074) )
    & ! [U_1072,U_1073,U_1074] :
        ( hBOOL(hAPP(fun(U_1074,bool),bool,finite_finite(U_1074),sK37(U_1074,U_1073,U_1072)))
        | ~ sP51(U_1072,U_1073,U_1074) )
    & ! [U_1072,U_1073,U_1074] :
        ( hBOOL(hAPP(fun(U_1074,bool),bool,U_1073,U_1072))
        | sP51(U_1072,U_1073,U_1074)
        | ~ hBOOL(hAPP(fun(U_1074,bool),bool,U_1073,hAPP(fun(U_1074,bool),fun(U_1074,bool),hAPP(U_1074,fun(fun(U_1074,bool),fun(U_1074,bool)),insert(U_1074),sK35(U_1074,U_1073,U_1072)),bot_bot(fun(U_1074,bool)))))
        | ti(fun(U_1074,bool),U_1072) = bot_bot(fun(U_1074,bool))
        | ~ hBOOL(hAPP(fun(U_1074,bool),bool,finite_finite(U_1074),U_1072)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP51])],[f_290_5]) ).

cnf(f_290_7,plain,
    ( hBOOL(hAPP(fun(U_1074,bool),bool,U_1073,U_1072))
    | sP51(U_1072,U_1073,U_1074)
    | ~ hBOOL(hAPP(fun(U_1074,bool),bool,U_1073,hAPP(fun(U_1074,bool),fun(U_1074,bool),hAPP(U_1074,fun(fun(U_1074,bool),fun(U_1074,bool)),insert(U_1074),sK35(U_1074,U_1073,U_1072)),bot_bot(fun(U_1074,bool)))))
    | ti(fun(U_1074,bool),U_1072) = bot_bot(fun(U_1074,bool))
    | ~ hBOOL(hAPP(fun(U_1074,bool),bool,finite_finite(U_1074),U_1072)) ),
    inference(clausify,[status(thm)],[f_290_6]) ).

cnf(f_290_8,plain,
    ( hBOOL(hAPP(fun(U_1074,bool),bool,finite_finite(U_1074),sK37(U_1074,U_1073,U_1072)))
    | ~ sP51(U_1072,U_1073,U_1074) ),
    inference(clausify,[status(thm)],[f_290_6]) ).

cnf(f_290_9,plain,
    ( ti(fun(U_1074,bool),sK37(U_1074,U_1073,U_1072)) != bot_bot(fun(U_1074,bool))
    | ~ sP51(U_1072,U_1073,U_1074) ),
    inference(clausify,[status(thm)],[f_290_6]) ).

cnf(f_290_10,plain,
    ( ~ hBOOL(hAPP(fun(U_1074,bool),bool,hAPP(U_1074,fun(fun(U_1074,bool),bool),member(U_1074),sK36(U_1074,U_1073,U_1072)),sK37(U_1074,U_1073,U_1072)))
    | ~ sP51(U_1072,U_1073,U_1074) ),
    inference(clausify,[status(thm)],[f_290_6]) ).

cnf(f_290_11,plain,
    ( hBOOL(hAPP(fun(U_1074,bool),bool,U_1073,sK37(U_1074,U_1073,U_1072)))
    | ~ sP51(U_1072,U_1073,U_1074) ),
    inference(clausify,[status(thm)],[f_290_6]) ).

cnf(f_290_12,plain,
    ( ~ hBOOL(hAPP(fun(U_1074,bool),bool,U_1073,hAPP(fun(U_1074,bool),fun(U_1074,bool),hAPP(U_1074,fun(fun(U_1074,bool),fun(U_1074,bool)),insert(U_1074),sK36(U_1074,U_1073,U_1072)),sK37(U_1074,U_1073,U_1072))))
    | ~ sP51(U_1072,U_1073,U_1074) ),
    inference(clausify,[status(thm)],[f_290_6]) ).

fof(f_291_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_220_the__elem__def]) ).

fof(f_291_2,plain,
    ! [U_1076,U_1075] : hAPP(fun(U_1076,bool),U_1076,the_elem(U_1076),U_1075) = hAPP(fun(U_1076,bool),U_1076,the(U_1076),hAPP(fun(U_1076,fun(U_1076,bool)),fun(U_1076,bool),hAPP(fun(fun(U_1076,bool),bool),fun(fun(U_1076,fun(U_1076,bool)),fun(U_1076,bool)),combb(fun(U_1076,bool),bool,U_1076),hAPP(fun(U_1076,bool),fun(fun(U_1076,bool),bool),fequal(fun(U_1076,bool)),U_1075)),hAPP(fun(U_1076,bool),fun(U_1076,fun(U_1076,bool)),hAPP(fun(U_1076,fun(fun(U_1076,bool),fun(U_1076,bool))),fun(fun(U_1076,bool),fun(U_1076,fun(U_1076,bool))),combc(U_1076,fun(U_1076,bool),fun(U_1076,bool)),insert(U_1076)),bot_bot(fun(U_1076,bool))))),
    inference(variable_rename,[status(thm)],[f_291_1]) ).

fof(f_291_3,plain,
    ! [U_1075,U_1076] : hAPP(fun(U_1076,bool),U_1076,the_elem(U_1076),U_1075) = hAPP(fun(U_1076,bool),U_1076,the(U_1076),hAPP(fun(U_1076,fun(U_1076,bool)),fun(U_1076,bool),hAPP(fun(fun(U_1076,bool),bool),fun(fun(U_1076,fun(U_1076,bool)),fun(U_1076,bool)),combb(fun(U_1076,bool),bool,U_1076),hAPP(fun(U_1076,bool),fun(fun(U_1076,bool),bool),fequal(fun(U_1076,bool)),U_1075)),hAPP(fun(U_1076,bool),fun(U_1076,fun(U_1076,bool)),hAPP(fun(U_1076,fun(fun(U_1076,bool),fun(U_1076,bool))),fun(fun(U_1076,bool),fun(U_1076,fun(U_1076,bool))),combc(U_1076,fun(U_1076,bool),fun(U_1076,bool)),insert(U_1076)),bot_bot(fun(U_1076,bool))))),
    inference(definitional_conversion,[status(esa)],[f_291_2]) ).

cnf(f_291_4,plain,
    hAPP(fun(U_1076,bool),U_1076,the_elem(U_1076),U_1075) = hAPP(fun(U_1076,bool),U_1076,the(U_1076),hAPP(fun(U_1076,fun(U_1076,bool)),fun(U_1076,bool),hAPP(fun(fun(U_1076,bool),bool),fun(fun(U_1076,fun(U_1076,bool)),fun(U_1076,bool)),combb(fun(U_1076,bool),bool,U_1076),hAPP(fun(U_1076,bool),fun(fun(U_1076,bool),bool),fequal(fun(U_1076,bool)),U_1075)),hAPP(fun(U_1076,bool),fun(U_1076,fun(U_1076,bool)),hAPP(fun(U_1076,fun(fun(U_1076,bool),fun(U_1076,bool))),fun(fun(U_1076,bool),fun(U_1076,fun(U_1076,bool))),combc(U_1076,fun(U_1076,bool),fun(U_1076,bool)),insert(U_1076)),bot_bot(fun(U_1076,bool))))),
    inference(clausify,[status(thm)],[f_291_3]) ).

fof(f_292_1,plain,
    ! [X_a] :
      ( ! [A_1,B,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)),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),C))
      | ~ ab_semigroup_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_221_ab__semigroup__add__class_Oadd__ac_I1_J]) ).

fof(f_292_2,plain,
    ! [U_1080] :
      ( ! [U_1079,U_1078,U_1077] : hAPP(U_1080,U_1080,hAPP(U_1080,fun(U_1080,U_1080),plus_plus(U_1080),hAPP(U_1080,U_1080,hAPP(U_1080,fun(U_1080,U_1080),plus_plus(U_1080),U_1079),U_1078)),U_1077) = hAPP(U_1080,U_1080,hAPP(U_1080,fun(U_1080,U_1080),plus_plus(U_1080),U_1079),hAPP(U_1080,U_1080,hAPP(U_1080,fun(U_1080,U_1080),plus_plus(U_1080),U_1078),U_1077))
      | ~ ab_semigroup_add(U_1080) ),
    inference(variable_rename,[status(thm)],[f_292_1]) ).

fof(f_292_3,plain,
    ! [U_1080,U_1078,U_1079,U_1077] :
      ( hAPP(U_1080,U_1080,hAPP(U_1080,fun(U_1080,U_1080),plus_plus(U_1080),hAPP(U_1080,U_1080,hAPP(U_1080,fun(U_1080,U_1080),plus_plus(U_1080),U_1079),U_1078)),U_1077) = hAPP(U_1080,U_1080,hAPP(U_1080,fun(U_1080,U_1080),plus_plus(U_1080),U_1079),hAPP(U_1080,U_1080,hAPP(U_1080,fun(U_1080,U_1080),plus_plus(U_1080),U_1078),U_1077))
      | ~ ab_semigroup_add(U_1080) ),
    inference(definitional_conversion,[status(esa)],[f_292_2]) ).

cnf(f_292_4,plain,
    ( hAPP(U_1080,U_1080,hAPP(U_1080,fun(U_1080,U_1080),plus_plus(U_1080),hAPP(U_1080,U_1080,hAPP(U_1080,fun(U_1080,U_1080),plus_plus(U_1080),U_1079),U_1078)),U_1077) = hAPP(U_1080,U_1080,hAPP(U_1080,fun(U_1080,U_1080),plus_plus(U_1080),U_1079),hAPP(U_1080,U_1080,hAPP(U_1080,fun(U_1080,U_1080),plus_plus(U_1080),U_1078),U_1077))
    | ~ ab_semigroup_add(U_1080) ),
    inference(clausify,[status(thm)],[f_292_3]) ).

fof(f_293_1,plain,
    ! [X_b] :
      ( ! [A_2,B_3,C_1] :
          ( ( hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),B_3) = 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_3) != ti(X_b,C_1) )
          & ( ti(X_b,B_3) = 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_3) != 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_222_add__left__cancel]) ).

fof(f_293_2,plain,
    ! [U_1084] :
      ( ! [U_1083,U_1082,U_1081] :
          ( ( hAPP(U_1084,U_1084,hAPP(U_1084,fun(U_1084,U_1084),plus_plus(U_1084),U_1083),U_1082) = hAPP(U_1084,U_1084,hAPP(U_1084,fun(U_1084,U_1084),plus_plus(U_1084),U_1083),U_1081)
            | ti(U_1084,U_1082) != ti(U_1084,U_1081) )
          & ( ti(U_1084,U_1082) = ti(U_1084,U_1081)
            | hAPP(U_1084,U_1084,hAPP(U_1084,fun(U_1084,U_1084),plus_plus(U_1084),U_1083),U_1082) != hAPP(U_1084,U_1084,hAPP(U_1084,fun(U_1084,U_1084),plus_plus(U_1084),U_1083),U_1081) ) )
      | ~ cancel_semigroup_add(U_1084) ),
    inference(variable_rename,[status(thm)],[f_293_1]) ).

fof(f_293_3,plain,
    ! [U_1084] :
      ( ( ! [U_1090,U_1088,U_1086] :
            ( hAPP(U_1084,U_1084,hAPP(U_1084,fun(U_1084,U_1084),plus_plus(U_1084),U_1090),U_1088) = hAPP(U_1084,U_1084,hAPP(U_1084,fun(U_1084,U_1084),plus_plus(U_1084),U_1090),U_1086)
            | ti(U_1084,U_1088) != ti(U_1084,U_1086) )
        & ! [U_1089,U_1087,U_1085] :
            ( ti(U_1084,U_1087) = ti(U_1084,U_1085)
            | hAPP(U_1084,U_1084,hAPP(U_1084,fun(U_1084,U_1084),plus_plus(U_1084),U_1089),U_1087) != hAPP(U_1084,U_1084,hAPP(U_1084,fun(U_1084,U_1084),plus_plus(U_1084),U_1089),U_1085) ) )
      | ~ cancel_semigroup_add(U_1084) ),
    inference(miniscope,[status(thm)],[f_293_2]) ).

fof(f_293_4,plain,
    ( ! [U_1088,U_1084,U_1086,U_1085,U_1090,U_1087,U_1089] :
        ( hAPP(U_1084,U_1084,hAPP(U_1084,fun(U_1084,U_1084),plus_plus(U_1084),U_1090),U_1088) = hAPP(U_1084,U_1084,hAPP(U_1084,fun(U_1084,U_1084),plus_plus(U_1084),U_1090),U_1086)
        | ti(U_1084,U_1088) != ti(U_1084,U_1086)
        | ~ sP52(U_1088,U_1084,U_1086,U_1085,U_1090,U_1087,U_1089) )
    & ! [U_1088,U_1084,U_1086,U_1085,U_1090,U_1087,U_1089] :
        ( ti(U_1084,U_1087) = ti(U_1084,U_1085)
        | hAPP(U_1084,U_1084,hAPP(U_1084,fun(U_1084,U_1084),plus_plus(U_1084),U_1089),U_1087) != hAPP(U_1084,U_1084,hAPP(U_1084,fun(U_1084,U_1084),plus_plus(U_1084),U_1089),U_1085)
        | ~ sP52(U_1088,U_1084,U_1086,U_1085,U_1090,U_1087,U_1089) )
    & ! [U_1088,U_1084,U_1086,U_1085,U_1090,U_1087,U_1089] :
        ( sP52(U_1088,U_1084,U_1086,U_1085,U_1090,U_1087,U_1089)
        | ~ cancel_semigroup_add(U_1084) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP52])],[f_293_3]) ).

cnf(f_293_5,plain,
    ( sP52(U_1088,U_1084,U_1086,U_1085,U_1090,U_1087,U_1089)
    | ~ cancel_semigroup_add(U_1084) ),
    inference(clausify,[status(thm)],[f_293_4]) ).

cnf(f_293_6,plain,
    ( ti(U_1084,U_1087) = ti(U_1084,U_1085)
    | hAPP(U_1084,U_1084,hAPP(U_1084,fun(U_1084,U_1084),plus_plus(U_1084),U_1089),U_1087) != hAPP(U_1084,U_1084,hAPP(U_1084,fun(U_1084,U_1084),plus_plus(U_1084),U_1089),U_1085)
    | ~ sP52(U_1088,U_1084,U_1086,U_1085,U_1090,U_1087,U_1089) ),
    inference(clausify,[status(thm)],[f_293_4]) ).

cnf(f_293_7,plain,
    ( hAPP(U_1084,U_1084,hAPP(U_1084,fun(U_1084,U_1084),plus_plus(U_1084),U_1090),U_1088) = hAPP(U_1084,U_1084,hAPP(U_1084,fun(U_1084,U_1084),plus_plus(U_1084),U_1090),U_1086)
    | ti(U_1084,U_1088) != ti(U_1084,U_1086)
    | ~ sP52(U_1088,U_1084,U_1086,U_1085,U_1090,U_1087,U_1089) ),
    inference(clausify,[status(thm)],[f_293_4]) ).

fof(f_294_1,plain,
    ! [X_b] :
      ( ! [B_3,A_2,C_1] :
          ( ( hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),B_3),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_3) != ti(X_b,C_1) )
          & ( ti(X_b,B_3) = ti(X_b,C_1)
            | hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),B_3),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_223_add__right__cancel]) ).

fof(f_294_2,plain,
    ! [U_1094] :
      ( ! [U_1093,U_1092,U_1091] :
          ( ( hAPP(U_1094,U_1094,hAPP(U_1094,fun(U_1094,U_1094),plus_plus(U_1094),U_1093),U_1092) = hAPP(U_1094,U_1094,hAPP(U_1094,fun(U_1094,U_1094),plus_plus(U_1094),U_1091),U_1092)
            | ti(U_1094,U_1093) != ti(U_1094,U_1091) )
          & ( ti(U_1094,U_1093) = ti(U_1094,U_1091)
            | hAPP(U_1094,U_1094,hAPP(U_1094,fun(U_1094,U_1094),plus_plus(U_1094),U_1093),U_1092) != hAPP(U_1094,U_1094,hAPP(U_1094,fun(U_1094,U_1094),plus_plus(U_1094),U_1091),U_1092) ) )
      | ~ cancel_semigroup_add(U_1094) ),
    inference(variable_rename,[status(thm)],[f_294_1]) ).

fof(f_294_3,plain,
    ! [U_1094] :
      ( ( ! [U_1100,U_1098,U_1096] :
            ( hAPP(U_1094,U_1094,hAPP(U_1094,fun(U_1094,U_1094),plus_plus(U_1094),U_1100),U_1098) = hAPP(U_1094,U_1094,hAPP(U_1094,fun(U_1094,U_1094),plus_plus(U_1094),U_1096),U_1098)
            | ti(U_1094,U_1100) != ti(U_1094,U_1096) )
        & ! [U_1099,U_1097,U_1095] :
            ( ti(U_1094,U_1099) = ti(U_1094,U_1095)
            | hAPP(U_1094,U_1094,hAPP(U_1094,fun(U_1094,U_1094),plus_plus(U_1094),U_1099),U_1097) != hAPP(U_1094,U_1094,hAPP(U_1094,fun(U_1094,U_1094),plus_plus(U_1094),U_1095),U_1097) ) )
      | ~ cancel_semigroup_add(U_1094) ),
    inference(miniscope,[status(thm)],[f_294_2]) ).

fof(f_294_4,plain,
    ( ! [U_1094,U_1100,U_1098,U_1096,U_1095,U_1097,U_1099] :
        ( hAPP(U_1094,U_1094,hAPP(U_1094,fun(U_1094,U_1094),plus_plus(U_1094),U_1100),U_1098) = hAPP(U_1094,U_1094,hAPP(U_1094,fun(U_1094,U_1094),plus_plus(U_1094),U_1096),U_1098)
        | ti(U_1094,U_1100) != ti(U_1094,U_1096)
        | ~ sP53(U_1094,U_1100,U_1098,U_1096,U_1095,U_1097,U_1099) )
    & ! [U_1094,U_1100,U_1098,U_1096,U_1095,U_1097,U_1099] :
        ( ti(U_1094,U_1099) = ti(U_1094,U_1095)
        | hAPP(U_1094,U_1094,hAPP(U_1094,fun(U_1094,U_1094),plus_plus(U_1094),U_1099),U_1097) != hAPP(U_1094,U_1094,hAPP(U_1094,fun(U_1094,U_1094),plus_plus(U_1094),U_1095),U_1097)
        | ~ sP53(U_1094,U_1100,U_1098,U_1096,U_1095,U_1097,U_1099) )
    & ! [U_1094,U_1100,U_1098,U_1096,U_1095,U_1097,U_1099] :
        ( sP53(U_1094,U_1100,U_1098,U_1096,U_1095,U_1097,U_1099)
        | ~ cancel_semigroup_add(U_1094) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP53])],[f_294_3]) ).

cnf(f_294_5,plain,
    ( sP53(U_1094,U_1100,U_1098,U_1096,U_1095,U_1097,U_1099)
    | ~ cancel_semigroup_add(U_1094) ),
    inference(clausify,[status(thm)],[f_294_4]) ).

cnf(f_294_6,plain,
    ( ti(U_1094,U_1099) = ti(U_1094,U_1095)
    | hAPP(U_1094,U_1094,hAPP(U_1094,fun(U_1094,U_1094),plus_plus(U_1094),U_1099),U_1097) != hAPP(U_1094,U_1094,hAPP(U_1094,fun(U_1094,U_1094),plus_plus(U_1094),U_1095),U_1097)
    | ~ sP53(U_1094,U_1100,U_1098,U_1096,U_1095,U_1097,U_1099) ),
    inference(clausify,[status(thm)],[f_294_4]) ).

cnf(f_294_7,plain,
    ( hAPP(U_1094,U_1094,hAPP(U_1094,fun(U_1094,U_1094),plus_plus(U_1094),U_1100),U_1098) = hAPP(U_1094,U_1094,hAPP(U_1094,fun(U_1094,U_1094),plus_plus(U_1094),U_1096),U_1098)
    | ti(U_1094,U_1100) != ti(U_1094,U_1096)
    | ~ sP53(U_1094,U_1100,U_1098,U_1096,U_1095,U_1097,U_1099) ),
    inference(clausify,[status(thm)],[f_294_4]) ).

fof(f_295_1,plain,
    ! [X_a] :
      ( ! [A_1,B,C] :
          ( ti(X_a,B) = ti(X_a,C)
          | hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B) != 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_224_add__left__imp__eq]) ).

fof(f_295_2,plain,
    ! [U_1104] :
      ( ! [U_1103,U_1102,U_1101] :
          ( ti(U_1104,U_1102) = ti(U_1104,U_1101)
          | hAPP(U_1104,U_1104,hAPP(U_1104,fun(U_1104,U_1104),plus_plus(U_1104),U_1103),U_1102) != hAPP(U_1104,U_1104,hAPP(U_1104,fun(U_1104,U_1104),plus_plus(U_1104),U_1103),U_1101) )
      | ~ cancel_semigroup_add(U_1104) ),
    inference(variable_rename,[status(thm)],[f_295_1]) ).

fof(f_295_3,plain,
    ! [U_1102,U_1103,U_1104,U_1101] :
      ( ti(U_1104,U_1102) = ti(U_1104,U_1101)
      | hAPP(U_1104,U_1104,hAPP(U_1104,fun(U_1104,U_1104),plus_plus(U_1104),U_1103),U_1102) != hAPP(U_1104,U_1104,hAPP(U_1104,fun(U_1104,U_1104),plus_plus(U_1104),U_1103),U_1101)
      | ~ cancel_semigroup_add(U_1104) ),
    inference(definitional_conversion,[status(esa)],[f_295_2]) ).

cnf(f_295_4,plain,
    ( ti(U_1104,U_1102) = ti(U_1104,U_1101)
    | hAPP(U_1104,U_1104,hAPP(U_1104,fun(U_1104,U_1104),plus_plus(U_1104),U_1103),U_1102) != hAPP(U_1104,U_1104,hAPP(U_1104,fun(U_1104,U_1104),plus_plus(U_1104),U_1103),U_1101)
    | ~ cancel_semigroup_add(U_1104) ),
    inference(clausify,[status(thm)],[f_295_3]) ).

fof(f_296_1,plain,
    ! [X_a] :
      ( ! [A_1,B,C] :
          ( ti(X_a,B) = ti(X_a,C)
          | hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B) != 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_225_add__imp__eq]) ).

fof(f_296_2,plain,
    ! [U_1108] :
      ( ! [U_1107,U_1106,U_1105] :
          ( ti(U_1108,U_1106) = ti(U_1108,U_1105)
          | hAPP(U_1108,U_1108,hAPP(U_1108,fun(U_1108,U_1108),plus_plus(U_1108),U_1107),U_1106) != hAPP(U_1108,U_1108,hAPP(U_1108,fun(U_1108,U_1108),plus_plus(U_1108),U_1107),U_1105) )
      | ~ cancel146912293up_add(U_1108) ),
    inference(variable_rename,[status(thm)],[f_296_1]) ).

fof(f_296_3,plain,
    ! [U_1105,U_1106,U_1108,U_1107] :
      ( ti(U_1108,U_1106) = ti(U_1108,U_1105)
      | hAPP(U_1108,U_1108,hAPP(U_1108,fun(U_1108,U_1108),plus_plus(U_1108),U_1107),U_1106) != hAPP(U_1108,U_1108,hAPP(U_1108,fun(U_1108,U_1108),plus_plus(U_1108),U_1107),U_1105)
      | ~ cancel146912293up_add(U_1108) ),
    inference(definitional_conversion,[status(esa)],[f_296_2]) ).

cnf(f_296_4,plain,
    ( ti(U_1108,U_1106) = ti(U_1108,U_1105)
    | hAPP(U_1108,U_1108,hAPP(U_1108,fun(U_1108,U_1108),plus_plus(U_1108),U_1107),U_1106) != hAPP(U_1108,U_1108,hAPP(U_1108,fun(U_1108,U_1108),plus_plus(U_1108),U_1107),U_1105)
    | ~ cancel146912293up_add(U_1108) ),
    inference(clausify,[status(thm)],[f_296_3]) ).

fof(f_297_1,plain,
    ! [X_a] :
      ( ! [B,A_1,C] :
          ( ti(X_a,B) = ti(X_a,C)
          | hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),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_226_add__right__imp__eq]) ).

fof(f_297_2,plain,
    ! [U_1112] :
      ( ! [U_1111,U_1110,U_1109] :
          ( ti(U_1112,U_1111) = ti(U_1112,U_1109)
          | hAPP(U_1112,U_1112,hAPP(U_1112,fun(U_1112,U_1112),plus_plus(U_1112),U_1111),U_1110) != hAPP(U_1112,U_1112,hAPP(U_1112,fun(U_1112,U_1112),plus_plus(U_1112),U_1109),U_1110) )
      | ~ cancel_semigroup_add(U_1112) ),
    inference(variable_rename,[status(thm)],[f_297_1]) ).

fof(f_297_3,plain,
    ! [U_1109,U_1110,U_1111,U_1112] :
      ( ti(U_1112,U_1111) = ti(U_1112,U_1109)
      | hAPP(U_1112,U_1112,hAPP(U_1112,fun(U_1112,U_1112),plus_plus(U_1112),U_1111),U_1110) != hAPP(U_1112,U_1112,hAPP(U_1112,fun(U_1112,U_1112),plus_plus(U_1112),U_1109),U_1110)
      | ~ cancel_semigroup_add(U_1112) ),
    inference(definitional_conversion,[status(esa)],[f_297_2]) ).

cnf(f_297_4,plain,
    ( ti(U_1112,U_1111) = ti(U_1112,U_1109)
    | hAPP(U_1112,U_1112,hAPP(U_1112,fun(U_1112,U_1112),plus_plus(U_1112),U_1111),U_1110) != hAPP(U_1112,U_1112,hAPP(U_1112,fun(U_1112,U_1112),plus_plus(U_1112),U_1109),U_1110)
    | ~ cancel_semigroup_add(U_1112) ),
    inference(clausify,[status(thm)],[f_297_3]) ).

fof(f_298_1,plain,
    ! [X_b,X_1,F,F_1] :
      ( 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_1)) ),
    inference(fof_nnf,[status(thm)],[fact_227_folding__one__idem_Oidem]) ).

fof(f_298_2,plain,
    ! [U_1116,U_1115,U_1114,U_1113] :
      ( hAPP(U_1116,U_1116,hAPP(U_1116,fun(U_1116,U_1116),U_1114,U_1115),U_1115) = ti(U_1116,U_1115)
      | ~ hBOOL(hAPP(fun(fun(U_1116,bool),U_1116),bool,hAPP(fun(U_1116,fun(U_1116,U_1116)),fun(fun(fun(U_1116,bool),U_1116),bool),finite2073411215e_idem(U_1116),U_1114),U_1113)) ),
    inference(variable_rename,[status(thm)],[f_298_1]) ).

fof(f_298_3,plain,
    ! [U_1116,U_1115,U_1114] :
      ( ! [U_1113] : ~ hBOOL(hAPP(fun(fun(U_1116,bool),U_1116),bool,hAPP(fun(U_1116,fun(U_1116,U_1116)),fun(fun(fun(U_1116,bool),U_1116),bool),finite2073411215e_idem(U_1116),U_1114),U_1113))
      | hAPP(U_1116,U_1116,hAPP(U_1116,fun(U_1116,U_1116),U_1114,U_1115),U_1115) = ti(U_1116,U_1115) ),
    inference(miniscope,[status(thm)],[f_298_2]) ).

fof(f_298_4,plain,
    ! [U_1113,U_1114,U_1115,U_1116] :
      ( ~ hBOOL(hAPP(fun(fun(U_1116,bool),U_1116),bool,hAPP(fun(U_1116,fun(U_1116,U_1116)),fun(fun(fun(U_1116,bool),U_1116),bool),finite2073411215e_idem(U_1116),U_1114),U_1113))
      | hAPP(U_1116,U_1116,hAPP(U_1116,fun(U_1116,U_1116),U_1114,U_1115),U_1115) = ti(U_1116,U_1115) ),
    inference(definitional_conversion,[status(esa)],[f_298_3]) ).

cnf(f_298_5,plain,
    ( ~ hBOOL(hAPP(fun(fun(U_1116,bool),U_1116),bool,hAPP(fun(U_1116,fun(U_1116,U_1116)),fun(fun(fun(U_1116,bool),U_1116),bool),finite2073411215e_idem(U_1116),U_1114),U_1113))
    | hAPP(U_1116,U_1116,hAPP(U_1116,fun(U_1116,U_1116),U_1114,U_1115),U_1115) = ti(U_1116,U_1115) ),
    inference(clausify,[status(thm)],[f_298_4]) ).

fof(f_299_1,plain,
    ! [M_1,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M_1),
    inference(fof_nnf,[status(thm)],[fact_228_nat__add__commute]) ).

fof(f_299_2,plain,
    ! [U_1118,U_1117] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1118),U_1117) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1117),U_1118),
    inference(variable_rename,[status(thm)],[f_299_1]) ).

fof(f_299_3,plain,
    ! [U_1118,U_1117] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1118),U_1117) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1117),U_1118),
    inference(definitional_conversion,[status(esa)],[f_299_2]) ).

cnf(f_299_4,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1118),U_1117) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1117),U_1118),
    inference(clausify,[status(thm)],[f_299_3]) ).

fof(f_300_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_229_nat__add__left__commute]) ).

fof(f_300_2,plain,
    ! [U_1121,U_1120,U_1119] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1121),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1120),U_1119)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1120),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1121),U_1119)),
    inference(variable_rename,[status(thm)],[f_300_1]) ).

fof(f_300_3,plain,
    ! [U_1119,U_1121,U_1120] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1121),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1120),U_1119)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1120),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1121),U_1119)),
    inference(definitional_conversion,[status(esa)],[f_300_2]) ).

cnf(f_300_4,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1121),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1120),U_1119)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1120),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1121),U_1119)),
    inference(clausify,[status(thm)],[f_300_3]) ).

fof(f_301_1,plain,
    ! [M_1,N,K_1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N)),K_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),K_1)),
    inference(fof_nnf,[status(thm)],[fact_230_nat__add__assoc]) ).

fof(f_301_2,plain,
    ! [U_1124,U_1123,U_1122] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1124),U_1123)),U_1122) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1124),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1123),U_1122)),
    inference(variable_rename,[status(thm)],[f_301_1]) ).

fof(f_301_3,plain,
    ! [U_1122,U_1123,U_1124] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1124),U_1123)),U_1122) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1124),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1123),U_1122)),
    inference(definitional_conversion,[status(esa)],[f_301_2]) ).

cnf(f_301_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_1124),U_1123)),U_1122) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1124),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1123),U_1122)),
    inference(clausify,[status(thm)],[f_301_3]) ).

fof(f_302_1,plain,
    ! [K,M,Na] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),M) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),Na)
        | M != Na )
      & ( M = Na
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),M) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),Na) ) ),
    inference(fof_nnf,[status(thm)],[fact_231_nat__add__left__cancel]) ).

fof(f_302_2,plain,
    ! [U_1127,U_1126,U_1125] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1127),U_1126) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1127),U_1125)
        | U_1126 != U_1125 )
      & ( U_1126 = U_1125
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1127),U_1126) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1127),U_1125) ) ),
    inference(variable_rename,[status(thm)],[f_302_1]) ).

fof(f_302_3,plain,
    ( ! [U_1133,U_1131,U_1129] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1133),U_1131) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1133),U_1129)
        | U_1131 != U_1129 )
    & ! [U_1132,U_1130,U_1128] :
        ( U_1130 = U_1128
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1132),U_1130) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1132),U_1128) ) ),
    inference(miniscope,[status(thm)],[f_302_2]) ).

fof(f_302_4,plain,
    ( ! [U_1133,U_1131,U_1129] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1133),U_1131) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1133),U_1129)
        | U_1131 != U_1129 )
    & ! [U_1132,U_1128,U_1130] :
        ( U_1130 = U_1128
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1132),U_1130) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1132),U_1128) ) ),
    inference(definitional_conversion,[status(esa)],[f_302_3]) ).

cnf(f_302_5,plain,
    ( U_1130 = U_1128
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1132),U_1130) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1132),U_1128) ),
    inference(clausify,[status(thm)],[f_302_4]) ).

cnf(f_302_6,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1133),U_1131) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1133),U_1129)
    | U_1131 != U_1129 ),
    inference(clausify,[status(thm)],[f_302_4]) ).

fof(f_303_1,plain,
    ! [M,K,Na] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Na),K)
        | M != Na )
      & ( M = Na
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Na),K) ) ),
    inference(fof_nnf,[status(thm)],[fact_232_nat__add__right__cancel]) ).

fof(f_303_2,plain,
    ! [U_1136,U_1135,U_1134] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1136),U_1135) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1134),U_1135)
        | U_1136 != U_1134 )
      & ( U_1136 = U_1134
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1136),U_1135) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1134),U_1135) ) ),
    inference(variable_rename,[status(thm)],[f_303_1]) ).

fof(f_303_3,plain,
    ( ! [U_1142,U_1140,U_1138] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1142),U_1140) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1138),U_1140)
        | U_1142 != U_1138 )
    & ! [U_1141,U_1139,U_1137] :
        ( U_1141 = U_1137
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1141),U_1139) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1137),U_1139) ) ),
    inference(miniscope,[status(thm)],[f_303_2]) ).

fof(f_303_4,plain,
    ( ! [U_1140,U_1142,U_1138] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1142),U_1140) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1138),U_1140)
        | U_1142 != U_1138 )
    & ! [U_1137,U_1139,U_1141] :
        ( U_1141 = U_1137
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1141),U_1139) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1137),U_1139) ) ),
    inference(definitional_conversion,[status(esa)],[f_303_3]) ).

cnf(f_303_5,plain,
    ( U_1141 = U_1137
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1141),U_1139) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1137),U_1139) ),
    inference(clausify,[status(thm)],[f_303_4]) ).

cnf(f_303_6,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1142),U_1140) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1138),U_1140)
    | U_1142 != U_1138 ),
    inference(clausify,[status(thm)],[f_303_4]) ).

fof(f_304_1,plain,
    ! [X_b] :
      ( ! [A_2,C_1,B_3] :
          ( ( 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_3),C_1)))
            | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),B_3)) )
          & ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),B_3))
            | ~ 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_3),C_1))) ) )
      | ~ ordere236663937imp_le(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_233_add__le__cancel__right]) ).

fof(f_304_2,plain,
    ! [U_1146] :
      ( ! [U_1145,U_1144,U_1143] :
          ( ( hBOOL(hAPP(U_1146,bool,hAPP(U_1146,fun(U_1146,bool),ord_less_eq(U_1146),hAPP(U_1146,U_1146,hAPP(U_1146,fun(U_1146,U_1146),plus_plus(U_1146),U_1145),U_1144)),hAPP(U_1146,U_1146,hAPP(U_1146,fun(U_1146,U_1146),plus_plus(U_1146),U_1143),U_1144)))
            | ~ hBOOL(hAPP(U_1146,bool,hAPP(U_1146,fun(U_1146,bool),ord_less_eq(U_1146),U_1145),U_1143)) )
          & ( hBOOL(hAPP(U_1146,bool,hAPP(U_1146,fun(U_1146,bool),ord_less_eq(U_1146),U_1145),U_1143))
            | ~ hBOOL(hAPP(U_1146,bool,hAPP(U_1146,fun(U_1146,bool),ord_less_eq(U_1146),hAPP(U_1146,U_1146,hAPP(U_1146,fun(U_1146,U_1146),plus_plus(U_1146),U_1145),U_1144)),hAPP(U_1146,U_1146,hAPP(U_1146,fun(U_1146,U_1146),plus_plus(U_1146),U_1143),U_1144))) ) )
      | ~ ordere236663937imp_le(U_1146) ),
    inference(variable_rename,[status(thm)],[f_304_1]) ).

fof(f_304_3,plain,
    ! [U_1146] :
      ( ( ! [U_1152,U_1150,U_1148] :
            ( hBOOL(hAPP(U_1146,bool,hAPP(U_1146,fun(U_1146,bool),ord_less_eq(U_1146),hAPP(U_1146,U_1146,hAPP(U_1146,fun(U_1146,U_1146),plus_plus(U_1146),U_1152),U_1150)),hAPP(U_1146,U_1146,hAPP(U_1146,fun(U_1146,U_1146),plus_plus(U_1146),U_1148),U_1150)))
            | ~ hBOOL(hAPP(U_1146,bool,hAPP(U_1146,fun(U_1146,bool),ord_less_eq(U_1146),U_1152),U_1148)) )
        & ! [U_1151,U_1149,U_1147] :
            ( hBOOL(hAPP(U_1146,bool,hAPP(U_1146,fun(U_1146,bool),ord_less_eq(U_1146),U_1151),U_1147))
            | ~ hBOOL(hAPP(U_1146,bool,hAPP(U_1146,fun(U_1146,bool),ord_less_eq(U_1146),hAPP(U_1146,U_1146,hAPP(U_1146,fun(U_1146,U_1146),plus_plus(U_1146),U_1151),U_1149)),hAPP(U_1146,U_1146,hAPP(U_1146,fun(U_1146,U_1146),plus_plus(U_1146),U_1147),U_1149))) ) )
      | ~ ordere236663937imp_le(U_1146) ),
    inference(miniscope,[status(thm)],[f_304_2]) ).

fof(f_304_4,plain,
    ( ! [U_1146,U_1149,U_1151,U_1147,U_1148,U_1152,U_1150] :
        ( hBOOL(hAPP(U_1146,bool,hAPP(U_1146,fun(U_1146,bool),ord_less_eq(U_1146),hAPP(U_1146,U_1146,hAPP(U_1146,fun(U_1146,U_1146),plus_plus(U_1146),U_1152),U_1150)),hAPP(U_1146,U_1146,hAPP(U_1146,fun(U_1146,U_1146),plus_plus(U_1146),U_1148),U_1150)))
        | ~ hBOOL(hAPP(U_1146,bool,hAPP(U_1146,fun(U_1146,bool),ord_less_eq(U_1146),U_1152),U_1148))
        | ~ sP54(U_1146,U_1149,U_1151,U_1147,U_1148,U_1152,U_1150) )
    & ! [U_1146,U_1149,U_1151,U_1147,U_1148,U_1152,U_1150] :
        ( hBOOL(hAPP(U_1146,bool,hAPP(U_1146,fun(U_1146,bool),ord_less_eq(U_1146),U_1151),U_1147))
        | ~ hBOOL(hAPP(U_1146,bool,hAPP(U_1146,fun(U_1146,bool),ord_less_eq(U_1146),hAPP(U_1146,U_1146,hAPP(U_1146,fun(U_1146,U_1146),plus_plus(U_1146),U_1151),U_1149)),hAPP(U_1146,U_1146,hAPP(U_1146,fun(U_1146,U_1146),plus_plus(U_1146),U_1147),U_1149)))
        | ~ sP54(U_1146,U_1149,U_1151,U_1147,U_1148,U_1152,U_1150) )
    & ! [U_1146,U_1149,U_1151,U_1147,U_1148,U_1152,U_1150] :
        ( sP54(U_1146,U_1149,U_1151,U_1147,U_1148,U_1152,U_1150)
        | ~ ordere236663937imp_le(U_1146) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP54])],[f_304_3]) ).

cnf(f_304_5,plain,
    ( sP54(U_1146,U_1149,U_1151,U_1147,U_1148,U_1152,U_1150)
    | ~ ordere236663937imp_le(U_1146) ),
    inference(clausify,[status(thm)],[f_304_4]) ).

cnf(f_304_6,plain,
    ( hBOOL(hAPP(U_1146,bool,hAPP(U_1146,fun(U_1146,bool),ord_less_eq(U_1146),U_1151),U_1147))
    | ~ hBOOL(hAPP(U_1146,bool,hAPP(U_1146,fun(U_1146,bool),ord_less_eq(U_1146),hAPP(U_1146,U_1146,hAPP(U_1146,fun(U_1146,U_1146),plus_plus(U_1146),U_1151),U_1149)),hAPP(U_1146,U_1146,hAPP(U_1146,fun(U_1146,U_1146),plus_plus(U_1146),U_1147),U_1149)))
    | ~ sP54(U_1146,U_1149,U_1151,U_1147,U_1148,U_1152,U_1150) ),
    inference(clausify,[status(thm)],[f_304_4]) ).

cnf(f_304_7,plain,
    ( hBOOL(hAPP(U_1146,bool,hAPP(U_1146,fun(U_1146,bool),ord_less_eq(U_1146),hAPP(U_1146,U_1146,hAPP(U_1146,fun(U_1146,U_1146),plus_plus(U_1146),U_1152),U_1150)),hAPP(U_1146,U_1146,hAPP(U_1146,fun(U_1146,U_1146),plus_plus(U_1146),U_1148),U_1150)))
    | ~ hBOOL(hAPP(U_1146,bool,hAPP(U_1146,fun(U_1146,bool),ord_less_eq(U_1146),U_1152),U_1148))
    | ~ sP54(U_1146,U_1149,U_1151,U_1147,U_1148,U_1152,U_1150) ),
    inference(clausify,[status(thm)],[f_304_4]) ).

fof(f_305_1,plain,
    ! [X_b] :
      ( ! [C_1,A_2,B_3] :
          ( ( 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_3)))
            | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),B_3)) )
          & ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),B_3))
            | ~ 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_3))) ) )
      | ~ ordere236663937imp_le(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_234_add__le__cancel__left]) ).

fof(f_305_2,plain,
    ! [U_1156] :
      ( ! [U_1155,U_1154,U_1153] :
          ( ( hBOOL(hAPP(U_1156,bool,hAPP(U_1156,fun(U_1156,bool),ord_less_eq(U_1156),hAPP(U_1156,U_1156,hAPP(U_1156,fun(U_1156,U_1156),plus_plus(U_1156),U_1155),U_1154)),hAPP(U_1156,U_1156,hAPP(U_1156,fun(U_1156,U_1156),plus_plus(U_1156),U_1155),U_1153)))
            | ~ hBOOL(hAPP(U_1156,bool,hAPP(U_1156,fun(U_1156,bool),ord_less_eq(U_1156),U_1154),U_1153)) )
          & ( hBOOL(hAPP(U_1156,bool,hAPP(U_1156,fun(U_1156,bool),ord_less_eq(U_1156),U_1154),U_1153))
            | ~ hBOOL(hAPP(U_1156,bool,hAPP(U_1156,fun(U_1156,bool),ord_less_eq(U_1156),hAPP(U_1156,U_1156,hAPP(U_1156,fun(U_1156,U_1156),plus_plus(U_1156),U_1155),U_1154)),hAPP(U_1156,U_1156,hAPP(U_1156,fun(U_1156,U_1156),plus_plus(U_1156),U_1155),U_1153))) ) )
      | ~ ordere236663937imp_le(U_1156) ),
    inference(variable_rename,[status(thm)],[f_305_1]) ).

fof(f_305_3,plain,
    ! [U_1156] :
      ( ( ! [U_1162,U_1160,U_1158] :
            ( hBOOL(hAPP(U_1156,bool,hAPP(U_1156,fun(U_1156,bool),ord_less_eq(U_1156),hAPP(U_1156,U_1156,hAPP(U_1156,fun(U_1156,U_1156),plus_plus(U_1156),U_1162),U_1160)),hAPP(U_1156,U_1156,hAPP(U_1156,fun(U_1156,U_1156),plus_plus(U_1156),U_1162),U_1158)))
            | ~ hBOOL(hAPP(U_1156,bool,hAPP(U_1156,fun(U_1156,bool),ord_less_eq(U_1156),U_1160),U_1158)) )
        & ! [U_1161,U_1159,U_1157] :
            ( hBOOL(hAPP(U_1156,bool,hAPP(U_1156,fun(U_1156,bool),ord_less_eq(U_1156),U_1159),U_1157))
            | ~ hBOOL(hAPP(U_1156,bool,hAPP(U_1156,fun(U_1156,bool),ord_less_eq(U_1156),hAPP(U_1156,U_1156,hAPP(U_1156,fun(U_1156,U_1156),plus_plus(U_1156),U_1161),U_1159)),hAPP(U_1156,U_1156,hAPP(U_1156,fun(U_1156,U_1156),plus_plus(U_1156),U_1161),U_1157))) ) )
      | ~ ordere236663937imp_le(U_1156) ),
    inference(miniscope,[status(thm)],[f_305_2]) ).

fof(f_305_4,plain,
    ( ! [U_1156,U_1157,U_1161,U_1159,U_1158,U_1160,U_1162] :
        ( hBOOL(hAPP(U_1156,bool,hAPP(U_1156,fun(U_1156,bool),ord_less_eq(U_1156),hAPP(U_1156,U_1156,hAPP(U_1156,fun(U_1156,U_1156),plus_plus(U_1156),U_1162),U_1160)),hAPP(U_1156,U_1156,hAPP(U_1156,fun(U_1156,U_1156),plus_plus(U_1156),U_1162),U_1158)))
        | ~ hBOOL(hAPP(U_1156,bool,hAPP(U_1156,fun(U_1156,bool),ord_less_eq(U_1156),U_1160),U_1158))
        | ~ sP55(U_1156,U_1157,U_1161,U_1159,U_1158,U_1160,U_1162) )
    & ! [U_1156,U_1157,U_1161,U_1159,U_1158,U_1160,U_1162] :
        ( hBOOL(hAPP(U_1156,bool,hAPP(U_1156,fun(U_1156,bool),ord_less_eq(U_1156),U_1159),U_1157))
        | ~ hBOOL(hAPP(U_1156,bool,hAPP(U_1156,fun(U_1156,bool),ord_less_eq(U_1156),hAPP(U_1156,U_1156,hAPP(U_1156,fun(U_1156,U_1156),plus_plus(U_1156),U_1161),U_1159)),hAPP(U_1156,U_1156,hAPP(U_1156,fun(U_1156,U_1156),plus_plus(U_1156),U_1161),U_1157)))
        | ~ sP55(U_1156,U_1157,U_1161,U_1159,U_1158,U_1160,U_1162) )
    & ! [U_1156,U_1157,U_1161,U_1159,U_1158,U_1160,U_1162] :
        ( sP55(U_1156,U_1157,U_1161,U_1159,U_1158,U_1160,U_1162)
        | ~ ordere236663937imp_le(U_1156) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP55])],[f_305_3]) ).

cnf(f_305_5,plain,
    ( sP55(U_1156,U_1157,U_1161,U_1159,U_1158,U_1160,U_1162)
    | ~ ordere236663937imp_le(U_1156) ),
    inference(clausify,[status(thm)],[f_305_4]) ).

cnf(f_305_6,plain,
    ( hBOOL(hAPP(U_1156,bool,hAPP(U_1156,fun(U_1156,bool),ord_less_eq(U_1156),U_1159),U_1157))
    | ~ hBOOL(hAPP(U_1156,bool,hAPP(U_1156,fun(U_1156,bool),ord_less_eq(U_1156),hAPP(U_1156,U_1156,hAPP(U_1156,fun(U_1156,U_1156),plus_plus(U_1156),U_1161),U_1159)),hAPP(U_1156,U_1156,hAPP(U_1156,fun(U_1156,U_1156),plus_plus(U_1156),U_1161),U_1157)))
    | ~ sP55(U_1156,U_1157,U_1161,U_1159,U_1158,U_1160,U_1162) ),
    inference(clausify,[status(thm)],[f_305_4]) ).

cnf(f_305_7,plain,
    ( hBOOL(hAPP(U_1156,bool,hAPP(U_1156,fun(U_1156,bool),ord_less_eq(U_1156),hAPP(U_1156,U_1156,hAPP(U_1156,fun(U_1156,U_1156),plus_plus(U_1156),U_1162),U_1160)),hAPP(U_1156,U_1156,hAPP(U_1156,fun(U_1156,U_1156),plus_plus(U_1156),U_1162),U_1158)))
    | ~ hBOOL(hAPP(U_1156,bool,hAPP(U_1156,fun(U_1156,bool),ord_less_eq(U_1156),U_1160),U_1158))
    | ~ sP55(U_1156,U_1157,U_1161,U_1159,U_1158,U_1160,U_1162) ),
    inference(clausify,[status(thm)],[f_305_4]) ).

fof(f_306_1,plain,
    ! [X_a] :
      ( ! [C,A_1,B] :
          ( 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),C)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) )
      | ~ ordere779506340up_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_235_add__right__mono]) ).

fof(f_306_2,plain,
    ! [U_1166] :
      ( ! [U_1165,U_1164,U_1163] :
          ( hBOOL(hAPP(U_1166,bool,hAPP(U_1166,fun(U_1166,bool),ord_less_eq(U_1166),hAPP(U_1166,U_1166,hAPP(U_1166,fun(U_1166,U_1166),plus_plus(U_1166),U_1164),U_1165)),hAPP(U_1166,U_1166,hAPP(U_1166,fun(U_1166,U_1166),plus_plus(U_1166),U_1163),U_1165)))
          | ~ hBOOL(hAPP(U_1166,bool,hAPP(U_1166,fun(U_1166,bool),ord_less_eq(U_1166),U_1164),U_1163)) )
      | ~ ordere779506340up_add(U_1166) ),
    inference(variable_rename,[status(thm)],[f_306_1]) ).

fof(f_306_3,plain,
    ! [U_1166,U_1164,U_1163,U_1165] :
      ( hBOOL(hAPP(U_1166,bool,hAPP(U_1166,fun(U_1166,bool),ord_less_eq(U_1166),hAPP(U_1166,U_1166,hAPP(U_1166,fun(U_1166,U_1166),plus_plus(U_1166),U_1164),U_1165)),hAPP(U_1166,U_1166,hAPP(U_1166,fun(U_1166,U_1166),plus_plus(U_1166),U_1163),U_1165)))
      | ~ hBOOL(hAPP(U_1166,bool,hAPP(U_1166,fun(U_1166,bool),ord_less_eq(U_1166),U_1164),U_1163))
      | ~ ordere779506340up_add(U_1166) ),
    inference(definitional_conversion,[status(esa)],[f_306_2]) ).

cnf(f_306_4,plain,
    ( hBOOL(hAPP(U_1166,bool,hAPP(U_1166,fun(U_1166,bool),ord_less_eq(U_1166),hAPP(U_1166,U_1166,hAPP(U_1166,fun(U_1166,U_1166),plus_plus(U_1166),U_1164),U_1165)),hAPP(U_1166,U_1166,hAPP(U_1166,fun(U_1166,U_1166),plus_plus(U_1166),U_1163),U_1165)))
    | ~ hBOOL(hAPP(U_1166,bool,hAPP(U_1166,fun(U_1166,bool),ord_less_eq(U_1166),U_1164),U_1163))
    | ~ ordere779506340up_add(U_1166) ),
    inference(clausify,[status(thm)],[f_306_3]) ).

fof(f_307_1,plain,
    ! [X_a] :
      ( ! [C,A_1,B] :
          ( 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)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) )
      | ~ ordere779506340up_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_236_add__left__mono]) ).

fof(f_307_2,plain,
    ! [U_1170] :
      ( ! [U_1169,U_1168,U_1167] :
          ( hBOOL(hAPP(U_1170,bool,hAPP(U_1170,fun(U_1170,bool),ord_less_eq(U_1170),hAPP(U_1170,U_1170,hAPP(U_1170,fun(U_1170,U_1170),plus_plus(U_1170),U_1169),U_1168)),hAPP(U_1170,U_1170,hAPP(U_1170,fun(U_1170,U_1170),plus_plus(U_1170),U_1169),U_1167)))
          | ~ hBOOL(hAPP(U_1170,bool,hAPP(U_1170,fun(U_1170,bool),ord_less_eq(U_1170),U_1168),U_1167)) )
      | ~ ordere779506340up_add(U_1170) ),
    inference(variable_rename,[status(thm)],[f_307_1]) ).

fof(f_307_3,plain,
    ! [U_1170,U_1167,U_1168,U_1169] :
      ( hBOOL(hAPP(U_1170,bool,hAPP(U_1170,fun(U_1170,bool),ord_less_eq(U_1170),hAPP(U_1170,U_1170,hAPP(U_1170,fun(U_1170,U_1170),plus_plus(U_1170),U_1169),U_1168)),hAPP(U_1170,U_1170,hAPP(U_1170,fun(U_1170,U_1170),plus_plus(U_1170),U_1169),U_1167)))
      | ~ hBOOL(hAPP(U_1170,bool,hAPP(U_1170,fun(U_1170,bool),ord_less_eq(U_1170),U_1168),U_1167))
      | ~ ordere779506340up_add(U_1170) ),
    inference(definitional_conversion,[status(esa)],[f_307_2]) ).

cnf(f_307_4,plain,
    ( hBOOL(hAPP(U_1170,bool,hAPP(U_1170,fun(U_1170,bool),ord_less_eq(U_1170),hAPP(U_1170,U_1170,hAPP(U_1170,fun(U_1170,U_1170),plus_plus(U_1170),U_1169),U_1168)),hAPP(U_1170,U_1170,hAPP(U_1170,fun(U_1170,U_1170),plus_plus(U_1170),U_1169),U_1167)))
    | ~ hBOOL(hAPP(U_1170,bool,hAPP(U_1170,fun(U_1170,bool),ord_less_eq(U_1170),U_1168),U_1167))
    | ~ ordere779506340up_add(U_1170) ),
    inference(clausify,[status(thm)],[f_307_3]) ).

fof(f_308_1,plain,
    ! [X_a] :
      ( ! [C,D,A_1,B] :
          ( 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),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)) )
      | ~ ordere779506340up_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_237_add__mono]) ).

fof(f_308_2,plain,
    ! [U_1175] :
      ( ! [U_1174,U_1173,U_1172,U_1171] :
          ( hBOOL(hAPP(U_1175,bool,hAPP(U_1175,fun(U_1175,bool),ord_less_eq(U_1175),hAPP(U_1175,U_1175,hAPP(U_1175,fun(U_1175,U_1175),plus_plus(U_1175),U_1172),U_1174)),hAPP(U_1175,U_1175,hAPP(U_1175,fun(U_1175,U_1175),plus_plus(U_1175),U_1171),U_1173)))
          | ~ hBOOL(hAPP(U_1175,bool,hAPP(U_1175,fun(U_1175,bool),ord_less_eq(U_1175),U_1174),U_1173))
          | ~ hBOOL(hAPP(U_1175,bool,hAPP(U_1175,fun(U_1175,bool),ord_less_eq(U_1175),U_1172),U_1171)) )
      | ~ ordere779506340up_add(U_1175) ),
    inference(variable_rename,[status(thm)],[f_308_1]) ).

fof(f_308_3,plain,
    ! [U_1172,U_1175,U_1171,U_1173,U_1174] :
      ( hBOOL(hAPP(U_1175,bool,hAPP(U_1175,fun(U_1175,bool),ord_less_eq(U_1175),hAPP(U_1175,U_1175,hAPP(U_1175,fun(U_1175,U_1175),plus_plus(U_1175),U_1172),U_1174)),hAPP(U_1175,U_1175,hAPP(U_1175,fun(U_1175,U_1175),plus_plus(U_1175),U_1171),U_1173)))
      | ~ hBOOL(hAPP(U_1175,bool,hAPP(U_1175,fun(U_1175,bool),ord_less_eq(U_1175),U_1174),U_1173))
      | ~ hBOOL(hAPP(U_1175,bool,hAPP(U_1175,fun(U_1175,bool),ord_less_eq(U_1175),U_1172),U_1171))
      | ~ ordere779506340up_add(U_1175) ),
    inference(definitional_conversion,[status(esa)],[f_308_2]) ).

cnf(f_308_4,plain,
    ( hBOOL(hAPP(U_1175,bool,hAPP(U_1175,fun(U_1175,bool),ord_less_eq(U_1175),hAPP(U_1175,U_1175,hAPP(U_1175,fun(U_1175,U_1175),plus_plus(U_1175),U_1172),U_1174)),hAPP(U_1175,U_1175,hAPP(U_1175,fun(U_1175,U_1175),plus_plus(U_1175),U_1171),U_1173)))
    | ~ hBOOL(hAPP(U_1175,bool,hAPP(U_1175,fun(U_1175,bool),ord_less_eq(U_1175),U_1174),U_1173))
    | ~ hBOOL(hAPP(U_1175,bool,hAPP(U_1175,fun(U_1175,bool),ord_less_eq(U_1175),U_1172),U_1171))
    | ~ ordere779506340up_add(U_1175) ),
    inference(clausify,[status(thm)],[f_308_3]) ).

fof(f_309_1,plain,
    ! [X_a] :
      ( ! [A_1,C,B] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B))
          | ~ 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),C))) )
      | ~ ordere236663937imp_le(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_238_add__le__imp__le__right]) ).

fof(f_309_2,plain,
    ! [U_1179] :
      ( ! [U_1178,U_1177,U_1176] :
          ( hBOOL(hAPP(U_1179,bool,hAPP(U_1179,fun(U_1179,bool),ord_less_eq(U_1179),U_1178),U_1176))
          | ~ hBOOL(hAPP(U_1179,bool,hAPP(U_1179,fun(U_1179,bool),ord_less_eq(U_1179),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))) )
      | ~ ordere236663937imp_le(U_1179) ),
    inference(variable_rename,[status(thm)],[f_309_1]) ).

fof(f_309_3,plain,
    ! [U_1177,U_1179,U_1176,U_1178] :
      ( hBOOL(hAPP(U_1179,bool,hAPP(U_1179,fun(U_1179,bool),ord_less_eq(U_1179),U_1178),U_1176))
      | ~ hBOOL(hAPP(U_1179,bool,hAPP(U_1179,fun(U_1179,bool),ord_less_eq(U_1179),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)))
      | ~ ordere236663937imp_le(U_1179) ),
    inference(definitional_conversion,[status(esa)],[f_309_2]) ).

cnf(f_309_4,plain,
    ( hBOOL(hAPP(U_1179,bool,hAPP(U_1179,fun(U_1179,bool),ord_less_eq(U_1179),U_1178),U_1176))
    | ~ hBOOL(hAPP(U_1179,bool,hAPP(U_1179,fun(U_1179,bool),ord_less_eq(U_1179),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)))
    | ~ ordere236663937imp_le(U_1179) ),
    inference(clausify,[status(thm)],[f_309_3]) ).

fof(f_310_1,plain,
    ! [X_a] :
      ( ! [C,A_1,B] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B))
          | ~ 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))) )
      | ~ ordere236663937imp_le(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_239_add__le__imp__le__left]) ).

fof(f_310_2,plain,
    ! [U_1183] :
      ( ! [U_1182,U_1181,U_1180] :
          ( hBOOL(hAPP(U_1183,bool,hAPP(U_1183,fun(U_1183,bool),ord_less_eq(U_1183),U_1181),U_1180))
          | ~ hBOOL(hAPP(U_1183,bool,hAPP(U_1183,fun(U_1183,bool),ord_less_eq(U_1183),hAPP(U_1183,U_1183,hAPP(U_1183,fun(U_1183,U_1183),plus_plus(U_1183),U_1182),U_1181)),hAPP(U_1183,U_1183,hAPP(U_1183,fun(U_1183,U_1183),plus_plus(U_1183),U_1182),U_1180))) )
      | ~ ordere236663937imp_le(U_1183) ),
    inference(variable_rename,[status(thm)],[f_310_1]) ).

fof(f_310_3,plain,
    ! [U_1180,U_1183,U_1181,U_1182] :
      ( hBOOL(hAPP(U_1183,bool,hAPP(U_1183,fun(U_1183,bool),ord_less_eq(U_1183),U_1181),U_1180))
      | ~ hBOOL(hAPP(U_1183,bool,hAPP(U_1183,fun(U_1183,bool),ord_less_eq(U_1183),hAPP(U_1183,U_1183,hAPP(U_1183,fun(U_1183,U_1183),plus_plus(U_1183),U_1182),U_1181)),hAPP(U_1183,U_1183,hAPP(U_1183,fun(U_1183,U_1183),plus_plus(U_1183),U_1182),U_1180)))
      | ~ ordere236663937imp_le(U_1183) ),
    inference(definitional_conversion,[status(esa)],[f_310_2]) ).

cnf(f_310_4,plain,
    ( hBOOL(hAPP(U_1183,bool,hAPP(U_1183,fun(U_1183,bool),ord_less_eq(U_1183),U_1181),U_1180))
    | ~ hBOOL(hAPP(U_1183,bool,hAPP(U_1183,fun(U_1183,bool),ord_less_eq(U_1183),hAPP(U_1183,U_1183,hAPP(U_1183,fun(U_1183,U_1183),plus_plus(U_1183),U_1182),U_1181)),hAPP(U_1183,U_1183,hAPP(U_1183,fun(U_1183,U_1183),plus_plus(U_1183),U_1182),U_1180)))
    | ~ ordere236663937imp_le(U_1183) ),
    inference(clausify,[status(thm)],[f_310_3]) ).

fof(f_311_1,plain,
    ! [X_a] :
      ( ! [A_1,B] : 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)),B) = ti(X_a,A_1)
      | ~ group_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_240_diff__add__cancel]) ).

fof(f_311_2,plain,
    ! [U_1186] :
      ( ! [U_1185,U_1184] : hAPP(U_1186,U_1186,hAPP(U_1186,fun(U_1186,U_1186),plus_plus(U_1186),hAPP(U_1186,U_1186,hAPP(U_1186,fun(U_1186,U_1186),minus_minus(U_1186),U_1185),U_1184)),U_1184) = ti(U_1186,U_1185)
      | ~ group_add(U_1186) ),
    inference(variable_rename,[status(thm)],[f_311_1]) ).

fof(f_311_3,plain,
    ! [U_1184,U_1186,U_1185] :
      ( hAPP(U_1186,U_1186,hAPP(U_1186,fun(U_1186,U_1186),plus_plus(U_1186),hAPP(U_1186,U_1186,hAPP(U_1186,fun(U_1186,U_1186),minus_minus(U_1186),U_1185),U_1184)),U_1184) = ti(U_1186,U_1185)
      | ~ group_add(U_1186) ),
    inference(definitional_conversion,[status(esa)],[f_311_2]) ).

cnf(f_311_4,plain,
    ( hAPP(U_1186,U_1186,hAPP(U_1186,fun(U_1186,U_1186),plus_plus(U_1186),hAPP(U_1186,U_1186,hAPP(U_1186,fun(U_1186,U_1186),minus_minus(U_1186),U_1185),U_1184)),U_1184) = ti(U_1186,U_1185)
    | ~ group_add(U_1186) ),
    inference(clausify,[status(thm)],[f_311_3]) ).

fof(f_312_1,plain,
    ! [X_a] :
      ( ! [A_1,B] : 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)),B) = ti(X_a,A_1)
      | ~ group_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_241_add__diff__cancel]) ).

fof(f_312_2,plain,
    ! [U_1189] :
      ( ! [U_1188,U_1187] : hAPP(U_1189,U_1189,hAPP(U_1189,fun(U_1189,U_1189),minus_minus(U_1189),hAPP(U_1189,U_1189,hAPP(U_1189,fun(U_1189,U_1189),plus_plus(U_1189),U_1188),U_1187)),U_1187) = ti(U_1189,U_1188)
      | ~ group_add(U_1189) ),
    inference(variable_rename,[status(thm)],[f_312_1]) ).

fof(f_312_3,plain,
    ! [U_1189,U_1187,U_1188] :
      ( hAPP(U_1189,U_1189,hAPP(U_1189,fun(U_1189,U_1189),minus_minus(U_1189),hAPP(U_1189,U_1189,hAPP(U_1189,fun(U_1189,U_1189),plus_plus(U_1189),U_1188),U_1187)),U_1187) = ti(U_1189,U_1188)
      | ~ group_add(U_1189) ),
    inference(definitional_conversion,[status(esa)],[f_312_2]) ).

cnf(f_312_4,plain,
    ( hAPP(U_1189,U_1189,hAPP(U_1189,fun(U_1189,U_1189),minus_minus(U_1189),hAPP(U_1189,U_1189,hAPP(U_1189,fun(U_1189,U_1189),plus_plus(U_1189),U_1188),U_1187)),U_1187) = ti(U_1189,U_1188)
    | ~ group_add(U_1189) ),
    inference(clausify,[status(thm)],[f_312_3]) ).

fof(f_313_1,plain,
    ! [M_1,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),hAPP(nat,nat,suc,N)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N)),
    inference(fof_nnf,[status(thm)],[fact_242_add__Suc__right]) ).

fof(f_313_2,plain,
    ! [U_1191,U_1190] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1191),hAPP(nat,nat,suc,U_1190)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1191),U_1190)),
    inference(variable_rename,[status(thm)],[f_313_1]) ).

fof(f_313_3,plain,
    ! [U_1190,U_1191] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1191),hAPP(nat,nat,suc,U_1190)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1191),U_1190)),
    inference(definitional_conversion,[status(esa)],[f_313_2]) ).

cnf(f_313_4,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1191),hAPP(nat,nat,suc,U_1190)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1191),U_1190)),
    inference(clausify,[status(thm)],[f_313_3]) ).

fof(f_314_1,plain,
    ! [M_1,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M_1)),N) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N)),
    inference(fof_nnf,[status(thm)],[fact_243_add__Suc]) ).

fof(f_314_2,plain,
    ! [U_1193,U_1192] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,U_1193)),U_1192) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1193),U_1192)),
    inference(variable_rename,[status(thm)],[f_314_1]) ).

fof(f_314_3,plain,
    ! [U_1192,U_1193] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,U_1193)),U_1192) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1193),U_1192)),
    inference(definitional_conversion,[status(esa)],[f_314_2]) ).

cnf(f_314_4,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,U_1193)),U_1192) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1193),U_1192)),
    inference(clausify,[status(thm)],[f_314_3]) ).

fof(f_315_1,plain,
    ! [M_1,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M_1)),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),hAPP(nat,nat,suc,N)),
    inference(fof_nnf,[status(thm)],[fact_244_add__Suc__shift]) ).

fof(f_315_2,plain,
    ! [U_1195,U_1194] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,U_1195)),U_1194) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1195),hAPP(nat,nat,suc,U_1194)),
    inference(variable_rename,[status(thm)],[f_315_1]) ).

fof(f_315_3,plain,
    ! [U_1194,U_1195] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,U_1195)),U_1194) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1195),hAPP(nat,nat,suc,U_1194)),
    inference(definitional_conversion,[status(esa)],[f_315_2]) ).

cnf(f_315_4,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,U_1195)),U_1194) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1195),hAPP(nat,nat,suc,U_1194)),
    inference(clausify,[status(thm)],[f_315_3]) ).

fof(f_316_1,plain,
    ! [N,M_1] : 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_1),N))),
    inference(fof_nnf,[status(thm)],[fact_245_le__add2]) ).

fof(f_316_2,plain,
    ! [U_1197,U_1196] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1197),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1196),U_1197))),
    inference(variable_rename,[status(thm)],[f_316_1]) ).

fof(f_316_3,plain,
    ! [U_1197,U_1196] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1197),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1196),U_1197))),
    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_1197),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1196),U_1197))),
    inference(clausify,[status(thm)],[f_316_3]) ).

fof(f_317_1,plain,
    ! [N,M_1] : 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_1))),
    inference(fof_nnf,[status(thm)],[fact_246_le__add1]) ).

fof(f_317_2,plain,
    ! [U_1199,U_1198] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1199),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1199),U_1198))),
    inference(variable_rename,[status(thm)],[f_317_1]) ).

fof(f_317_3,plain,
    ! [U_1199,U_1198] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1199),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1199),U_1198))),
    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_1199),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1199),U_1198))),
    inference(clausify,[status(thm)],[f_317_3]) ).

fof(f_318_1,plain,
    ! [M,Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na))
        | ! [K_2] : Na != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_2) )
      & ( ? [K_2] : Na = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_2)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_247_le__iff__add]) ).

fof(f_318_2,plain,
    ! [U_1203,U_1202] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1203),U_1202))
        | ! [U_1201] : U_1202 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1203),U_1201) )
      & ( ? [U_1200] : U_1202 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1203),U_1200)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1203),U_1202)) ) ),
    inference(variable_rename,[status(thm)],[f_318_1]) ).

fof(f_318_3,plain,
    ( ! [U_1207,U_1205] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1207),U_1205))
        | ! [U_1201] : U_1205 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1207),U_1201) )
    & ! [U_1206,U_1204] :
        ( ? [U_1200] : U_1204 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1206),U_1200)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1206),U_1204)) ) ),
    inference(miniscope,[status(thm)],[f_318_2]) ).

fof(f_318_4,plain,
    ( ! [U_1207,U_1205] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1207),U_1205))
        | ! [U_1201] : U_1205 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1207),U_1201) )
    & ! [U_1206,U_1204] :
        ( U_1204 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1206),sK38(U_1206,U_1204))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1206),U_1204)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK38]),skolemize(U_1200,sK38(U_1206,U_1204))],[f_318_3]) ).

fof(f_318_5,plain,
    ( ! [U_1207,U_1205,U_1201] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1207),U_1205))
        | U_1205 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1207),U_1201) )
    & ! [U_1204,U_1206] :
        ( U_1204 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1206),sK38(U_1206,U_1204))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1206),U_1204)) ) ),
    inference(definitional_conversion,[status(esa)],[f_318_4]) ).

cnf(f_318_6,plain,
    ( U_1204 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1206),sK38(U_1206,U_1204))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1206),U_1204)) ),
    inference(clausify,[status(thm)],[f_318_5]) ).

cnf(f_318_7,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1207),U_1205))
    | U_1205 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1207),U_1201) ),
    inference(clausify,[status(thm)],[f_318_5]) ).

fof(f_319_1,plain,
    ! [K,M,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),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),Na)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),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),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_248_nat__add__left__cancel__le]) ).

fof(f_319_2,plain,
    ! [U_1210,U_1209,U_1208] :
      ( ( 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_1210),U_1209)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1210),U_1208)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1209),U_1208)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1209),U_1208))
        | ~ 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_1210),U_1209)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1210),U_1208))) ) ),
    inference(variable_rename,[status(thm)],[f_319_1]) ).

fof(f_319_3,plain,
    ( ! [U_1216,U_1214,U_1212] :
        ( 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_1216),U_1214)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1216),U_1212)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1214),U_1212)) )
    & ! [U_1215,U_1213,U_1211] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1213),U_1211))
        | ~ 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_1215),U_1213)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1215),U_1211))) ) ),
    inference(miniscope,[status(thm)],[f_319_2]) ).

fof(f_319_4,plain,
    ( ! [U_1212,U_1214,U_1216] :
        ( 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_1216),U_1214)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1216),U_1212)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1214),U_1212)) )
    & ! [U_1211,U_1213,U_1215] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1213),U_1211))
        | ~ 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_1215),U_1213)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1215),U_1211))) ) ),
    inference(definitional_conversion,[status(esa)],[f_319_3]) ).

cnf(f_319_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1213),U_1211))
    | ~ 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_1215),U_1213)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1215),U_1211))) ),
    inference(clausify,[status(thm)],[f_319_4]) ).

cnf(f_319_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_1216),U_1214)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1216),U_1212)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1214),U_1212)) ),
    inference(clausify,[status(thm)],[f_319_4]) ).

fof(f_320_1,plain,
    ! [M_1,I_2,J] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),M_1)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),J)) ),
    inference(fof_nnf,[status(thm)],[fact_249_trans__le__add1]) ).

fof(f_320_2,plain,
    ! [U_1219,U_1218,U_1217] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1218),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1217),U_1219)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1218),U_1217)) ),
    inference(variable_rename,[status(thm)],[f_320_1]) ).

fof(f_320_3,plain,
    ! [U_1218,U_1217,U_1219] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1218),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1217),U_1219)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1218),U_1217)) ),
    inference(definitional_conversion,[status(esa)],[f_320_2]) ).

cnf(f_320_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1218),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1217),U_1219)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1218),U_1217)) ),
    inference(clausify,[status(thm)],[f_320_3]) ).

fof(f_321_1,plain,
    ! [M_1,I_2,J] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),J)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),J)) ),
    inference(fof_nnf,[status(thm)],[fact_250_trans__le__add2]) ).

fof(f_321_2,plain,
    ! [U_1222,U_1221,U_1220] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1221),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1222),U_1220)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1221),U_1220)) ),
    inference(variable_rename,[status(thm)],[f_321_1]) ).

fof(f_321_3,plain,
    ! [U_1221,U_1220,U_1222] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1221),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1222),U_1220)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1221),U_1220)) ),
    inference(definitional_conversion,[status(esa)],[f_321_2]) ).

cnf(f_321_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1221),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1222),U_1220)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1221),U_1220)) ),
    inference(clausify,[status(thm)],[f_321_3]) ).

fof(f_322_1,plain,
    ! [K_1,I_2,J] :
      ( 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_2),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),K_1)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),J)) ),
    inference(fof_nnf,[status(thm)],[fact_251_add__le__mono1]) ).

fof(f_322_2,plain,
    ! [U_1225,U_1224,U_1223] :
      ( 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_1224),U_1225)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1223),U_1225)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1224),U_1223)) ),
    inference(variable_rename,[status(thm)],[f_322_1]) ).

fof(f_322_3,plain,
    ! [U_1223,U_1224,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_1224),U_1225)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1223),U_1225)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1224),U_1223)) ),
    inference(definitional_conversion,[status(esa)],[f_322_2]) ).

cnf(f_322_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_1224),U_1225)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1223),U_1225)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1224),U_1223)) ),
    inference(clausify,[status(thm)],[f_322_3]) ).

fof(f_323_1,plain,
    ! [K_1,L_1,I_2,J] :
      ( 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_2),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),L_1)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),L_1))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),J)) ),
    inference(fof_nnf,[status(thm)],[fact_252_add__le__mono]) ).

fof(f_323_2,plain,
    ! [U_1229,U_1228,U_1227,U_1226] :
      ( 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_1229)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1226),U_1228)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1229),U_1228))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1227),U_1226)) ),
    inference(variable_rename,[status(thm)],[f_323_1]) ).

fof(f_323_3,plain,
    ! [U_1226,U_1227,U_1228,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_1227),U_1229)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1226),U_1228)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1229),U_1228))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1227),U_1226)) ),
    inference(definitional_conversion,[status(esa)],[f_323_2]) ).

cnf(f_323_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_1227),U_1229)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1226),U_1228)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1229),U_1228))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1227),U_1226)) ),
    inference(clausify,[status(thm)],[f_323_3]) ).

fof(f_324_1,plain,
    ! [M_1,K_1,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),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_1),K_1)),N)) ),
    inference(fof_nnf,[status(thm)],[fact_253_add__leD2]) ).

fof(f_324_2,plain,
    ! [U_1232,U_1231,U_1230] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1231),U_1230))
      | ~ 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_1231)),U_1230)) ),
    inference(variable_rename,[status(thm)],[f_324_1]) ).

fof(f_324_3,plain,
    ! [U_1231,U_1230,U_1232] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1231),U_1230))
      | ~ 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_1231)),U_1230)) ),
    inference(definitional_conversion,[status(esa)],[f_324_2]) ).

cnf(f_324_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1231),U_1230))
    | ~ 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_1231)),U_1230)) ),
    inference(clausify,[status(thm)],[f_324_3]) ).

fof(f_325_1,plain,
    ! [M_1,K_1,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),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_1),K_1)),N)) ),
    inference(fof_nnf,[status(thm)],[fact_254_add__leD1]) ).

fof(f_325_2,plain,
    ! [U_1235,U_1234,U_1233] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1235),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_1235),U_1234)),U_1233)) ),
    inference(variable_rename,[status(thm)],[f_325_1]) ).

fof(f_325_3,plain,
    ! [U_1233,U_1234,U_1235] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1235),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_1235),U_1234)),U_1233)) ),
    inference(definitional_conversion,[status(esa)],[f_325_2]) ).

cnf(f_325_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1235),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_1235),U_1234)),U_1233)) ),
    inference(clausify,[status(thm)],[f_325_3]) ).

fof(f_326_1,plain,
    ! [M_1,K_1,N] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N))
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),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_1),K_1)),N)) ),
    inference(fof_nnf,[status(thm)],[fact_255_add__leE]) ).

fof(f_326_2,plain,
    ! [U_1238,U_1237,U_1236] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1237),U_1236))
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1238),U_1236)) )
      | ~ 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_1238),U_1237)),U_1236)) ),
    inference(variable_rename,[status(thm)],[f_326_1]) ).

fof(f_326_3,plain,
    ( ! [U_1236,U_1237,U_1238] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1237),U_1236))
        | ~ sP56(U_1236,U_1237,U_1238) )
    & ! [U_1236,U_1237,U_1238] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1238),U_1236))
        | ~ sP56(U_1236,U_1237,U_1238) )
    & ! [U_1236,U_1237,U_1238] :
        ( sP56(U_1236,U_1237,U_1238)
        | ~ 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_1238),U_1237)),U_1236)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP56])],[f_326_2]) ).

cnf(f_326_4,plain,
    ( sP56(U_1236,U_1237,U_1238)
    | ~ 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_1238),U_1237)),U_1236)) ),
    inference(clausify,[status(thm)],[f_326_3]) ).

cnf(f_326_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1238),U_1236))
    | ~ sP56(U_1236,U_1237,U_1238) ),
    inference(clausify,[status(thm)],[f_326_3]) ).

cnf(f_326_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1237),U_1236))
    | ~ sP56(U_1236,U_1237,U_1238) ),
    inference(clausify,[status(thm)],[f_326_3]) ).

fof(f_327_1,plain,
    ! [M_1,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N)),N) = M_1,
    inference(fof_nnf,[status(thm)],[fact_256_diff__add__inverse2]) ).

fof(f_327_2,plain,
    ! [U_1240,U_1239] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1240),U_1239)),U_1239) = U_1240,
    inference(variable_rename,[status(thm)],[f_327_1]) ).

fof(f_327_3,plain,
    ! [U_1239,U_1240] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1240),U_1239)),U_1239) = U_1240,
    inference(definitional_conversion,[status(esa)],[f_327_2]) ).

cnf(f_327_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_1240),U_1239)),U_1239) = U_1240,
    inference(clausify,[status(thm)],[f_327_3]) ).

fof(f_328_1,plain,
    ! [N,M_1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M_1)),N) = M_1,
    inference(fof_nnf,[status(thm)],[fact_257_diff__add__inverse]) ).

fof(f_328_2,plain,
    ! [U_1242,U_1241] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1242),U_1241)),U_1242) = U_1241,
    inference(variable_rename,[status(thm)],[f_328_1]) ).

fof(f_328_3,plain,
    ! [U_1241,U_1242] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1242),U_1241)),U_1242) = U_1241,
    inference(definitional_conversion,[status(esa)],[f_328_2]) ).

cnf(f_328_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_1242),U_1241)),U_1242) = U_1241,
    inference(clausify,[status(thm)],[f_328_3]) ).

fof(f_329_1,plain,
    ! [I_2,J,K_1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_2),J)),K_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),K_1)),
    inference(fof_nnf,[status(thm)],[fact_258_diff__diff__left]) ).

fof(f_329_2,plain,
    ! [U_1245,U_1244,U_1243] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1245),U_1244)),U_1243) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1245),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1244),U_1243)),
    inference(variable_rename,[status(thm)],[f_329_1]) ).

fof(f_329_3,plain,
    ! [U_1243,U_1244,U_1245] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1245),U_1244)),U_1243) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1245),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1244),U_1243)),
    inference(definitional_conversion,[status(esa)],[f_329_2]) ).

cnf(f_329_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_1245),U_1244)),U_1243) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1245),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1244),U_1243)),
    inference(clausify,[status(thm)],[f_329_3]) ).

fof(f_330_1,plain,
    ! [K_1,M_1,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N),
    inference(fof_nnf,[status(thm)],[fact_259_diff__cancel]) ).

fof(f_330_2,plain,
    ! [U_1248,U_1247,U_1246] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1248),U_1247)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1248),U_1246)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1247),U_1246),
    inference(variable_rename,[status(thm)],[f_330_1]) ).

fof(f_330_3,plain,
    ! [U_1246,U_1247,U_1248] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1248),U_1247)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1248),U_1246)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1247),U_1246),
    inference(definitional_conversion,[status(esa)],[f_330_2]) ).

cnf(f_330_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_1248),U_1247)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1248),U_1246)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1247),U_1246),
    inference(clausify,[status(thm)],[f_330_3]) ).

fof(f_331_1,plain,
    ! [M_1,K_1,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),K_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N),
    inference(fof_nnf,[status(thm)],[fact_260_diff__cancel2]) ).

fof(f_331_2,plain,
    ! [U_1251,U_1250,U_1249] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1251),U_1250)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1249),U_1250)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1251),U_1249),
    inference(variable_rename,[status(thm)],[f_331_1]) ).

fof(f_331_3,plain,
    ! [U_1249,U_1250,U_1251] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1251),U_1250)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1249),U_1250)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1251),U_1249),
    inference(definitional_conversion,[status(esa)],[f_331_2]) ).

cnf(f_331_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_1251),U_1250)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1249),U_1250)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1251),U_1249),
    inference(clausify,[status(thm)],[f_331_3]) ).

fof(f_332_1,plain,
    ! [I_2,K_1,J] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),K_1)),J)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),J)) ),
    inference(fof_nnf,[status(thm)],[fact_261_diff__diff__right]) ).

fof(f_332_2,plain,
    ! [U_1254,U_1253,U_1252] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1254),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1252),U_1253)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1254),U_1253)),U_1252)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1253),U_1252)) ),
    inference(variable_rename,[status(thm)],[f_332_1]) ).

fof(f_332_3,plain,
    ! [U_1252,U_1253,U_1254] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1254),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1252),U_1253)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1254),U_1253)),U_1252)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1253),U_1252)) ),
    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_1254),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1252),U_1253)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1254),U_1253)),U_1252)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1253),U_1252)) ),
    inference(clausify,[status(thm)],[f_332_3]) ).

fof(f_333_1,plain,
    ! [J_1,K,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)),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))) )
      & ( 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)))
        | ~ 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)),I_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_262_le__diff__conv]) ).

fof(f_333_2,plain,
    ! [U_1257,U_1256,U_1255] :
      ( ( 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_1257),U_1256)),U_1255))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1257),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1255),U_1256))) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1257),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1255),U_1256)))
        | ~ 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_1257),U_1256)),U_1255)) ) ),
    inference(variable_rename,[status(thm)],[f_333_1]) ).

fof(f_333_3,plain,
    ( ! [U_1263,U_1261,U_1259] :
        ( 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_1263),U_1261)),U_1259))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1263),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1259),U_1261))) )
    & ! [U_1262,U_1260,U_1258] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1262),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1258),U_1260)))
        | ~ 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_1262),U_1260)),U_1258)) ) ),
    inference(miniscope,[status(thm)],[f_333_2]) ).

fof(f_333_4,plain,
    ( ! [U_1263,U_1259,U_1261] :
        ( 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_1263),U_1261)),U_1259))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1263),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1259),U_1261))) )
    & ! [U_1260,U_1258,U_1262] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1262),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1258),U_1260)))
        | ~ 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_1262),U_1260)),U_1258)) ) ),
    inference(definitional_conversion,[status(esa)],[f_333_3]) ).

cnf(f_333_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1262),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1258),U_1260)))
    | ~ 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_1262),U_1260)),U_1258)) ),
    inference(clausify,[status(thm)],[f_333_4]) ).

cnf(f_333_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_1263),U_1261)),U_1259))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1263),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1259),U_1261))) ),
    inference(clausify,[status(thm)],[f_333_4]) ).

fof(f_334_1,plain,
    ! [M_1,K_1,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M_1)),K_1)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N)) ),
    inference(fof_nnf,[status(thm)],[fact_263_le__add__diff]) ).

fof(f_334_2,plain,
    ! [U_1266,U_1265,U_1264] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1266),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1264),U_1266)),U_1265)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1265),U_1264)) ),
    inference(variable_rename,[status(thm)],[f_334_1]) ).

fof(f_334_3,plain,
    ! [U_1264,U_1265,U_1266] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1266),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1264),U_1266)),U_1265)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1265),U_1264)) ),
    inference(definitional_conversion,[status(esa)],[f_334_2]) ).

cnf(f_334_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1266),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1264),U_1266)),U_1265)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1265),U_1264)) ),
    inference(clausify,[status(thm)],[f_334_3]) ).

fof(f_335_1,plain,
    ! [N,M_1] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N)) = M_1
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M_1)) ),
    inference(fof_nnf,[status(thm)],[fact_264_le__add__diff__inverse]) ).

fof(f_335_2,plain,
    ! [U_1268,U_1267] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1268),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1267),U_1268)) = U_1267
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1268),U_1267)) ),
    inference(variable_rename,[status(thm)],[f_335_1]) ).

fof(f_335_3,plain,
    ! [U_1268,U_1267] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1268),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1267),U_1268)) = U_1267
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1268),U_1267)) ),
    inference(definitional_conversion,[status(esa)],[f_335_2]) ).

cnf(f_335_4,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1268),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1267),U_1268)) = U_1267
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1268),U_1267)) ),
    inference(clausify,[status(thm)],[f_335_3]) ).

fof(f_336_1,plain,
    ! [I_2,K_1,J] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),J)),K_1)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),J)) ),
    inference(fof_nnf,[status(thm)],[fact_265_add__diff__assoc]) ).

fof(f_336_2,plain,
    ! [U_1271,U_1270,U_1269] :
      ( 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)) = 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)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1270),U_1269)) ),
    inference(variable_rename,[status(thm)],[f_336_1]) ).

fof(f_336_3,plain,
    ! [U_1269,U_1270,U_1271] :
      ( 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)) = 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)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1270),U_1269)) ),
    inference(definitional_conversion,[status(esa)],[f_336_2]) ).

cnf(f_336_4,plain,
    ( 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)) = 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)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1270),U_1269)) ),
    inference(clausify,[status(thm)],[f_336_3]) ).

fof(f_337_1,plain,
    ! [I_1,K,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)))
          | ~ 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)),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)),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))) ) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J_1)) ),
    inference(fof_nnf,[status(thm)],[fact_266_le__diff__conv2]) ).

fof(f_337_2,plain,
    ! [U_1274,U_1273,U_1272] :
      ( ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1274),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1272),U_1273)))
          | ~ 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_1274),U_1273)),U_1272)) )
        & ( 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_1274),U_1273)),U_1272))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1274),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1272),U_1273))) ) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1273),U_1272)) ),
    inference(variable_rename,[status(thm)],[f_337_1]) ).

fof(f_337_3,plain,
    ( ! [U_1272,U_1273,U_1274] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1274),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1272),U_1273)))
        | ~ 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_1274),U_1273)),U_1272))
        | ~ sP57(U_1272,U_1273,U_1274) )
    & ! [U_1272,U_1273,U_1274] :
        ( 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_1274),U_1273)),U_1272))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1274),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1272),U_1273)))
        | ~ sP57(U_1272,U_1273,U_1274) )
    & ! [U_1272,U_1273,U_1274] :
        ( sP57(U_1272,U_1273,U_1274)
        | ~ 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,[sP57])],[f_337_2]) ).

cnf(f_337_4,plain,
    ( sP57(U_1272,U_1273,U_1274)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1273),U_1272)) ),
    inference(clausify,[status(thm)],[f_337_3]) ).

cnf(f_337_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_1274),U_1273)),U_1272))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1274),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1272),U_1273)))
    | ~ sP57(U_1272,U_1273,U_1274) ),
    inference(clausify,[status(thm)],[f_337_3]) ).

cnf(f_337_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1274),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1272),U_1273)))
    | ~ 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_1274),U_1273)),U_1272))
    | ~ sP57(U_1272,U_1273,U_1274) ),
    inference(clausify,[status(thm)],[f_337_3]) ).

fof(f_338_1,plain,
    ! [N,M_1] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N)),N) = M_1
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M_1)) ),
    inference(fof_nnf,[status(thm)],[fact_267_le__add__diff__inverse2]) ).

fof(f_338_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_338_1]) ).

fof(f_338_3,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(definitional_conversion,[status(esa)],[f_338_2]) ).

cnf(f_338_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_338_3]) ).

fof(f_339_1,plain,
    ! [K,I_1,J_1] :
      ( ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),I_1) = K
          | J_1 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),I_1) )
        & ( J_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),I_1)
          | hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),I_1) != K ) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_1)) ),
    inference(fof_nnf,[status(thm)],[fact_268_le__imp__diff__is__add]) ).

fof(f_339_2,plain,
    ! [U_1279,U_1278,U_1277] :
      ( ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1277),U_1278) = U_1279
          | U_1277 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1279),U_1278) )
        & ( U_1277 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1279),U_1278)
          | hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1277),U_1278) != U_1279 ) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1278),U_1277)) ),
    inference(variable_rename,[status(thm)],[f_339_1]) ).

fof(f_339_3,plain,
    ( ! [U_1278,U_1277,U_1279] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1277),U_1278) = U_1279
        | U_1277 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1279),U_1278)
        | ~ sP58(U_1278,U_1277,U_1279) )
    & ! [U_1278,U_1277,U_1279] :
        ( U_1277 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1279),U_1278)
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1277),U_1278) != U_1279
        | ~ sP58(U_1278,U_1277,U_1279) )
    & ! [U_1278,U_1277,U_1279] :
        ( sP58(U_1278,U_1277,U_1279)
        | ~ 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,[sP58])],[f_339_2]) ).

cnf(f_339_4,plain,
    ( sP58(U_1278,U_1277,U_1279)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1278),U_1277)) ),
    inference(clausify,[status(thm)],[f_339_3]) ).

cnf(f_339_5,plain,
    ( U_1277 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1279),U_1278)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1277),U_1278) != U_1279
    | ~ sP58(U_1278,U_1277,U_1279) ),
    inference(clausify,[status(thm)],[f_339_3]) ).

cnf(f_339_6,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1277),U_1278) = U_1279
    | U_1277 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1279),U_1278)
    | ~ sP58(U_1278,U_1277,U_1279) ),
    inference(clausify,[status(thm)],[f_339_3]) ).

fof(f_340_1,plain,
    ! [I_2,K_1,J] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),J)),K_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K_1))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),J)) ),
    inference(fof_nnf,[status(thm)],[fact_269_diff__add__assoc]) ).

fof(f_340_2,plain,
    ! [U_1282,U_1281,U_1280] :
      ( 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) = 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))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1281),U_1280)) ),
    inference(variable_rename,[status(thm)],[f_340_1]) ).

fof(f_340_3,plain,
    ! [U_1281,U_1280,U_1282] :
      ( 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) = 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))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1281),U_1280)) ),
    inference(definitional_conversion,[status(esa)],[f_340_2]) ).

cnf(f_340_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_1282),U_1280)),U_1281) = 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))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1281),U_1280)) ),
    inference(clausify,[status(thm)],[f_340_3]) ).

fof(f_341_1,plain,
    ! [I_2,K_1,J] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K_1)),I_2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),I_2)),K_1)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),J)) ),
    inference(fof_nnf,[status(thm)],[fact_270_add__diff__assoc2]) ).

fof(f_341_2,plain,
    ! [U_1285,U_1284,U_1283] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1283),U_1284)),U_1285) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1283),U_1285)),U_1284)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1284),U_1283)) ),
    inference(variable_rename,[status(thm)],[f_341_1]) ).

fof(f_341_3,plain,
    ! [U_1284,U_1283,U_1285] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1283),U_1284)),U_1285) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1283),U_1285)),U_1284)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1284),U_1283)) ),
    inference(definitional_conversion,[status(esa)],[f_341_2]) ).

cnf(f_341_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_1283),U_1284)),U_1285) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1283),U_1285)),U_1284)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1284),U_1283)) ),
    inference(clausify,[status(thm)],[f_341_3]) ).

fof(f_342_1,plain,
    ! [I_2,K_1,J] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),I_2)),K_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K_1)),I_2)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),J)) ),
    inference(fof_nnf,[status(thm)],[fact_271_diff__add__assoc2]) ).

fof(f_342_2,plain,
    ! [U_1288,U_1287,U_1286] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1286),U_1288)),U_1287) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1286),U_1287)),U_1288)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1287),U_1286)) ),
    inference(variable_rename,[status(thm)],[f_342_1]) ).

fof(f_342_3,plain,
    ! [U_1287,U_1286,U_1288] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1286),U_1288)),U_1287) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1286),U_1287)),U_1288)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1287),U_1286)) ),
    inference(definitional_conversion,[status(esa)],[f_342_2]) ).

cnf(f_342_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_1286),U_1288)),U_1287) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1286),U_1287)),U_1288)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1287),U_1286)) ),
    inference(clausify,[status(thm)],[f_342_3]) ).

fof(f_343_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_272_Suc__eq__plus1__left]) ).

fof(f_343_2,plain,
    ! [U_1289] : hAPP(nat,nat,suc,U_1289) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),U_1289),
    inference(variable_rename,[status(thm)],[f_343_1]) ).

fof(f_343_3,plain,
    ! [U_1289] : hAPP(nat,nat,suc,U_1289) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),U_1289),
    inference(definitional_conversion,[status(esa)],[f_343_2]) ).

cnf(f_343_4,plain,
    hAPP(nat,nat,suc,U_1289) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),U_1289),
    inference(clausify,[status(thm)],[f_343_3]) ).

fof(f_344_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_273_Suc__eq__plus1]) ).

fof(f_344_2,plain,
    ! [U_1290] : hAPP(nat,nat,suc,U_1290) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1290),one_one(nat)),
    inference(variable_rename,[status(thm)],[f_344_1]) ).

fof(f_344_3,plain,
    ! [U_1290] : hAPP(nat,nat,suc,U_1290) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1290),one_one(nat)),
    inference(definitional_conversion,[status(esa)],[f_344_2]) ).

cnf(f_344_4,plain,
    hAPP(nat,nat,suc,U_1290) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1290),one_one(nat)),
    inference(clausify,[status(thm)],[f_344_3]) ).

fof(f_345_1,plain,
    ! [X_b,X_1,A_3,F,F_1] :
      ( hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),hAPP(fun(X_b,bool),X_b,F_1,A_3)) = hAPP(fun(X_b,bool),X_b,F_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))
      | ~ 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_1)) ),
    inference(fof_nnf,[status(thm)],[fact_274_folding__one__idem_Oin__idem]) ).

fof(f_345_2,plain,
    ! [U_1295,U_1294,U_1293,U_1292,U_1291] :
      ( hAPP(U_1295,U_1295,hAPP(U_1295,fun(U_1295,U_1295),U_1292,U_1294),hAPP(fun(U_1295,bool),U_1295,U_1291,U_1293)) = hAPP(fun(U_1295,bool),U_1295,U_1291,U_1293)
      | ~ hBOOL(hAPP(fun(U_1295,bool),bool,hAPP(U_1295,fun(fun(U_1295,bool),bool),member(U_1295),U_1294),U_1293))
      | ~ hBOOL(hAPP(fun(U_1295,bool),bool,finite_finite(U_1295),U_1293))
      | ~ hBOOL(hAPP(fun(fun(U_1295,bool),U_1295),bool,hAPP(fun(U_1295,fun(U_1295,U_1295)),fun(fun(fun(U_1295,bool),U_1295),bool),finite2073411215e_idem(U_1295),U_1292),U_1291)) ),
    inference(variable_rename,[status(thm)],[f_345_1]) ).

fof(f_345_3,plain,
    ! [U_1295,U_1291,U_1292,U_1293,U_1294] :
      ( hAPP(U_1295,U_1295,hAPP(U_1295,fun(U_1295,U_1295),U_1292,U_1294),hAPP(fun(U_1295,bool),U_1295,U_1291,U_1293)) = hAPP(fun(U_1295,bool),U_1295,U_1291,U_1293)
      | ~ hBOOL(hAPP(fun(U_1295,bool),bool,hAPP(U_1295,fun(fun(U_1295,bool),bool),member(U_1295),U_1294),U_1293))
      | ~ hBOOL(hAPP(fun(U_1295,bool),bool,finite_finite(U_1295),U_1293))
      | ~ hBOOL(hAPP(fun(fun(U_1295,bool),U_1295),bool,hAPP(fun(U_1295,fun(U_1295,U_1295)),fun(fun(fun(U_1295,bool),U_1295),bool),finite2073411215e_idem(U_1295),U_1292),U_1291)) ),
    inference(definitional_conversion,[status(esa)],[f_345_2]) ).

cnf(f_345_4,plain,
    ( hAPP(U_1295,U_1295,hAPP(U_1295,fun(U_1295,U_1295),U_1292,U_1294),hAPP(fun(U_1295,bool),U_1295,U_1291,U_1293)) = hAPP(fun(U_1295,bool),U_1295,U_1291,U_1293)
    | ~ hBOOL(hAPP(fun(U_1295,bool),bool,hAPP(U_1295,fun(fun(U_1295,bool),bool),member(U_1295),U_1294),U_1293))
    | ~ hBOOL(hAPP(fun(U_1295,bool),bool,finite_finite(U_1295),U_1293))
    | ~ hBOOL(hAPP(fun(fun(U_1295,bool),U_1295),bool,hAPP(fun(U_1295,fun(U_1295,U_1295)),fun(fun(fun(U_1295,bool),U_1295),bool),finite2073411215e_idem(U_1295),U_1292),U_1291)) ),
    inference(clausify,[status(thm)],[f_345_3]) ).

fof(f_346_1,plain,
    ! [M_1,K_1,J] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K_1))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_1)),hAPP(nat,nat,suc,J))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),J)) ),
    inference(fof_nnf,[status(thm)],[fact_275_diff__Suc__diff__eq1]) ).

fof(f_346_2,plain,
    ! [U_1298,U_1297,U_1296] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1298),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1296),U_1297))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1298),U_1297)),hAPP(nat,nat,suc,U_1296))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1297),U_1296)) ),
    inference(variable_rename,[status(thm)],[f_346_1]) ).

fof(f_346_3,plain,
    ! [U_1296,U_1297,U_1298] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1298),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1296),U_1297))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1298),U_1297)),hAPP(nat,nat,suc,U_1296))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1297),U_1296)) ),
    inference(definitional_conversion,[status(esa)],[f_346_2]) ).

cnf(f_346_4,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1298),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1296),U_1297))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1298),U_1297)),hAPP(nat,nat,suc,U_1296))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1297),U_1296)) ),
    inference(clausify,[status(thm)],[f_346_3]) ).

fof(f_347_1,plain,
    ! [M_1,K_1,J] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K_1))),M_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,J)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),M_1))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),J)) ),
    inference(fof_nnf,[status(thm)],[fact_276_diff__Suc__diff__eq2]) ).

fof(f_347_2,plain,
    ! [U_1301,U_1300,U_1299] :
      ( 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_1299),U_1300))),U_1301) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,U_1299)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1300),U_1301))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1300),U_1299)) ),
    inference(variable_rename,[status(thm)],[f_347_1]) ).

fof(f_347_3,plain,
    ! [U_1299,U_1300,U_1301] :
      ( 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_1299),U_1300))),U_1301) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,U_1299)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1300),U_1301))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1300),U_1299)) ),
    inference(definitional_conversion,[status(esa)],[f_347_2]) ).

cnf(f_347_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_1299),U_1300))),U_1301) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,U_1299)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1300),U_1301))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1300),U_1299)) ),
    inference(clausify,[status(thm)],[f_347_3]) ).

fof(f_348_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_277_card_Oinsert]) ).

fof(f_348_2,plain,
    ! [U_1304,U_1303,U_1302] :
      ( hAPP(fun(U_1304,bool),nat,finite_card(U_1304),hAPP(fun(U_1304,bool),fun(U_1304,bool),hAPP(U_1304,fun(fun(U_1304,bool),fun(U_1304,bool)),insert(U_1304),U_1303),U_1302)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(fun(U_1304,bool),nat,finite_card(U_1304),U_1302))
      | hBOOL(hAPP(fun(U_1304,bool),bool,hAPP(U_1304,fun(fun(U_1304,bool),bool),member(U_1304),U_1303),U_1302))
      | ~ hBOOL(hAPP(fun(U_1304,bool),bool,finite_finite(U_1304),U_1302)) ),
    inference(variable_rename,[status(thm)],[f_348_1]) ).

fof(f_348_3,plain,
    ! [U_1302,U_1303,U_1304] :
      ( hAPP(fun(U_1304,bool),nat,finite_card(U_1304),hAPP(fun(U_1304,bool),fun(U_1304,bool),hAPP(U_1304,fun(fun(U_1304,bool),fun(U_1304,bool)),insert(U_1304),U_1303),U_1302)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(fun(U_1304,bool),nat,finite_card(U_1304),U_1302))
      | hBOOL(hAPP(fun(U_1304,bool),bool,hAPP(U_1304,fun(fun(U_1304,bool),bool),member(U_1304),U_1303),U_1302))
      | ~ hBOOL(hAPP(fun(U_1304,bool),bool,finite_finite(U_1304),U_1302)) ),
    inference(definitional_conversion,[status(esa)],[f_348_2]) ).

cnf(f_348_4,plain,
    ( hAPP(fun(U_1304,bool),nat,finite_card(U_1304),hAPP(fun(U_1304,bool),fun(U_1304,bool),hAPP(U_1304,fun(fun(U_1304,bool),fun(U_1304,bool)),insert(U_1304),U_1303),U_1302)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(fun(U_1304,bool),nat,finite_card(U_1304),U_1302))
    | hBOOL(hAPP(fun(U_1304,bool),bool,hAPP(U_1304,fun(fun(U_1304,bool),bool),member(U_1304),U_1303),U_1302))
    | ~ hBOOL(hAPP(fun(U_1304,bool),bool,finite_finite(U_1304),U_1302)) ),
    inference(clausify,[status(thm)],[f_348_3]) ).

fof(f_349_1,plain,
    ! [X_b,N_2,H,F,F_1] :
      ( hAPP(X_b,X_b,H,hAPP(fun(X_b,bool),X_b,F_1,N_2)) = hAPP(fun(X_b,bool),X_b,F_1,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_2))
      | ti(fun(X_b,bool),N_2) = bot_bot(fun(X_b,bool))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),N_2))
      | ? [X_2,Y_1] : hAPP(X_b,X_b,H,hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_2),Y_1)) != 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_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_1)) ),
    inference(fof_nnf,[status(thm)],[fact_278_folding__one__idem_Ohom__commute]) ).

fof(f_349_2,plain,
    ! [U_1311,U_1310,U_1309,U_1308,U_1307] :
      ( hAPP(U_1311,U_1311,U_1309,hAPP(fun(U_1311,bool),U_1311,U_1307,U_1310)) = hAPP(fun(U_1311,bool),U_1311,U_1307,hAPP(fun(U_1311,bool),fun(U_1311,bool),hAPP(fun(U_1311,U_1311),fun(fun(U_1311,bool),fun(U_1311,bool)),image(U_1311,U_1311),U_1309),U_1310))
      | ti(fun(U_1311,bool),U_1310) = bot_bot(fun(U_1311,bool))
      | ~ hBOOL(hAPP(fun(U_1311,bool),bool,finite_finite(U_1311),U_1310))
      | ? [U_1306,U_1305] : hAPP(U_1311,U_1311,U_1309,hAPP(U_1311,U_1311,hAPP(U_1311,fun(U_1311,U_1311),U_1308,U_1306),U_1305)) != hAPP(U_1311,U_1311,hAPP(U_1311,fun(U_1311,U_1311),U_1308,hAPP(U_1311,U_1311,U_1309,U_1306)),hAPP(U_1311,U_1311,U_1309,U_1305))
      | ~ hBOOL(hAPP(fun(fun(U_1311,bool),U_1311),bool,hAPP(fun(U_1311,fun(U_1311,U_1311)),fun(fun(fun(U_1311,bool),U_1311),bool),finite2073411215e_idem(U_1311),U_1308),U_1307)) ),
    inference(variable_rename,[status(thm)],[f_349_1]) ).

fof(f_349_3,plain,
    ! [U_1311,U_1310,U_1309,U_1308,U_1307] :
      ( hAPP(U_1311,U_1311,U_1309,hAPP(fun(U_1311,bool),U_1311,U_1307,U_1310)) = hAPP(fun(U_1311,bool),U_1311,U_1307,hAPP(fun(U_1311,bool),fun(U_1311,bool),hAPP(fun(U_1311,U_1311),fun(fun(U_1311,bool),fun(U_1311,bool)),image(U_1311,U_1311),U_1309),U_1310))
      | ti(fun(U_1311,bool),U_1310) = bot_bot(fun(U_1311,bool))
      | ~ hBOOL(hAPP(fun(U_1311,bool),bool,finite_finite(U_1311),U_1310))
      | ? [U_1305] : hAPP(U_1311,U_1311,U_1309,hAPP(U_1311,U_1311,hAPP(U_1311,fun(U_1311,U_1311),U_1308,sK39(U_1311,U_1310,U_1309,U_1308,U_1307)),U_1305)) != hAPP(U_1311,U_1311,hAPP(U_1311,fun(U_1311,U_1311),U_1308,hAPP(U_1311,U_1311,U_1309,sK39(U_1311,U_1310,U_1309,U_1308,U_1307))),hAPP(U_1311,U_1311,U_1309,U_1305))
      | ~ hBOOL(hAPP(fun(fun(U_1311,bool),U_1311),bool,hAPP(fun(U_1311,fun(U_1311,U_1311)),fun(fun(fun(U_1311,bool),U_1311),bool),finite2073411215e_idem(U_1311),U_1308),U_1307)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(U_1306,sK39(U_1311,U_1310,U_1309,U_1308,U_1307))],[f_349_2]) ).

fof(f_349_4,plain,
    ! [U_1311,U_1310,U_1309,U_1308,U_1307] :
      ( hAPP(U_1311,U_1311,U_1309,hAPP(fun(U_1311,bool),U_1311,U_1307,U_1310)) = hAPP(fun(U_1311,bool),U_1311,U_1307,hAPP(fun(U_1311,bool),fun(U_1311,bool),hAPP(fun(U_1311,U_1311),fun(fun(U_1311,bool),fun(U_1311,bool)),image(U_1311,U_1311),U_1309),U_1310))
      | ti(fun(U_1311,bool),U_1310) = bot_bot(fun(U_1311,bool))
      | ~ hBOOL(hAPP(fun(U_1311,bool),bool,finite_finite(U_1311),U_1310))
      | hAPP(U_1311,U_1311,U_1309,hAPP(U_1311,U_1311,hAPP(U_1311,fun(U_1311,U_1311),U_1308,sK39(U_1311,U_1310,U_1309,U_1308,U_1307)),sK40(U_1311,U_1310,U_1309,U_1308,U_1307))) != hAPP(U_1311,U_1311,hAPP(U_1311,fun(U_1311,U_1311),U_1308,hAPP(U_1311,U_1311,U_1309,sK39(U_1311,U_1310,U_1309,U_1308,U_1307))),hAPP(U_1311,U_1311,U_1309,sK40(U_1311,U_1310,U_1309,U_1308,U_1307)))
      | ~ hBOOL(hAPP(fun(fun(U_1311,bool),U_1311),bool,hAPP(fun(U_1311,fun(U_1311,U_1311)),fun(fun(fun(U_1311,bool),U_1311),bool),finite2073411215e_idem(U_1311),U_1308),U_1307)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK40]),skolemize(U_1305,sK40(U_1311,U_1310,U_1309,U_1308,U_1307))],[f_349_3]) ).

fof(f_349_5,plain,
    ! [U_1309,U_1307,U_1308,U_1310,U_1311] :
      ( hAPP(U_1311,U_1311,U_1309,hAPP(fun(U_1311,bool),U_1311,U_1307,U_1310)) = hAPP(fun(U_1311,bool),U_1311,U_1307,hAPP(fun(U_1311,bool),fun(U_1311,bool),hAPP(fun(U_1311,U_1311),fun(fun(U_1311,bool),fun(U_1311,bool)),image(U_1311,U_1311),U_1309),U_1310))
      | ti(fun(U_1311,bool),U_1310) = bot_bot(fun(U_1311,bool))
      | ~ hBOOL(hAPP(fun(U_1311,bool),bool,finite_finite(U_1311),U_1310))
      | hAPP(U_1311,U_1311,U_1309,hAPP(U_1311,U_1311,hAPP(U_1311,fun(U_1311,U_1311),U_1308,sK39(U_1311,U_1310,U_1309,U_1308,U_1307)),sK40(U_1311,U_1310,U_1309,U_1308,U_1307))) != hAPP(U_1311,U_1311,hAPP(U_1311,fun(U_1311,U_1311),U_1308,hAPP(U_1311,U_1311,U_1309,sK39(U_1311,U_1310,U_1309,U_1308,U_1307))),hAPP(U_1311,U_1311,U_1309,sK40(U_1311,U_1310,U_1309,U_1308,U_1307)))
      | ~ hBOOL(hAPP(fun(fun(U_1311,bool),U_1311),bool,hAPP(fun(U_1311,fun(U_1311,U_1311)),fun(fun(fun(U_1311,bool),U_1311),bool),finite2073411215e_idem(U_1311),U_1308),U_1307)) ),
    inference(definitional_conversion,[status(esa)],[f_349_4]) ).

cnf(f_349_6,plain,
    ( hAPP(U_1311,U_1311,U_1309,hAPP(fun(U_1311,bool),U_1311,U_1307,U_1310)) = hAPP(fun(U_1311,bool),U_1311,U_1307,hAPP(fun(U_1311,bool),fun(U_1311,bool),hAPP(fun(U_1311,U_1311),fun(fun(U_1311,bool),fun(U_1311,bool)),image(U_1311,U_1311),U_1309),U_1310))
    | ti(fun(U_1311,bool),U_1310) = bot_bot(fun(U_1311,bool))
    | ~ hBOOL(hAPP(fun(U_1311,bool),bool,finite_finite(U_1311),U_1310))
    | hAPP(U_1311,U_1311,U_1309,hAPP(U_1311,U_1311,hAPP(U_1311,fun(U_1311,U_1311),U_1308,sK39(U_1311,U_1310,U_1309,U_1308,U_1307)),sK40(U_1311,U_1310,U_1309,U_1308,U_1307))) != hAPP(U_1311,U_1311,hAPP(U_1311,fun(U_1311,U_1311),U_1308,hAPP(U_1311,U_1311,U_1309,sK39(U_1311,U_1310,U_1309,U_1308,U_1307))),hAPP(U_1311,U_1311,U_1309,sK40(U_1311,U_1310,U_1309,U_1308,U_1307)))
    | ~ hBOOL(hAPP(fun(fun(U_1311,bool),U_1311),bool,hAPP(fun(U_1311,fun(U_1311,U_1311)),fun(fun(fun(U_1311,bool),U_1311),bool),finite2073411215e_idem(U_1311),U_1308),U_1307)) ),
    inference(clausify,[status(thm)],[f_349_5]) ).

fof(f_350_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_279_termination__basic__simps_I4_J]) ).

fof(f_350_2,plain,
    ! [U_1314,U_1313,U_1312] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1313),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1314),U_1312)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1313),U_1312)) ),
    inference(variable_rename,[status(thm)],[f_350_1]) ).

fof(f_350_3,plain,
    ! [U_1312,U_1314,U_1313] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1313),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1314),U_1312)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1313),U_1312)) ),
    inference(definitional_conversion,[status(esa)],[f_350_2]) ).

cnf(f_350_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1313),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1314),U_1312)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1313),U_1312)) ),
    inference(clausify,[status(thm)],[f_350_3]) ).

fof(f_351_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_280_termination__basic__simps_I3_J]) ).

fof(f_351_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_351_1]) ).

fof(f_351_3,plain,
    ! [U_1315,U_1316,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_351_2]) ).

cnf(f_351_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_351_3]) ).

fof(f_352_1,plain,
    ! [X_b,A_3,B_3] :
      ( ( hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),partial_flat_lub(X_b),B_3),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_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),B_3),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_3),A_3) = ti(X_b,B_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),B_3),bot_bot(fun(X_b,bool))))) ) ),
    inference(fof_nnf,[status(thm)],[fact_281_flat__lub__def]) ).

fof(f_352_2,plain,
    ! [U_1320,U_1319,U_1318] :
      ( ( hAPP(fun(U_1320,bool),U_1320,hAPP(U_1320,fun(fun(U_1320,bool),U_1320),partial_flat_lub(U_1320),U_1318),U_1319) = hAPP(fun(U_1320,bool),U_1320,the(U_1320),hAPP(fun(U_1320,bool),fun(U_1320,bool),hAPP(fun(U_1320,fun(fun(U_1320,bool),bool)),fun(fun(U_1320,bool),fun(U_1320,bool)),combc(U_1320,fun(U_1320,bool),bool),member(U_1320)),hAPP(fun(U_1320,bool),fun(U_1320,bool),hAPP(fun(U_1320,bool),fun(fun(U_1320,bool),fun(U_1320,bool)),minus_minus(fun(U_1320,bool)),U_1319),hAPP(fun(U_1320,bool),fun(U_1320,bool),hAPP(U_1320,fun(fun(U_1320,bool),fun(U_1320,bool)),insert(U_1320),U_1318),bot_bot(fun(U_1320,bool))))))
        | hBOOL(hAPP(fun(U_1320,bool),bool,hAPP(fun(U_1320,bool),fun(fun(U_1320,bool),bool),ord_less_eq(fun(U_1320,bool)),U_1319),hAPP(fun(U_1320,bool),fun(U_1320,bool),hAPP(U_1320,fun(fun(U_1320,bool),fun(U_1320,bool)),insert(U_1320),U_1318),bot_bot(fun(U_1320,bool))))) )
      & ( hAPP(fun(U_1320,bool),U_1320,hAPP(U_1320,fun(fun(U_1320,bool),U_1320),partial_flat_lub(U_1320),U_1318),U_1319) = ti(U_1320,U_1318)
        | ~ hBOOL(hAPP(fun(U_1320,bool),bool,hAPP(fun(U_1320,bool),fun(fun(U_1320,bool),bool),ord_less_eq(fun(U_1320,bool)),U_1319),hAPP(fun(U_1320,bool),fun(U_1320,bool),hAPP(U_1320,fun(fun(U_1320,bool),fun(U_1320,bool)),insert(U_1320),U_1318),bot_bot(fun(U_1320,bool))))) ) ),
    inference(variable_rename,[status(thm)],[f_352_1]) ).

fof(f_352_3,plain,
    ( ! [U_1326,U_1324,U_1322] :
        ( hAPP(fun(U_1326,bool),U_1326,hAPP(U_1326,fun(fun(U_1326,bool),U_1326),partial_flat_lub(U_1326),U_1322),U_1324) = hAPP(fun(U_1326,bool),U_1326,the(U_1326),hAPP(fun(U_1326,bool),fun(U_1326,bool),hAPP(fun(U_1326,fun(fun(U_1326,bool),bool)),fun(fun(U_1326,bool),fun(U_1326,bool)),combc(U_1326,fun(U_1326,bool),bool),member(U_1326)),hAPP(fun(U_1326,bool),fun(U_1326,bool),hAPP(fun(U_1326,bool),fun(fun(U_1326,bool),fun(U_1326,bool)),minus_minus(fun(U_1326,bool)),U_1324),hAPP(fun(U_1326,bool),fun(U_1326,bool),hAPP(U_1326,fun(fun(U_1326,bool),fun(U_1326,bool)),insert(U_1326),U_1322),bot_bot(fun(U_1326,bool))))))
        | hBOOL(hAPP(fun(U_1326,bool),bool,hAPP(fun(U_1326,bool),fun(fun(U_1326,bool),bool),ord_less_eq(fun(U_1326,bool)),U_1324),hAPP(fun(U_1326,bool),fun(U_1326,bool),hAPP(U_1326,fun(fun(U_1326,bool),fun(U_1326,bool)),insert(U_1326),U_1322),bot_bot(fun(U_1326,bool))))) )
    & ! [U_1325,U_1323,U_1321] :
        ( hAPP(fun(U_1325,bool),U_1325,hAPP(U_1325,fun(fun(U_1325,bool),U_1325),partial_flat_lub(U_1325),U_1321),U_1323) = ti(U_1325,U_1321)
        | ~ hBOOL(hAPP(fun(U_1325,bool),bool,hAPP(fun(U_1325,bool),fun(fun(U_1325,bool),bool),ord_less_eq(fun(U_1325,bool)),U_1323),hAPP(fun(U_1325,bool),fun(U_1325,bool),hAPP(U_1325,fun(fun(U_1325,bool),fun(U_1325,bool)),insert(U_1325),U_1321),bot_bot(fun(U_1325,bool))))) ) ),
    inference(miniscope,[status(thm)],[f_352_2]) ).

fof(f_352_4,plain,
    ( ! [U_1324,U_1322,U_1326] :
        ( hAPP(fun(U_1326,bool),U_1326,hAPP(U_1326,fun(fun(U_1326,bool),U_1326),partial_flat_lub(U_1326),U_1322),U_1324) = hAPP(fun(U_1326,bool),U_1326,the(U_1326),hAPP(fun(U_1326,bool),fun(U_1326,bool),hAPP(fun(U_1326,fun(fun(U_1326,bool),bool)),fun(fun(U_1326,bool),fun(U_1326,bool)),combc(U_1326,fun(U_1326,bool),bool),member(U_1326)),hAPP(fun(U_1326,bool),fun(U_1326,bool),hAPP(fun(U_1326,bool),fun(fun(U_1326,bool),fun(U_1326,bool)),minus_minus(fun(U_1326,bool)),U_1324),hAPP(fun(U_1326,bool),fun(U_1326,bool),hAPP(U_1326,fun(fun(U_1326,bool),fun(U_1326,bool)),insert(U_1326),U_1322),bot_bot(fun(U_1326,bool))))))
        | hBOOL(hAPP(fun(U_1326,bool),bool,hAPP(fun(U_1326,bool),fun(fun(U_1326,bool),bool),ord_less_eq(fun(U_1326,bool)),U_1324),hAPP(fun(U_1326,bool),fun(U_1326,bool),hAPP(U_1326,fun(fun(U_1326,bool),fun(U_1326,bool)),insert(U_1326),U_1322),bot_bot(fun(U_1326,bool))))) )
    & ! [U_1325,U_1321,U_1323] :
        ( hAPP(fun(U_1325,bool),U_1325,hAPP(U_1325,fun(fun(U_1325,bool),U_1325),partial_flat_lub(U_1325),U_1321),U_1323) = ti(U_1325,U_1321)
        | ~ hBOOL(hAPP(fun(U_1325,bool),bool,hAPP(fun(U_1325,bool),fun(fun(U_1325,bool),bool),ord_less_eq(fun(U_1325,bool)),U_1323),hAPP(fun(U_1325,bool),fun(U_1325,bool),hAPP(U_1325,fun(fun(U_1325,bool),fun(U_1325,bool)),insert(U_1325),U_1321),bot_bot(fun(U_1325,bool))))) ) ),
    inference(definitional_conversion,[status(esa)],[f_352_3]) ).

cnf(f_352_5,plain,
    ( hAPP(fun(U_1325,bool),U_1325,hAPP(U_1325,fun(fun(U_1325,bool),U_1325),partial_flat_lub(U_1325),U_1321),U_1323) = ti(U_1325,U_1321)
    | ~ hBOOL(hAPP(fun(U_1325,bool),bool,hAPP(fun(U_1325,bool),fun(fun(U_1325,bool),bool),ord_less_eq(fun(U_1325,bool)),U_1323),hAPP(fun(U_1325,bool),fun(U_1325,bool),hAPP(U_1325,fun(fun(U_1325,bool),fun(U_1325,bool)),insert(U_1325),U_1321),bot_bot(fun(U_1325,bool))))) ),
    inference(clausify,[status(thm)],[f_352_4]) ).

cnf(f_352_6,plain,
    ( hAPP(fun(U_1326,bool),U_1326,hAPP(U_1326,fun(fun(U_1326,bool),U_1326),partial_flat_lub(U_1326),U_1322),U_1324) = hAPP(fun(U_1326,bool),U_1326,the(U_1326),hAPP(fun(U_1326,bool),fun(U_1326,bool),hAPP(fun(U_1326,fun(fun(U_1326,bool),bool)),fun(fun(U_1326,bool),fun(U_1326,bool)),combc(U_1326,fun(U_1326,bool),bool),member(U_1326)),hAPP(fun(U_1326,bool),fun(U_1326,bool),hAPP(fun(U_1326,bool),fun(fun(U_1326,bool),fun(U_1326,bool)),minus_minus(fun(U_1326,bool)),U_1324),hAPP(fun(U_1326,bool),fun(U_1326,bool),hAPP(U_1326,fun(fun(U_1326,bool),fun(U_1326,bool)),insert(U_1326),U_1322),bot_bot(fun(U_1326,bool))))))
    | hBOOL(hAPP(fun(U_1326,bool),bool,hAPP(fun(U_1326,bool),fun(fun(U_1326,bool),bool),ord_less_eq(fun(U_1326,bool)),U_1324),hAPP(fun(U_1326,bool),fun(U_1326,bool),hAPP(U_1326,fun(fun(U_1326,bool),fun(U_1326,bool)),insert(U_1326),U_1322),bot_bot(fun(U_1326,bool))))) ),
    inference(clausify,[status(thm)],[f_352_4]) ).

fof(f_353_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_282_comp__fun__idem__remove]) ).

fof(f_353_2,plain,
    ! [U_1327] : hBOOL(hAPP(fun(U_1327,fun(fun(U_1327,bool),fun(U_1327,bool))),bool,finite_comp_fun_idem(U_1327,fun(U_1327,bool)),hAPP(fun(U_1327,fun(U_1327,bool)),fun(U_1327,fun(fun(U_1327,bool),fun(U_1327,bool))),hAPP(fun(fun(U_1327,bool),fun(fun(U_1327,bool),fun(U_1327,bool))),fun(fun(U_1327,fun(U_1327,bool)),fun(U_1327,fun(fun(U_1327,bool),fun(U_1327,bool)))),combb(fun(U_1327,bool),fun(fun(U_1327,bool),fun(U_1327,bool)),U_1327),hAPP(fun(fun(U_1327,bool),fun(fun(U_1327,bool),fun(U_1327,bool))),fun(fun(U_1327,bool),fun(fun(U_1327,bool),fun(U_1327,bool))),combc(fun(U_1327,bool),fun(U_1327,bool),fun(U_1327,bool)),minus_minus(fun(U_1327,bool)))),hAPP(fun(U_1327,bool),fun(U_1327,fun(U_1327,bool)),hAPP(fun(U_1327,fun(fun(U_1327,bool),fun(U_1327,bool))),fun(fun(U_1327,bool),fun(U_1327,fun(U_1327,bool))),combc(U_1327,fun(U_1327,bool),fun(U_1327,bool)),insert(U_1327)),bot_bot(fun(U_1327,bool)))))),
    inference(variable_rename,[status(thm)],[f_353_1]) ).

fof(f_353_3,plain,
    ! [U_1327] : hBOOL(hAPP(fun(U_1327,fun(fun(U_1327,bool),fun(U_1327,bool))),bool,finite_comp_fun_idem(U_1327,fun(U_1327,bool)),hAPP(fun(U_1327,fun(U_1327,bool)),fun(U_1327,fun(fun(U_1327,bool),fun(U_1327,bool))),hAPP(fun(fun(U_1327,bool),fun(fun(U_1327,bool),fun(U_1327,bool))),fun(fun(U_1327,fun(U_1327,bool)),fun(U_1327,fun(fun(U_1327,bool),fun(U_1327,bool)))),combb(fun(U_1327,bool),fun(fun(U_1327,bool),fun(U_1327,bool)),U_1327),hAPP(fun(fun(U_1327,bool),fun(fun(U_1327,bool),fun(U_1327,bool))),fun(fun(U_1327,bool),fun(fun(U_1327,bool),fun(U_1327,bool))),combc(fun(U_1327,bool),fun(U_1327,bool),fun(U_1327,bool)),minus_minus(fun(U_1327,bool)))),hAPP(fun(U_1327,bool),fun(U_1327,fun(U_1327,bool)),hAPP(fun(U_1327,fun(fun(U_1327,bool),fun(U_1327,bool))),fun(fun(U_1327,bool),fun(U_1327,fun(U_1327,bool))),combc(U_1327,fun(U_1327,bool),fun(U_1327,bool)),insert(U_1327)),bot_bot(fun(U_1327,bool)))))),
    inference(definitional_conversion,[status(esa)],[f_353_2]) ).

cnf(f_353_4,plain,
    hBOOL(hAPP(fun(U_1327,fun(fun(U_1327,bool),fun(U_1327,bool))),bool,finite_comp_fun_idem(U_1327,fun(U_1327,bool)),hAPP(fun(U_1327,fun(U_1327,bool)),fun(U_1327,fun(fun(U_1327,bool),fun(U_1327,bool))),hAPP(fun(fun(U_1327,bool),fun(fun(U_1327,bool),fun(U_1327,bool))),fun(fun(U_1327,fun(U_1327,bool)),fun(U_1327,fun(fun(U_1327,bool),fun(U_1327,bool)))),combb(fun(U_1327,bool),fun(fun(U_1327,bool),fun(U_1327,bool)),U_1327),hAPP(fun(fun(U_1327,bool),fun(fun(U_1327,bool),fun(U_1327,bool))),fun(fun(U_1327,bool),fun(fun(U_1327,bool),fun(U_1327,bool))),combc(fun(U_1327,bool),fun(U_1327,bool),fun(U_1327,bool)),minus_minus(fun(U_1327,bool)))),hAPP(fun(U_1327,bool),fun(U_1327,fun(U_1327,bool)),hAPP(fun(U_1327,fun(fun(U_1327,bool),fun(U_1327,bool))),fun(fun(U_1327,bool),fun(U_1327,fun(U_1327,bool))),combc(U_1327,fun(U_1327,bool),fun(U_1327,bool)),insert(U_1327)),bot_bot(fun(U_1327,bool)))))),
    inference(clausify,[status(thm)],[f_353_3]) ).

fof(f_354_1,plain,
    ! [X_b,X_1,Y_2,Pa] :
      ( ( ti(X_b,Y_2) = 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_2))))
        | 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_2))))
        | ~ hBOOL(Pa) ) ),
    inference(fof_nnf,[status(thm)],[fact_283_If__def]) ).

fof(f_354_2,plain,
    ! [U_1331,U_1330,U_1329,U_1328] :
      ( ( ti(U_1331,U_1329) = hAPP(fun(U_1331,bool),U_1331,the(U_1331),hAPP(fun(U_1331,bool),fun(U_1331,bool),hAPP(fun(U_1331,fun(bool,bool)),fun(fun(U_1331,bool),fun(U_1331,bool)),combs(U_1331,bool,bool),hAPP(fun(U_1331,bool),fun(U_1331,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_1331,bool),fun(U_1331,fun(bool,bool))),combb(bool,fun(bool,bool),U_1331),fconj),hAPP(fun(U_1331,bool),fun(U_1331,bool),hAPP(fun(bool,bool),fun(fun(U_1331,bool),fun(U_1331,bool)),combb(bool,bool,U_1331),hAPP(bool,fun(bool,bool),fimplies,U_1328)),hAPP(U_1331,fun(U_1331,bool),hAPP(fun(U_1331,fun(U_1331,bool)),fun(U_1331,fun(U_1331,bool)),combc(U_1331,U_1331,bool),fequal(U_1331)),U_1330)))),hAPP(fun(U_1331,bool),fun(U_1331,bool),hAPP(fun(bool,bool),fun(fun(U_1331,bool),fun(U_1331,bool)),combb(bool,bool,U_1331),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,U_1328))),hAPP(U_1331,fun(U_1331,bool),hAPP(fun(U_1331,fun(U_1331,bool)),fun(U_1331,fun(U_1331,bool)),combc(U_1331,U_1331,bool),fequal(U_1331)),U_1329))))
        | hBOOL(U_1328) )
      & ( ti(U_1331,U_1330) = hAPP(fun(U_1331,bool),U_1331,the(U_1331),hAPP(fun(U_1331,bool),fun(U_1331,bool),hAPP(fun(U_1331,fun(bool,bool)),fun(fun(U_1331,bool),fun(U_1331,bool)),combs(U_1331,bool,bool),hAPP(fun(U_1331,bool),fun(U_1331,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_1331,bool),fun(U_1331,fun(bool,bool))),combb(bool,fun(bool,bool),U_1331),fconj),hAPP(fun(U_1331,bool),fun(U_1331,bool),hAPP(fun(bool,bool),fun(fun(U_1331,bool),fun(U_1331,bool)),combb(bool,bool,U_1331),hAPP(bool,fun(bool,bool),fimplies,U_1328)),hAPP(U_1331,fun(U_1331,bool),hAPP(fun(U_1331,fun(U_1331,bool)),fun(U_1331,fun(U_1331,bool)),combc(U_1331,U_1331,bool),fequal(U_1331)),U_1330)))),hAPP(fun(U_1331,bool),fun(U_1331,bool),hAPP(fun(bool,bool),fun(fun(U_1331,bool),fun(U_1331,bool)),combb(bool,bool,U_1331),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,U_1328))),hAPP(U_1331,fun(U_1331,bool),hAPP(fun(U_1331,fun(U_1331,bool)),fun(U_1331,fun(U_1331,bool)),combc(U_1331,U_1331,bool),fequal(U_1331)),U_1329))))
        | ~ hBOOL(U_1328) ) ),
    inference(variable_rename,[status(thm)],[f_354_1]) ).

fof(f_354_3,plain,
    ( ! [U_1339,U_1337,U_1335,U_1333] :
        ( ti(U_1339,U_1335) = hAPP(fun(U_1339,bool),U_1339,the(U_1339),hAPP(fun(U_1339,bool),fun(U_1339,bool),hAPP(fun(U_1339,fun(bool,bool)),fun(fun(U_1339,bool),fun(U_1339,bool)),combs(U_1339,bool,bool),hAPP(fun(U_1339,bool),fun(U_1339,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_1339,bool),fun(U_1339,fun(bool,bool))),combb(bool,fun(bool,bool),U_1339),fconj),hAPP(fun(U_1339,bool),fun(U_1339,bool),hAPP(fun(bool,bool),fun(fun(U_1339,bool),fun(U_1339,bool)),combb(bool,bool,U_1339),hAPP(bool,fun(bool,bool),fimplies,U_1333)),hAPP(U_1339,fun(U_1339,bool),hAPP(fun(U_1339,fun(U_1339,bool)),fun(U_1339,fun(U_1339,bool)),combc(U_1339,U_1339,bool),fequal(U_1339)),U_1337)))),hAPP(fun(U_1339,bool),fun(U_1339,bool),hAPP(fun(bool,bool),fun(fun(U_1339,bool),fun(U_1339,bool)),combb(bool,bool,U_1339),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,U_1333))),hAPP(U_1339,fun(U_1339,bool),hAPP(fun(U_1339,fun(U_1339,bool)),fun(U_1339,fun(U_1339,bool)),combc(U_1339,U_1339,bool),fequal(U_1339)),U_1335))))
        | hBOOL(U_1333) )
    & ! [U_1338,U_1336,U_1334,U_1332] :
        ( ti(U_1338,U_1336) = hAPP(fun(U_1338,bool),U_1338,the(U_1338),hAPP(fun(U_1338,bool),fun(U_1338,bool),hAPP(fun(U_1338,fun(bool,bool)),fun(fun(U_1338,bool),fun(U_1338,bool)),combs(U_1338,bool,bool),hAPP(fun(U_1338,bool),fun(U_1338,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_1338,bool),fun(U_1338,fun(bool,bool))),combb(bool,fun(bool,bool),U_1338),fconj),hAPP(fun(U_1338,bool),fun(U_1338,bool),hAPP(fun(bool,bool),fun(fun(U_1338,bool),fun(U_1338,bool)),combb(bool,bool,U_1338),hAPP(bool,fun(bool,bool),fimplies,U_1332)),hAPP(U_1338,fun(U_1338,bool),hAPP(fun(U_1338,fun(U_1338,bool)),fun(U_1338,fun(U_1338,bool)),combc(U_1338,U_1338,bool),fequal(U_1338)),U_1336)))),hAPP(fun(U_1338,bool),fun(U_1338,bool),hAPP(fun(bool,bool),fun(fun(U_1338,bool),fun(U_1338,bool)),combb(bool,bool,U_1338),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,U_1332))),hAPP(U_1338,fun(U_1338,bool),hAPP(fun(U_1338,fun(U_1338,bool)),fun(U_1338,fun(U_1338,bool)),combc(U_1338,U_1338,bool),fequal(U_1338)),U_1334))))
        | ~ hBOOL(U_1332) ) ),
    inference(miniscope,[status(thm)],[f_354_2]) ).

fof(f_354_4,plain,
    ( ! [U_1339,U_1333,U_1335,U_1337] :
        ( ti(U_1339,U_1335) = hAPP(fun(U_1339,bool),U_1339,the(U_1339),hAPP(fun(U_1339,bool),fun(U_1339,bool),hAPP(fun(U_1339,fun(bool,bool)),fun(fun(U_1339,bool),fun(U_1339,bool)),combs(U_1339,bool,bool),hAPP(fun(U_1339,bool),fun(U_1339,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_1339,bool),fun(U_1339,fun(bool,bool))),combb(bool,fun(bool,bool),U_1339),fconj),hAPP(fun(U_1339,bool),fun(U_1339,bool),hAPP(fun(bool,bool),fun(fun(U_1339,bool),fun(U_1339,bool)),combb(bool,bool,U_1339),hAPP(bool,fun(bool,bool),fimplies,U_1333)),hAPP(U_1339,fun(U_1339,bool),hAPP(fun(U_1339,fun(U_1339,bool)),fun(U_1339,fun(U_1339,bool)),combc(U_1339,U_1339,bool),fequal(U_1339)),U_1337)))),hAPP(fun(U_1339,bool),fun(U_1339,bool),hAPP(fun(bool,bool),fun(fun(U_1339,bool),fun(U_1339,bool)),combb(bool,bool,U_1339),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,U_1333))),hAPP(U_1339,fun(U_1339,bool),hAPP(fun(U_1339,fun(U_1339,bool)),fun(U_1339,fun(U_1339,bool)),combc(U_1339,U_1339,bool),fequal(U_1339)),U_1335))))
        | hBOOL(U_1333) )
    & ! [U_1334,U_1332,U_1338,U_1336] :
        ( ti(U_1338,U_1336) = hAPP(fun(U_1338,bool),U_1338,the(U_1338),hAPP(fun(U_1338,bool),fun(U_1338,bool),hAPP(fun(U_1338,fun(bool,bool)),fun(fun(U_1338,bool),fun(U_1338,bool)),combs(U_1338,bool,bool),hAPP(fun(U_1338,bool),fun(U_1338,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_1338,bool),fun(U_1338,fun(bool,bool))),combb(bool,fun(bool,bool),U_1338),fconj),hAPP(fun(U_1338,bool),fun(U_1338,bool),hAPP(fun(bool,bool),fun(fun(U_1338,bool),fun(U_1338,bool)),combb(bool,bool,U_1338),hAPP(bool,fun(bool,bool),fimplies,U_1332)),hAPP(U_1338,fun(U_1338,bool),hAPP(fun(U_1338,fun(U_1338,bool)),fun(U_1338,fun(U_1338,bool)),combc(U_1338,U_1338,bool),fequal(U_1338)),U_1336)))),hAPP(fun(U_1338,bool),fun(U_1338,bool),hAPP(fun(bool,bool),fun(fun(U_1338,bool),fun(U_1338,bool)),combb(bool,bool,U_1338),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,U_1332))),hAPP(U_1338,fun(U_1338,bool),hAPP(fun(U_1338,fun(U_1338,bool)),fun(U_1338,fun(U_1338,bool)),combc(U_1338,U_1338,bool),fequal(U_1338)),U_1334))))
        | ~ hBOOL(U_1332) ) ),
    inference(definitional_conversion,[status(esa)],[f_354_3]) ).

cnf(f_354_5,plain,
    ( ti(U_1338,U_1336) = hAPP(fun(U_1338,bool),U_1338,the(U_1338),hAPP(fun(U_1338,bool),fun(U_1338,bool),hAPP(fun(U_1338,fun(bool,bool)),fun(fun(U_1338,bool),fun(U_1338,bool)),combs(U_1338,bool,bool),hAPP(fun(U_1338,bool),fun(U_1338,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_1338,bool),fun(U_1338,fun(bool,bool))),combb(bool,fun(bool,bool),U_1338),fconj),hAPP(fun(U_1338,bool),fun(U_1338,bool),hAPP(fun(bool,bool),fun(fun(U_1338,bool),fun(U_1338,bool)),combb(bool,bool,U_1338),hAPP(bool,fun(bool,bool),fimplies,U_1332)),hAPP(U_1338,fun(U_1338,bool),hAPP(fun(U_1338,fun(U_1338,bool)),fun(U_1338,fun(U_1338,bool)),combc(U_1338,U_1338,bool),fequal(U_1338)),U_1336)))),hAPP(fun(U_1338,bool),fun(U_1338,bool),hAPP(fun(bool,bool),fun(fun(U_1338,bool),fun(U_1338,bool)),combb(bool,bool,U_1338),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,U_1332))),hAPP(U_1338,fun(U_1338,bool),hAPP(fun(U_1338,fun(U_1338,bool)),fun(U_1338,fun(U_1338,bool)),combc(U_1338,U_1338,bool),fequal(U_1338)),U_1334))))
    | ~ hBOOL(U_1332) ),
    inference(clausify,[status(thm)],[f_354_4]) ).

cnf(f_354_6,plain,
    ( ti(U_1339,U_1335) = hAPP(fun(U_1339,bool),U_1339,the(U_1339),hAPP(fun(U_1339,bool),fun(U_1339,bool),hAPP(fun(U_1339,fun(bool,bool)),fun(fun(U_1339,bool),fun(U_1339,bool)),combs(U_1339,bool,bool),hAPP(fun(U_1339,bool),fun(U_1339,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_1339,bool),fun(U_1339,fun(bool,bool))),combb(bool,fun(bool,bool),U_1339),fconj),hAPP(fun(U_1339,bool),fun(U_1339,bool),hAPP(fun(bool,bool),fun(fun(U_1339,bool),fun(U_1339,bool)),combb(bool,bool,U_1339),hAPP(bool,fun(bool,bool),fimplies,U_1333)),hAPP(U_1339,fun(U_1339,bool),hAPP(fun(U_1339,fun(U_1339,bool)),fun(U_1339,fun(U_1339,bool)),combc(U_1339,U_1339,bool),fequal(U_1339)),U_1337)))),hAPP(fun(U_1339,bool),fun(U_1339,bool),hAPP(fun(bool,bool),fun(fun(U_1339,bool),fun(U_1339,bool)),combb(bool,bool,U_1339),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,U_1333))),hAPP(U_1339,fun(U_1339,bool),hAPP(fun(U_1339,fun(U_1339,bool)),fun(U_1339,fun(U_1339,bool)),combc(U_1339,U_1339,bool),fequal(U_1339)),U_1335))))
    | hBOOL(U_1333) ),
    inference(clausify,[status(thm)],[f_354_4]) ).

fof(f_355_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_284_the__eq__trivial]) ).

fof(f_355_2,plain,
    ! [U_1341,U_1340] : hAPP(fun(U_1341,bool),U_1341,the(U_1341),hAPP(U_1341,fun(U_1341,bool),hAPP(fun(U_1341,fun(U_1341,bool)),fun(U_1341,fun(U_1341,bool)),combc(U_1341,U_1341,bool),fequal(U_1341)),U_1340)) = ti(U_1341,U_1340),
    inference(variable_rename,[status(thm)],[f_355_1]) ).

fof(f_355_3,plain,
    ! [U_1340,U_1341] : hAPP(fun(U_1341,bool),U_1341,the(U_1341),hAPP(U_1341,fun(U_1341,bool),hAPP(fun(U_1341,fun(U_1341,bool)),fun(U_1341,fun(U_1341,bool)),combc(U_1341,U_1341,bool),fequal(U_1341)),U_1340)) = ti(U_1341,U_1340),
    inference(definitional_conversion,[status(esa)],[f_355_2]) ).

cnf(f_355_4,plain,
    hAPP(fun(U_1341,bool),U_1341,the(U_1341),hAPP(U_1341,fun(U_1341,bool),hAPP(fun(U_1341,fun(U_1341,bool)),fun(U_1341,fun(U_1341,bool)),combc(U_1341,U_1341,bool),fequal(U_1341)),U_1340)) = ti(U_1341,U_1340),
    inference(clausify,[status(thm)],[f_355_3]) ).

fof(f_356_1,plain,
    ! [X_b,X_c,X_1,Z_2,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_2)) = hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),Z_2)
      | ~ 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_285_comp__fun__idem_Ofun__left__idem]) ).

fof(f_356_2,plain,
    ! [U_1346,U_1345,U_1344,U_1343,U_1342] :
      ( hAPP(U_1345,U_1345,hAPP(U_1346,fun(U_1345,U_1345),U_1342,U_1344),hAPP(U_1345,U_1345,hAPP(U_1346,fun(U_1345,U_1345),U_1342,U_1344),U_1343)) = hAPP(U_1345,U_1345,hAPP(U_1346,fun(U_1345,U_1345),U_1342,U_1344),U_1343)
      | ~ hBOOL(hAPP(fun(U_1346,fun(U_1345,U_1345)),bool,finite_comp_fun_idem(U_1346,U_1345),U_1342)) ),
    inference(variable_rename,[status(thm)],[f_356_1]) ).

fof(f_356_3,plain,
    ! [U_1345,U_1344,U_1342,U_1343,U_1346] :
      ( hAPP(U_1345,U_1345,hAPP(U_1346,fun(U_1345,U_1345),U_1342,U_1344),hAPP(U_1345,U_1345,hAPP(U_1346,fun(U_1345,U_1345),U_1342,U_1344),U_1343)) = hAPP(U_1345,U_1345,hAPP(U_1346,fun(U_1345,U_1345),U_1342,U_1344),U_1343)
      | ~ hBOOL(hAPP(fun(U_1346,fun(U_1345,U_1345)),bool,finite_comp_fun_idem(U_1346,U_1345),U_1342)) ),
    inference(definitional_conversion,[status(esa)],[f_356_2]) ).

cnf(f_356_4,plain,
    ( hAPP(U_1345,U_1345,hAPP(U_1346,fun(U_1345,U_1345),U_1342,U_1344),hAPP(U_1345,U_1345,hAPP(U_1346,fun(U_1345,U_1345),U_1342,U_1344),U_1343)) = hAPP(U_1345,U_1345,hAPP(U_1346,fun(U_1345,U_1345),U_1342,U_1344),U_1343)
    | ~ hBOOL(hAPP(fun(U_1346,fun(U_1345,U_1345)),bool,finite_comp_fun_idem(U_1346,U_1345),U_1342)) ),
    inference(clausify,[status(thm)],[f_356_3]) ).

fof(f_357_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_286_comp__fun__idem__insert]) ).

fof(f_357_2,plain,
    ! [U_1347] : hBOOL(hAPP(fun(U_1347,fun(fun(U_1347,bool),fun(U_1347,bool))),bool,finite_comp_fun_idem(U_1347,fun(U_1347,bool)),insert(U_1347))),
    inference(variable_rename,[status(thm)],[f_357_1]) ).

fof(f_357_3,plain,
    ! [U_1347] : hBOOL(hAPP(fun(U_1347,fun(fun(U_1347,bool),fun(U_1347,bool))),bool,finite_comp_fun_idem(U_1347,fun(U_1347,bool)),insert(U_1347))),
    inference(definitional_conversion,[status(esa)],[f_357_2]) ).

cnf(f_357_4,plain,
    hBOOL(hAPP(fun(U_1347,fun(fun(U_1347,bool),fun(U_1347,bool))),bool,finite_comp_fun_idem(U_1347,fun(U_1347,bool)),insert(U_1347))),
    inference(clausify,[status(thm)],[f_357_3]) ).

fof(f_358_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_287_the__sym__eq__trivial]) ).

fof(f_358_2,plain,
    ! [U_1349,U_1348] : hAPP(fun(U_1349,bool),U_1349,the(U_1349),hAPP(U_1349,fun(U_1349,bool),fequal(U_1349),U_1348)) = ti(U_1349,U_1348),
    inference(variable_rename,[status(thm)],[f_358_1]) ).

fof(f_358_3,plain,
    ! [U_1348,U_1349] : hAPP(fun(U_1349,bool),U_1349,the(U_1349),hAPP(U_1349,fun(U_1349,bool),fequal(U_1349),U_1348)) = ti(U_1349,U_1348),
    inference(definitional_conversion,[status(esa)],[f_358_2]) ).

cnf(f_358_4,plain,
    hAPP(fun(U_1349,bool),U_1349,the(U_1349),hAPP(U_1349,fun(U_1349,bool),fequal(U_1349),U_1348)) = ti(U_1349,U_1348),
    inference(clausify,[status(thm)],[f_358_3]) ).

fof(f_359_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_288_the__equality]) ).

fof(f_359_2,plain,
    ! [U_1353,U_1352,U_1351] :
      ( hAPP(fun(U_1353,bool),U_1353,the(U_1353),U_1352) = ti(U_1353,U_1351)
      | ? [U_1350] :
          ( ti(U_1353,U_1350) != ti(U_1353,U_1351)
          & hBOOL(hAPP(U_1353,bool,U_1352,U_1350)) )
      | ~ hBOOL(hAPP(U_1353,bool,U_1352,U_1351)) ),
    inference(variable_rename,[status(thm)],[f_359_1]) ).

fof(f_359_3,plain,
    ! [U_1353,U_1352,U_1351] :
      ( hAPP(fun(U_1353,bool),U_1353,the(U_1353),U_1352) = ti(U_1353,U_1351)
      | ( ti(U_1353,sK41(U_1353,U_1352,U_1351)) != ti(U_1353,U_1351)
        & hBOOL(hAPP(U_1353,bool,U_1352,sK41(U_1353,U_1352,U_1351))) )
      | ~ hBOOL(hAPP(U_1353,bool,U_1352,U_1351)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK41]),skolemize(U_1350,sK41(U_1353,U_1352,U_1351))],[f_359_2]) ).

fof(f_359_4,plain,
    ( ! [U_1351,U_1352,U_1353] :
        ( ti(U_1353,sK41(U_1353,U_1352,U_1351)) != ti(U_1353,U_1351)
        | ~ sP59(U_1351,U_1352,U_1353) )
    & ! [U_1351,U_1352,U_1353] :
        ( hBOOL(hAPP(U_1353,bool,U_1352,sK41(U_1353,U_1352,U_1351)))
        | ~ sP59(U_1351,U_1352,U_1353) )
    & ! [U_1351,U_1352,U_1353] :
        ( hAPP(fun(U_1353,bool),U_1353,the(U_1353),U_1352) = ti(U_1353,U_1351)
        | sP59(U_1351,U_1352,U_1353)
        | ~ hBOOL(hAPP(U_1353,bool,U_1352,U_1351)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP59])],[f_359_3]) ).

cnf(f_359_5,plain,
    ( hAPP(fun(U_1353,bool),U_1353,the(U_1353),U_1352) = ti(U_1353,U_1351)
    | sP59(U_1351,U_1352,U_1353)
    | ~ hBOOL(hAPP(U_1353,bool,U_1352,U_1351)) ),
    inference(clausify,[status(thm)],[f_359_4]) ).

cnf(f_359_6,plain,
    ( hBOOL(hAPP(U_1353,bool,U_1352,sK41(U_1353,U_1352,U_1351)))
    | ~ sP59(U_1351,U_1352,U_1353) ),
    inference(clausify,[status(thm)],[f_359_4]) ).

cnf(f_359_7,plain,
    ( ti(U_1353,sK41(U_1353,U_1352,U_1351)) != ti(U_1353,U_1351)
    | ~ sP59(U_1351,U_1352,U_1353) ),
    inference(clausify,[status(thm)],[f_359_4]) ).

fof(f_360_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_1] :
              ( ti(X_b,Y_1) != ti(X_b,X_2)
              & hBOOL(hAPP(X_b,bool,Pa,Y_1)) )
          | ~ hBOOL(hAPP(X_b,bool,Pa,X_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_289_theI_H]) ).

fof(f_360_2,plain,
    ! [U_1357,U_1356] :
      ( hBOOL(hAPP(U_1357,bool,U_1356,hAPP(fun(U_1357,bool),U_1357,the(U_1357),U_1356)))
      | ! [U_1355] :
          ( ? [U_1354] :
              ( ti(U_1357,U_1354) != ti(U_1357,U_1355)
              & hBOOL(hAPP(U_1357,bool,U_1356,U_1354)) )
          | ~ hBOOL(hAPP(U_1357,bool,U_1356,U_1355)) ) ),
    inference(variable_rename,[status(thm)],[f_360_1]) ).

fof(f_360_3,plain,
    ! [U_1357,U_1356] :
      ( hBOOL(hAPP(U_1357,bool,U_1356,hAPP(fun(U_1357,bool),U_1357,the(U_1357),U_1356)))
      | ! [U_1355] :
          ( ( ti(U_1357,sK42(U_1357,U_1356,U_1355)) != ti(U_1357,U_1355)
            & hBOOL(hAPP(U_1357,bool,U_1356,sK42(U_1357,U_1356,U_1355))) )
          | ~ hBOOL(hAPP(U_1357,bool,U_1356,U_1355)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK42]),skolemize(U_1354,sK42(U_1357,U_1356,U_1355))],[f_360_2]) ).

fof(f_360_4,plain,
    ( ! [U_1355,U_1356,U_1357] :
        ( ti(U_1357,sK42(U_1357,U_1356,U_1355)) != ti(U_1357,U_1355)
        | ~ sP60(U_1355,U_1356,U_1357) )
    & ! [U_1355,U_1356,U_1357] :
        ( hBOOL(hAPP(U_1357,bool,U_1356,sK42(U_1357,U_1356,U_1355)))
        | ~ sP60(U_1355,U_1356,U_1357) )
    & ! [U_1355,U_1356,U_1357] :
        ( hBOOL(hAPP(U_1357,bool,U_1356,hAPP(fun(U_1357,bool),U_1357,the(U_1357),U_1356)))
        | sP60(U_1355,U_1356,U_1357)
        | ~ hBOOL(hAPP(U_1357,bool,U_1356,U_1355)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP60])],[f_360_3]) ).

cnf(f_360_5,plain,
    ( hBOOL(hAPP(U_1357,bool,U_1356,hAPP(fun(U_1357,bool),U_1357,the(U_1357),U_1356)))
    | sP60(U_1355,U_1356,U_1357)
    | ~ hBOOL(hAPP(U_1357,bool,U_1356,U_1355)) ),
    inference(clausify,[status(thm)],[f_360_4]) ).

cnf(f_360_6,plain,
    ( hBOOL(hAPP(U_1357,bool,U_1356,sK42(U_1357,U_1356,U_1355)))
    | ~ sP60(U_1355,U_1356,U_1357) ),
    inference(clausify,[status(thm)],[f_360_4]) ).

cnf(f_360_7,plain,
    ( ti(U_1357,sK42(U_1357,U_1356,U_1355)) != ti(U_1357,U_1355)
    | ~ sP60(U_1355,U_1356,U_1357) ),
    inference(clausify,[status(thm)],[f_360_4]) ).

fof(f_361_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_1] :
              ( ti(X_b,Y_1) != ti(X_b,X_2)
              & hBOOL(hAPP(X_b,bool,Pa,Y_1)) )
          | ~ hBOOL(hAPP(X_b,bool,Pa,X_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_290_the1__equality]) ).

fof(f_361_2,plain,
    ! [U_1362,U_1361,U_1360] :
      ( hAPP(fun(U_1362,bool),U_1362,the(U_1362),U_1360) = ti(U_1362,U_1361)
      | ~ hBOOL(hAPP(U_1362,bool,U_1360,U_1361))
      | ! [U_1359] :
          ( ? [U_1358] :
              ( ti(U_1362,U_1358) != ti(U_1362,U_1359)
              & hBOOL(hAPP(U_1362,bool,U_1360,U_1358)) )
          | ~ hBOOL(hAPP(U_1362,bool,U_1360,U_1359)) ) ),
    inference(variable_rename,[status(thm)],[f_361_1]) ).

fof(f_361_3,plain,
    ! [U_1362,U_1361,U_1360] :
      ( hAPP(fun(U_1362,bool),U_1362,the(U_1362),U_1360) = ti(U_1362,U_1361)
      | ~ hBOOL(hAPP(U_1362,bool,U_1360,U_1361))
      | ! [U_1359] :
          ( ( ti(U_1362,sK43(U_1362,U_1361,U_1360,U_1359)) != ti(U_1362,U_1359)
            & hBOOL(hAPP(U_1362,bool,U_1360,sK43(U_1362,U_1361,U_1360,U_1359))) )
          | ~ hBOOL(hAPP(U_1362,bool,U_1360,U_1359)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK43]),skolemize(U_1358,sK43(U_1362,U_1361,U_1360,U_1359))],[f_361_2]) ).

fof(f_361_4,plain,
    ( ! [U_1359,U_1360,U_1361,U_1362] :
        ( ti(U_1362,sK43(U_1362,U_1361,U_1360,U_1359)) != ti(U_1362,U_1359)
        | ~ sP61(U_1359,U_1360,U_1361,U_1362) )
    & ! [U_1359,U_1360,U_1361,U_1362] :
        ( hBOOL(hAPP(U_1362,bool,U_1360,sK43(U_1362,U_1361,U_1360,U_1359)))
        | ~ sP61(U_1359,U_1360,U_1361,U_1362) )
    & ! [U_1359,U_1360,U_1361,U_1362] :
        ( hAPP(fun(U_1362,bool),U_1362,the(U_1362),U_1360) = ti(U_1362,U_1361)
        | ~ hBOOL(hAPP(U_1362,bool,U_1360,U_1361))
        | sP61(U_1359,U_1360,U_1361,U_1362)
        | ~ hBOOL(hAPP(U_1362,bool,U_1360,U_1359)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP61])],[f_361_3]) ).

cnf(f_361_5,plain,
    ( hAPP(fun(U_1362,bool),U_1362,the(U_1362),U_1360) = ti(U_1362,U_1361)
    | ~ hBOOL(hAPP(U_1362,bool,U_1360,U_1361))
    | sP61(U_1359,U_1360,U_1361,U_1362)
    | ~ hBOOL(hAPP(U_1362,bool,U_1360,U_1359)) ),
    inference(clausify,[status(thm)],[f_361_4]) ).

cnf(f_361_6,plain,
    ( hBOOL(hAPP(U_1362,bool,U_1360,sK43(U_1362,U_1361,U_1360,U_1359)))
    | ~ sP61(U_1359,U_1360,U_1361,U_1362) ),
    inference(clausify,[status(thm)],[f_361_4]) ).

cnf(f_361_7,plain,
    ( ti(U_1362,sK43(U_1362,U_1361,U_1360,U_1359)) != ti(U_1362,U_1359)
    | ~ sP61(U_1359,U_1360,U_1361,U_1362) ),
    inference(clausify,[status(thm)],[f_361_4]) ).

fof(f_362_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_291_theI]) ).

fof(f_362_2,plain,
    ! [U_1366,U_1365,U_1364] :
      ( hBOOL(hAPP(U_1366,bool,U_1365,hAPP(fun(U_1366,bool),U_1366,the(U_1366),U_1365)))
      | ? [U_1363] :
          ( ti(U_1366,U_1363) != ti(U_1366,U_1364)
          & hBOOL(hAPP(U_1366,bool,U_1365,U_1363)) )
      | ~ hBOOL(hAPP(U_1366,bool,U_1365,U_1364)) ),
    inference(variable_rename,[status(thm)],[f_362_1]) ).

fof(f_362_3,plain,
    ! [U_1366,U_1365,U_1364] :
      ( hBOOL(hAPP(U_1366,bool,U_1365,hAPP(fun(U_1366,bool),U_1366,the(U_1366),U_1365)))
      | ( ti(U_1366,sK44(U_1366,U_1365,U_1364)) != ti(U_1366,U_1364)
        & hBOOL(hAPP(U_1366,bool,U_1365,sK44(U_1366,U_1365,U_1364))) )
      | ~ hBOOL(hAPP(U_1366,bool,U_1365,U_1364)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK44]),skolemize(U_1363,sK44(U_1366,U_1365,U_1364))],[f_362_2]) ).

fof(f_362_4,plain,
    ( ! [U_1366,U_1365,U_1364] :
        ( ti(U_1366,sK44(U_1366,U_1365,U_1364)) != ti(U_1366,U_1364)
        | ~ sP62(U_1366,U_1365,U_1364) )
    & ! [U_1366,U_1365,U_1364] :
        ( hBOOL(hAPP(U_1366,bool,U_1365,sK44(U_1366,U_1365,U_1364)))
        | ~ sP62(U_1366,U_1365,U_1364) )
    & ! [U_1366,U_1365,U_1364] :
        ( hBOOL(hAPP(U_1366,bool,U_1365,hAPP(fun(U_1366,bool),U_1366,the(U_1366),U_1365)))
        | sP62(U_1366,U_1365,U_1364)
        | ~ hBOOL(hAPP(U_1366,bool,U_1365,U_1364)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP62])],[f_362_3]) ).

cnf(f_362_5,plain,
    ( hBOOL(hAPP(U_1366,bool,U_1365,hAPP(fun(U_1366,bool),U_1366,the(U_1366),U_1365)))
    | sP62(U_1366,U_1365,U_1364)
    | ~ hBOOL(hAPP(U_1366,bool,U_1365,U_1364)) ),
    inference(clausify,[status(thm)],[f_362_4]) ).

cnf(f_362_6,plain,
    ( hBOOL(hAPP(U_1366,bool,U_1365,sK44(U_1366,U_1365,U_1364)))
    | ~ sP62(U_1366,U_1365,U_1364) ),
    inference(clausify,[status(thm)],[f_362_4]) ).

cnf(f_362_7,plain,
    ( ti(U_1366,sK44(U_1366,U_1365,U_1364)) != ti(U_1366,U_1364)
    | ~ sP62(U_1366,U_1365,U_1364) ),
    inference(clausify,[status(thm)],[f_362_4]) ).

fof(f_363_1,plain,
    ! [X_b,Y_2,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_2),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_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)) ),
    inference(fof_nnf,[status(thm)],[fact_292_card__Diff2__less]) ).

fof(f_363_2,plain,
    ! [U_1370,U_1369,U_1368,U_1367] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(U_1370,bool),nat,finite_card(U_1370),hAPP(fun(U_1370,bool),fun(U_1370,bool),hAPP(fun(U_1370,bool),fun(fun(U_1370,bool),fun(U_1370,bool)),minus_minus(fun(U_1370,bool)),hAPP(fun(U_1370,bool),fun(U_1370,bool),hAPP(fun(U_1370,bool),fun(fun(U_1370,bool),fun(U_1370,bool)),minus_minus(fun(U_1370,bool)),U_1367),hAPP(fun(U_1370,bool),fun(U_1370,bool),hAPP(U_1370,fun(fun(U_1370,bool),fun(U_1370,bool)),insert(U_1370),U_1368),bot_bot(fun(U_1370,bool))))),hAPP(fun(U_1370,bool),fun(U_1370,bool),hAPP(U_1370,fun(fun(U_1370,bool),fun(U_1370,bool)),insert(U_1370),U_1369),bot_bot(fun(U_1370,bool)))))),hAPP(fun(U_1370,bool),nat,finite_card(U_1370),U_1367)))
      | ~ hBOOL(hAPP(fun(U_1370,bool),bool,hAPP(U_1370,fun(fun(U_1370,bool),bool),member(U_1370),U_1369),U_1367))
      | ~ hBOOL(hAPP(fun(U_1370,bool),bool,hAPP(U_1370,fun(fun(U_1370,bool),bool),member(U_1370),U_1368),U_1367))
      | ~ hBOOL(hAPP(fun(U_1370,bool),bool,finite_finite(U_1370),U_1367)) ),
    inference(variable_rename,[status(thm)],[f_363_1]) ).

fof(f_363_3,plain,
    ! [U_1370,U_1368,U_1367,U_1369] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(U_1370,bool),nat,finite_card(U_1370),hAPP(fun(U_1370,bool),fun(U_1370,bool),hAPP(fun(U_1370,bool),fun(fun(U_1370,bool),fun(U_1370,bool)),minus_minus(fun(U_1370,bool)),hAPP(fun(U_1370,bool),fun(U_1370,bool),hAPP(fun(U_1370,bool),fun(fun(U_1370,bool),fun(U_1370,bool)),minus_minus(fun(U_1370,bool)),U_1367),hAPP(fun(U_1370,bool),fun(U_1370,bool),hAPP(U_1370,fun(fun(U_1370,bool),fun(U_1370,bool)),insert(U_1370),U_1368),bot_bot(fun(U_1370,bool))))),hAPP(fun(U_1370,bool),fun(U_1370,bool),hAPP(U_1370,fun(fun(U_1370,bool),fun(U_1370,bool)),insert(U_1370),U_1369),bot_bot(fun(U_1370,bool)))))),hAPP(fun(U_1370,bool),nat,finite_card(U_1370),U_1367)))
      | ~ hBOOL(hAPP(fun(U_1370,bool),bool,hAPP(U_1370,fun(fun(U_1370,bool),bool),member(U_1370),U_1369),U_1367))
      | ~ hBOOL(hAPP(fun(U_1370,bool),bool,hAPP(U_1370,fun(fun(U_1370,bool),bool),member(U_1370),U_1368),U_1367))
      | ~ hBOOL(hAPP(fun(U_1370,bool),bool,finite_finite(U_1370),U_1367)) ),
    inference(definitional_conversion,[status(esa)],[f_363_2]) ).

cnf(f_363_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(U_1370,bool),nat,finite_card(U_1370),hAPP(fun(U_1370,bool),fun(U_1370,bool),hAPP(fun(U_1370,bool),fun(fun(U_1370,bool),fun(U_1370,bool)),minus_minus(fun(U_1370,bool)),hAPP(fun(U_1370,bool),fun(U_1370,bool),hAPP(fun(U_1370,bool),fun(fun(U_1370,bool),fun(U_1370,bool)),minus_minus(fun(U_1370,bool)),U_1367),hAPP(fun(U_1370,bool),fun(U_1370,bool),hAPP(U_1370,fun(fun(U_1370,bool),fun(U_1370,bool)),insert(U_1370),U_1368),bot_bot(fun(U_1370,bool))))),hAPP(fun(U_1370,bool),fun(U_1370,bool),hAPP(U_1370,fun(fun(U_1370,bool),fun(U_1370,bool)),insert(U_1370),U_1369),bot_bot(fun(U_1370,bool)))))),hAPP(fun(U_1370,bool),nat,finite_card(U_1370),U_1367)))
    | ~ hBOOL(hAPP(fun(U_1370,bool),bool,hAPP(U_1370,fun(fun(U_1370,bool),bool),member(U_1370),U_1369),U_1367))
    | ~ hBOOL(hAPP(fun(U_1370,bool),bool,hAPP(U_1370,fun(fun(U_1370,bool),bool),member(U_1370),U_1368),U_1367))
    | ~ hBOOL(hAPP(fun(U_1370,bool),bool,finite_finite(U_1370),U_1367)) ),
    inference(clausify,[status(thm)],[f_363_3]) ).

fof(f_364_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_293_card__Diff1__less]) ).

fof(f_364_2,plain,
    ! [U_1373,U_1372,U_1371] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(U_1373,bool),nat,finite_card(U_1373),hAPP(fun(U_1373,bool),fun(U_1373,bool),hAPP(fun(U_1373,bool),fun(fun(U_1373,bool),fun(U_1373,bool)),minus_minus(fun(U_1373,bool)),U_1371),hAPP(fun(U_1373,bool),fun(U_1373,bool),hAPP(U_1373,fun(fun(U_1373,bool),fun(U_1373,bool)),insert(U_1373),U_1372),bot_bot(fun(U_1373,bool)))))),hAPP(fun(U_1373,bool),nat,finite_card(U_1373),U_1371)))
      | ~ hBOOL(hAPP(fun(U_1373,bool),bool,hAPP(U_1373,fun(fun(U_1373,bool),bool),member(U_1373),U_1372),U_1371))
      | ~ hBOOL(hAPP(fun(U_1373,bool),bool,finite_finite(U_1373),U_1371)) ),
    inference(variable_rename,[status(thm)],[f_364_1]) ).

fof(f_364_3,plain,
    ! [U_1373,U_1371,U_1372] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(U_1373,bool),nat,finite_card(U_1373),hAPP(fun(U_1373,bool),fun(U_1373,bool),hAPP(fun(U_1373,bool),fun(fun(U_1373,bool),fun(U_1373,bool)),minus_minus(fun(U_1373,bool)),U_1371),hAPP(fun(U_1373,bool),fun(U_1373,bool),hAPP(U_1373,fun(fun(U_1373,bool),fun(U_1373,bool)),insert(U_1373),U_1372),bot_bot(fun(U_1373,bool)))))),hAPP(fun(U_1373,bool),nat,finite_card(U_1373),U_1371)))
      | ~ hBOOL(hAPP(fun(U_1373,bool),bool,hAPP(U_1373,fun(fun(U_1373,bool),bool),member(U_1373),U_1372),U_1371))
      | ~ hBOOL(hAPP(fun(U_1373,bool),bool,finite_finite(U_1373),U_1371)) ),
    inference(definitional_conversion,[status(esa)],[f_364_2]) ).

cnf(f_364_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(U_1373,bool),nat,finite_card(U_1373),hAPP(fun(U_1373,bool),fun(U_1373,bool),hAPP(fun(U_1373,bool),fun(fun(U_1373,bool),fun(U_1373,bool)),minus_minus(fun(U_1373,bool)),U_1371),hAPP(fun(U_1373,bool),fun(U_1373,bool),hAPP(U_1373,fun(fun(U_1373,bool),fun(U_1373,bool)),insert(U_1373),U_1372),bot_bot(fun(U_1373,bool)))))),hAPP(fun(U_1373,bool),nat,finite_card(U_1373),U_1371)))
    | ~ hBOOL(hAPP(fun(U_1373,bool),bool,hAPP(U_1373,fun(fun(U_1373,bool),bool),member(U_1373),U_1372),U_1371))
    | ~ hBOOL(hAPP(fun(U_1373,bool),bool,finite_finite(U_1373),U_1371)) ),
    inference(clausify,[status(thm)],[f_364_3]) ).

fof(f_365_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_294_lessI]) ).

fof(f_365_2,plain,
    ! [U_1374] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1374),hAPP(nat,nat,suc,U_1374))),
    inference(variable_rename,[status(thm)],[f_365_1]) ).

fof(f_365_3,plain,
    ! [U_1374] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1374),hAPP(nat,nat,suc,U_1374))),
    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_1374),hAPP(nat,nat,suc,U_1374))),
    inference(clausify,[status(thm)],[f_365_3]) ).

fof(f_366_1,plain,
    ! [M_1,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_1)),hAPP(nat,nat,suc,N)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)) ),
    inference(fof_nnf,[status(thm)],[fact_295_Suc__mono]) ).

fof(f_366_2,plain,
    ! [U_1376,U_1375] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1376)),hAPP(nat,nat,suc,U_1375)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1376),U_1375)) ),
    inference(variable_rename,[status(thm)],[f_366_1]) ).

fof(f_366_3,plain,
    ! [U_1375,U_1376] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1376)),hAPP(nat,nat,suc,U_1375)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1376),U_1375)) ),
    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),hAPP(nat,nat,suc,U_1376)),hAPP(nat,nat,suc,U_1375)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1376),U_1375)) ),
    inference(clausify,[status(thm)],[f_366_3]) ).

fof(f_367_1,plain,
    ! [K] : 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)))),
    inference(fof_nnf,[status(thm)],[fact_296_finite__Collect__less__nat]) ).

fof(f_367_2,plain,
    ! [U_1377] : 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_1377)))),
    inference(variable_rename,[status(thm)],[f_367_1]) ).

fof(f_367_3,plain,
    ! [U_1377] : 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_1377)))),
    inference(definitional_conversion,[status(esa)],[f_367_2]) ).

cnf(f_367_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_1377)))),
    inference(clausify,[status(thm)],[f_367_3]) ).

fof(f_368_1,plain,
    ! [N] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N)),
    inference(fof_nnf,[status(thm)],[fact_297_less__not__refl]) ).

fof(f_368_2,plain,
    ! [U_1378] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1378),U_1378)),
    inference(variable_rename,[status(thm)],[f_368_1]) ).

fof(f_368_3,plain,
    ! [U_1378] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1378),U_1378)),
    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),U_1378),U_1378)),
    inference(clausify,[status(thm)],[f_368_3]) ).

fof(f_369_1,plain,
    ! [M,Na] :
      ( ( M != Na
        | ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M))
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)) ) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))
        | M = Na ) ),
    inference(fof_nnf,[status(thm)],[fact_298_nat__neq__iff]) ).

fof(f_369_2,plain,
    ! [U_1380,U_1379] :
      ( ( U_1380 != U_1379
        | ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1379),U_1380))
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1380),U_1379)) ) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1379),U_1380))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1380),U_1379))
        | U_1380 = U_1379 ) ),
    inference(variable_rename,[status(thm)],[f_369_1]) ).

fof(f_369_3,plain,
    ( ! [U_1384,U_1382] :
        ( U_1384 != U_1382
        | ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1382),U_1384))
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1384),U_1382)) ) )
    & ! [U_1383,U_1381] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1381),U_1383))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1383),U_1381))
        | U_1383 = U_1381 ) ),
    inference(miniscope,[status(thm)],[f_369_2]) ).

fof(f_369_4,plain,
    ( ! [U_1384,U_1382] :
        ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1382),U_1384))
        | ~ sP63(U_1384,U_1382) )
    & ! [U_1384,U_1382] :
        ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1384),U_1382))
        | ~ sP63(U_1384,U_1382) )
    & ! [U_1384,U_1382] :
        ( U_1384 != U_1382
        | sP63(U_1384,U_1382) )
    & ! [U_1381,U_1383] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1381),U_1383))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1383),U_1381))
        | U_1383 = U_1381 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP63])],[f_369_3]) ).

cnf(f_369_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1381),U_1383))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1383),U_1381))
    | U_1383 = U_1381 ),
    inference(clausify,[status(thm)],[f_369_4]) ).

cnf(f_369_6,plain,
    ( U_1384 != U_1382
    | sP63(U_1384,U_1382) ),
    inference(clausify,[status(thm)],[f_369_4]) ).

cnf(f_369_7,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1384),U_1382))
    | ~ sP63(U_1384,U_1382) ),
    inference(clausify,[status(thm)],[f_369_4]) ).

cnf(f_369_8,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1382),U_1384))
    | ~ sP63(U_1384,U_1382) ),
    inference(clausify,[status(thm)],[f_369_4]) ).

fof(f_370_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_299_linorder__neqE__nat]) ).

fof(f_370_2,plain,
    ! [U_1386,U_1385] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1385),U_1386))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1386),U_1385))
      | U_1386 = U_1385 ),
    inference(variable_rename,[status(thm)],[f_370_1]) ).

fof(f_370_3,plain,
    ! [U_1386,U_1385] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1385),U_1386))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1386),U_1385))
      | U_1386 = U_1385 ),
    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_1385),U_1386))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1386),U_1385))
    | U_1386 = U_1385 ),
    inference(clausify,[status(thm)],[f_370_3]) ).

fof(f_371_1,plain,
    ! [N] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N)),
    inference(fof_nnf,[status(thm)],[fact_300_less__irrefl__nat]) ).

fof(f_371_2,plain,
    ! [U_1387] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1387),U_1387)),
    inference(variable_rename,[status(thm)],[f_371_1]) ).

fof(f_371_3,plain,
    ! [U_1387] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1387),U_1387)),
    inference(definitional_conversion,[status(esa)],[f_371_2]) ).

cnf(f_371_4,plain,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1387),U_1387)),
    inference(clausify,[status(thm)],[f_371_3]) ).

fof(f_372_1,plain,
    ! [N,M_1] :
      ( M_1 != N
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M_1)) ),
    inference(fof_nnf,[status(thm)],[fact_301_less__not__refl2]) ).

fof(f_372_2,plain,
    ! [U_1389,U_1388] :
      ( U_1388 != U_1389
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1389),U_1388)) ),
    inference(variable_rename,[status(thm)],[f_372_1]) ).

fof(f_372_3,plain,
    ! [U_1389,U_1388] :
      ( U_1388 != U_1389
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1389),U_1388)) ),
    inference(definitional_conversion,[status(esa)],[f_372_2]) ).

cnf(f_372_4,plain,
    ( U_1388 != U_1389
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1389),U_1388)) ),
    inference(clausify,[status(thm)],[f_372_3]) ).

fof(f_373_1,plain,
    ! [S_1,T_4] :
      ( S_1 != T_4
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),S_1),T_4)) ),
    inference(fof_nnf,[status(thm)],[fact_302_less__not__refl3]) ).

fof(f_373_2,plain,
    ! [U_1391,U_1390] :
      ( U_1391 != U_1390
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1391),U_1390)) ),
    inference(variable_rename,[status(thm)],[f_373_1]) ).

fof(f_373_3,plain,
    ! [U_1391,U_1390] :
      ( U_1391 != U_1390
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1391),U_1390)) ),
    inference(definitional_conversion,[status(esa)],[f_373_2]) ).

cnf(f_373_4,plain,
    ( U_1391 != U_1390
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1391),U_1390)) ),
    inference(clausify,[status(thm)],[f_373_3]) ).

fof(f_374_1,plain,
    ! [Pa,M,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,Na),M))
      | ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,Na),M))
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M)) )
      | ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,Na),M))
        & M = Na )
      | ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,Na),M))
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_303_nat__less__cases]) ).

fof(f_374_2,plain,
    ! [U_1394,U_1393,U_1392] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1394,U_1392),U_1393))
      | ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1394,U_1392),U_1393))
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1392),U_1393)) )
      | ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1394,U_1392),U_1393))
        & U_1393 = U_1392 )
      | ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1394,U_1392),U_1393))
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1393),U_1392)) ) ),
    inference(variable_rename,[status(thm)],[f_374_1]) ).

fof(f_374_3,plain,
    ( ! [U_1393,U_1394,U_1392] :
        ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1394,U_1392),U_1393))
        | ~ sP66(U_1393,U_1394,U_1392) )
    & ! [U_1393,U_1394,U_1392] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1392),U_1393))
        | ~ sP66(U_1393,U_1394,U_1392) )
    & ! [U_1393,U_1394,U_1392] :
        ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1394,U_1392),U_1393))
        | ~ sP65(U_1393,U_1394,U_1392) )
    & ! [U_1393,U_1394,U_1392] :
        ( U_1393 = U_1392
        | ~ sP65(U_1393,U_1394,U_1392) )
    & ! [U_1393,U_1394,U_1392] :
        ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1394,U_1392),U_1393))
        | ~ sP64(U_1393,U_1394,U_1392) )
    & ! [U_1393,U_1394,U_1392] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1393),U_1392))
        | ~ sP64(U_1393,U_1394,U_1392) )
    & ! [U_1393,U_1394,U_1392] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1394,U_1392),U_1393))
        | sP66(U_1393,U_1394,U_1392)
        | sP65(U_1393,U_1394,U_1392)
        | sP64(U_1393,U_1394,U_1392) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP64,sP65,sP66])],[f_374_2]) ).

cnf(f_374_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1394,U_1392),U_1393))
    | sP66(U_1393,U_1394,U_1392)
    | sP65(U_1393,U_1394,U_1392)
    | sP64(U_1393,U_1394,U_1392) ),
    inference(clausify,[status(thm)],[f_374_3]) ).

cnf(f_374_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1393),U_1392))
    | ~ sP64(U_1393,U_1394,U_1392) ),
    inference(clausify,[status(thm)],[f_374_3]) ).

cnf(f_374_6,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1394,U_1392),U_1393))
    | ~ sP64(U_1393,U_1394,U_1392) ),
    inference(clausify,[status(thm)],[f_374_3]) ).

cnf(f_374_7,plain,
    ( U_1393 = U_1392
    | ~ sP65(U_1393,U_1394,U_1392) ),
    inference(clausify,[status(thm)],[f_374_3]) ).

cnf(f_374_8,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1394,U_1392),U_1393))
    | ~ sP65(U_1393,U_1394,U_1392) ),
    inference(clausify,[status(thm)],[f_374_3]) ).

cnf(f_374_9,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1392),U_1393))
    | ~ sP66(U_1393,U_1394,U_1392) ),
    inference(clausify,[status(thm)],[f_374_3]) ).

cnf(f_374_10,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1394,U_1392),U_1393))
    | ~ sP66(U_1393,U_1394,U_1392) ),
    inference(clausify,[status(thm)],[f_374_3]) ).

fof(f_375_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_304_order__less__irrefl]) ).

fof(f_375_2,plain,
    ! [U_1396] :
      ( ! [U_1395] : ~ hBOOL(hAPP(U_1396,bool,hAPP(U_1396,fun(U_1396,bool),ord_less(U_1396),U_1395),U_1395))
      | ~ preorder(U_1396) ),
    inference(variable_rename,[status(thm)],[f_375_1]) ).

fof(f_375_3,plain,
    ! [U_1396,U_1395] :
      ( ~ hBOOL(hAPP(U_1396,bool,hAPP(U_1396,fun(U_1396,bool),ord_less(U_1396),U_1395),U_1395))
      | ~ preorder(U_1396) ),
    inference(definitional_conversion,[status(esa)],[f_375_2]) ).

cnf(f_375_4,plain,
    ( ~ hBOOL(hAPP(U_1396,bool,hAPP(U_1396,fun(U_1396,bool),ord_less(U_1396),U_1395),U_1395))
    | ~ preorder(U_1396) ),
    inference(clausify,[status(thm)],[f_375_3]) ).

fof(f_376_1,plain,
    ! [X_b] :
      ( ! [X_1,Y_2] :
          ( ( ti(X_b,X_1) != ti(X_b,Y_2)
            | ( ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_1))
              & ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2)) ) )
          & ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_1))
            | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2))
            | ti(X_b,X_1) = ti(X_b,Y_2) ) )
      | ~ linorder(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_305_linorder__neq__iff]) ).

fof(f_376_2,plain,
    ! [U_1399] :
      ( ! [U_1398,U_1397] :
          ( ( ti(U_1399,U_1398) != ti(U_1399,U_1397)
            | ( ~ hBOOL(hAPP(U_1399,bool,hAPP(U_1399,fun(U_1399,bool),ord_less(U_1399),U_1397),U_1398))
              & ~ hBOOL(hAPP(U_1399,bool,hAPP(U_1399,fun(U_1399,bool),ord_less(U_1399),U_1398),U_1397)) ) )
          & ( hBOOL(hAPP(U_1399,bool,hAPP(U_1399,fun(U_1399,bool),ord_less(U_1399),U_1397),U_1398))
            | hBOOL(hAPP(U_1399,bool,hAPP(U_1399,fun(U_1399,bool),ord_less(U_1399),U_1398),U_1397))
            | ti(U_1399,U_1398) = ti(U_1399,U_1397) ) )
      | ~ linorder(U_1399) ),
    inference(variable_rename,[status(thm)],[f_376_1]) ).

fof(f_376_3,plain,
    ! [U_1399] :
      ( ( ! [U_1403,U_1401] :
            ( ti(U_1399,U_1403) != ti(U_1399,U_1401)
            | ( ~ hBOOL(hAPP(U_1399,bool,hAPP(U_1399,fun(U_1399,bool),ord_less(U_1399),U_1401),U_1403))
              & ~ hBOOL(hAPP(U_1399,bool,hAPP(U_1399,fun(U_1399,bool),ord_less(U_1399),U_1403),U_1401)) ) )
        & ! [U_1402,U_1400] :
            ( hBOOL(hAPP(U_1399,bool,hAPP(U_1399,fun(U_1399,bool),ord_less(U_1399),U_1400),U_1402))
            | hBOOL(hAPP(U_1399,bool,hAPP(U_1399,fun(U_1399,bool),ord_less(U_1399),U_1402),U_1400))
            | ti(U_1399,U_1402) = ti(U_1399,U_1400) ) )
      | ~ linorder(U_1399) ),
    inference(miniscope,[status(thm)],[f_376_2]) ).

fof(f_376_4,plain,
    ( ! [U_1403,U_1399,U_1401] :
        ( ~ hBOOL(hAPP(U_1399,bool,hAPP(U_1399,fun(U_1399,bool),ord_less(U_1399),U_1401),U_1403))
        | ~ sP67(U_1403,U_1399,U_1401) )
    & ! [U_1403,U_1399,U_1401] :
        ( ~ hBOOL(hAPP(U_1399,bool,hAPP(U_1399,fun(U_1399,bool),ord_less(U_1399),U_1403),U_1401))
        | ~ sP67(U_1403,U_1399,U_1401) )
    & ! [U_1403,U_1399,U_1400,U_1401,U_1402] :
        ( ti(U_1399,U_1403) != ti(U_1399,U_1401)
        | sP67(U_1403,U_1399,U_1401)
        | ~ sP68(U_1403,U_1399,U_1400,U_1401,U_1402) )
    & ! [U_1403,U_1399,U_1400,U_1401,U_1402] :
        ( hBOOL(hAPP(U_1399,bool,hAPP(U_1399,fun(U_1399,bool),ord_less(U_1399),U_1400),U_1402))
        | hBOOL(hAPP(U_1399,bool,hAPP(U_1399,fun(U_1399,bool),ord_less(U_1399),U_1402),U_1400))
        | ti(U_1399,U_1402) = ti(U_1399,U_1400)
        | ~ sP68(U_1403,U_1399,U_1400,U_1401,U_1402) )
    & ! [U_1403,U_1399,U_1400,U_1401,U_1402] :
        ( sP68(U_1403,U_1399,U_1400,U_1401,U_1402)
        | ~ linorder(U_1399) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP67,sP68])],[f_376_3]) ).

cnf(f_376_5,plain,
    ( sP68(U_1403,U_1399,U_1400,U_1401,U_1402)
    | ~ linorder(U_1399) ),
    inference(clausify,[status(thm)],[f_376_4]) ).

cnf(f_376_6,plain,
    ( hBOOL(hAPP(U_1399,bool,hAPP(U_1399,fun(U_1399,bool),ord_less(U_1399),U_1400),U_1402))
    | hBOOL(hAPP(U_1399,bool,hAPP(U_1399,fun(U_1399,bool),ord_less(U_1399),U_1402),U_1400))
    | ti(U_1399,U_1402) = ti(U_1399,U_1400)
    | ~ sP68(U_1403,U_1399,U_1400,U_1401,U_1402) ),
    inference(clausify,[status(thm)],[f_376_4]) ).

cnf(f_376_7,plain,
    ( ti(U_1399,U_1403) != ti(U_1399,U_1401)
    | sP67(U_1403,U_1399,U_1401)
    | ~ sP68(U_1403,U_1399,U_1400,U_1401,U_1402) ),
    inference(clausify,[status(thm)],[f_376_4]) ).

cnf(f_376_8,plain,
    ( ~ hBOOL(hAPP(U_1399,bool,hAPP(U_1399,fun(U_1399,bool),ord_less(U_1399),U_1403),U_1401))
    | ~ sP67(U_1403,U_1399,U_1401) ),
    inference(clausify,[status(thm)],[f_376_4]) ).

cnf(f_376_9,plain,
    ( ~ hBOOL(hAPP(U_1399,bool,hAPP(U_1399,fun(U_1399,bool),ord_less(U_1399),U_1401),U_1403))
    | ~ sP67(U_1403,U_1399,U_1401) ),
    inference(clausify,[status(thm)],[f_376_4]) ).

fof(f_377_1,plain,
    ! [X_b] :
      ( ! [X_1,Y_2] :
          ( ( ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2))
            | ( ti(X_b,X_1) != ti(X_b,Y_2)
              & ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_1)) ) )
          & ( ti(X_b,X_1) = ti(X_b,Y_2)
            | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_1))
            | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2)) ) )
      | ~ linorder(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_306_not__less__iff__gr__or__eq]) ).

fof(f_377_2,plain,
    ! [U_1406] :
      ( ! [U_1405,U_1404] :
          ( ( ~ hBOOL(hAPP(U_1406,bool,hAPP(U_1406,fun(U_1406,bool),ord_less(U_1406),U_1405),U_1404))
            | ( ti(U_1406,U_1405) != ti(U_1406,U_1404)
              & ~ hBOOL(hAPP(U_1406,bool,hAPP(U_1406,fun(U_1406,bool),ord_less(U_1406),U_1404),U_1405)) ) )
          & ( ti(U_1406,U_1405) = ti(U_1406,U_1404)
            | hBOOL(hAPP(U_1406,bool,hAPP(U_1406,fun(U_1406,bool),ord_less(U_1406),U_1404),U_1405))
            | hBOOL(hAPP(U_1406,bool,hAPP(U_1406,fun(U_1406,bool),ord_less(U_1406),U_1405),U_1404)) ) )
      | ~ linorder(U_1406) ),
    inference(variable_rename,[status(thm)],[f_377_1]) ).

fof(f_377_3,plain,
    ! [U_1406] :
      ( ( ! [U_1410,U_1408] :
            ( ~ hBOOL(hAPP(U_1406,bool,hAPP(U_1406,fun(U_1406,bool),ord_less(U_1406),U_1410),U_1408))
            | ( ti(U_1406,U_1410) != ti(U_1406,U_1408)
              & ~ hBOOL(hAPP(U_1406,bool,hAPP(U_1406,fun(U_1406,bool),ord_less(U_1406),U_1408),U_1410)) ) )
        & ! [U_1409,U_1407] :
            ( ti(U_1406,U_1409) = ti(U_1406,U_1407)
            | hBOOL(hAPP(U_1406,bool,hAPP(U_1406,fun(U_1406,bool),ord_less(U_1406),U_1407),U_1409))
            | hBOOL(hAPP(U_1406,bool,hAPP(U_1406,fun(U_1406,bool),ord_less(U_1406),U_1409),U_1407)) ) )
      | ~ linorder(U_1406) ),
    inference(miniscope,[status(thm)],[f_377_2]) ).

fof(f_377_4,plain,
    ( ! [U_1408,U_1406,U_1410] :
        ( ti(U_1406,U_1410) != ti(U_1406,U_1408)
        | ~ sP69(U_1408,U_1406,U_1410) )
    & ! [U_1408,U_1406,U_1410] :
        ( ~ hBOOL(hAPP(U_1406,bool,hAPP(U_1406,fun(U_1406,bool),ord_less(U_1406),U_1408),U_1410))
        | ~ sP69(U_1408,U_1406,U_1410) )
    & ! [U_1408,U_1406,U_1407,U_1409,U_1410] :
        ( ~ hBOOL(hAPP(U_1406,bool,hAPP(U_1406,fun(U_1406,bool),ord_less(U_1406),U_1410),U_1408))
        | sP69(U_1408,U_1406,U_1410)
        | ~ sP70(U_1408,U_1406,U_1407,U_1409,U_1410) )
    & ! [U_1408,U_1406,U_1407,U_1409,U_1410] :
        ( ti(U_1406,U_1409) = ti(U_1406,U_1407)
        | hBOOL(hAPP(U_1406,bool,hAPP(U_1406,fun(U_1406,bool),ord_less(U_1406),U_1407),U_1409))
        | hBOOL(hAPP(U_1406,bool,hAPP(U_1406,fun(U_1406,bool),ord_less(U_1406),U_1409),U_1407))
        | ~ sP70(U_1408,U_1406,U_1407,U_1409,U_1410) )
    & ! [U_1408,U_1406,U_1407,U_1409,U_1410] :
        ( sP70(U_1408,U_1406,U_1407,U_1409,U_1410)
        | ~ linorder(U_1406) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP69,sP70])],[f_377_3]) ).

cnf(f_377_5,plain,
    ( sP70(U_1408,U_1406,U_1407,U_1409,U_1410)
    | ~ linorder(U_1406) ),
    inference(clausify,[status(thm)],[f_377_4]) ).

cnf(f_377_6,plain,
    ( ti(U_1406,U_1409) = ti(U_1406,U_1407)
    | hBOOL(hAPP(U_1406,bool,hAPP(U_1406,fun(U_1406,bool),ord_less(U_1406),U_1407),U_1409))
    | hBOOL(hAPP(U_1406,bool,hAPP(U_1406,fun(U_1406,bool),ord_less(U_1406),U_1409),U_1407))
    | ~ sP70(U_1408,U_1406,U_1407,U_1409,U_1410) ),
    inference(clausify,[status(thm)],[f_377_4]) ).

cnf(f_377_7,plain,
    ( ~ hBOOL(hAPP(U_1406,bool,hAPP(U_1406,fun(U_1406,bool),ord_less(U_1406),U_1410),U_1408))
    | sP69(U_1408,U_1406,U_1410)
    | ~ sP70(U_1408,U_1406,U_1407,U_1409,U_1410) ),
    inference(clausify,[status(thm)],[f_377_4]) ).

cnf(f_377_8,plain,
    ( ~ hBOOL(hAPP(U_1406,bool,hAPP(U_1406,fun(U_1406,bool),ord_less(U_1406),U_1408),U_1410))
    | ~ sP69(U_1408,U_1406,U_1410) ),
    inference(clausify,[status(thm)],[f_377_4]) ).

cnf(f_377_9,plain,
    ( ti(U_1406,U_1410) != ti(U_1406,U_1408)
    | ~ sP69(U_1408,U_1406,U_1410) ),
    inference(clausify,[status(thm)],[f_377_4]) ).

fof(f_378_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_307_linorder__less__linear]) ).

fof(f_378_2,plain,
    ! [U_1413] :
      ( ! [U_1412,U_1411] :
          ( hBOOL(hAPP(U_1413,bool,hAPP(U_1413,fun(U_1413,bool),ord_less(U_1413),U_1411),U_1412))
          | ti(U_1413,U_1412) = ti(U_1413,U_1411)
          | hBOOL(hAPP(U_1413,bool,hAPP(U_1413,fun(U_1413,bool),ord_less(U_1413),U_1412),U_1411)) )
      | ~ linorder(U_1413) ),
    inference(variable_rename,[status(thm)],[f_378_1]) ).

fof(f_378_3,plain,
    ! [U_1412,U_1413,U_1411] :
      ( hBOOL(hAPP(U_1413,bool,hAPP(U_1413,fun(U_1413,bool),ord_less(U_1413),U_1411),U_1412))
      | ti(U_1413,U_1412) = ti(U_1413,U_1411)
      | hBOOL(hAPP(U_1413,bool,hAPP(U_1413,fun(U_1413,bool),ord_less(U_1413),U_1412),U_1411))
      | ~ linorder(U_1413) ),
    inference(definitional_conversion,[status(esa)],[f_378_2]) ).

cnf(f_378_4,plain,
    ( hBOOL(hAPP(U_1413,bool,hAPP(U_1413,fun(U_1413,bool),ord_less(U_1413),U_1411),U_1412))
    | ti(U_1413,U_1412) = ti(U_1413,U_1411)
    | hBOOL(hAPP(U_1413,bool,hAPP(U_1413,fun(U_1413,bool),ord_less(U_1413),U_1412),U_1411))
    | ~ linorder(U_1413) ),
    inference(clausify,[status(thm)],[f_378_3]) ).

fof(f_379_1,plain,
    ! [X_b] :
      ( ! [Y_2,X_1] :
          ( ( ( ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2))
              | ti(X_b,X_1) != ti(X_b,Y_2) )
            & ( ti(X_b,X_1) = ti(X_b,Y_2)
              | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2)) ) )
          | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_1)) )
      | ~ linorder(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_308_linorder__antisym__conv3]) ).

fof(f_379_2,plain,
    ! [U_1416] :
      ( ! [U_1415,U_1414] :
          ( ( ( ~ hBOOL(hAPP(U_1416,bool,hAPP(U_1416,fun(U_1416,bool),ord_less(U_1416),U_1414),U_1415))
              | ti(U_1416,U_1414) != ti(U_1416,U_1415) )
            & ( ti(U_1416,U_1414) = ti(U_1416,U_1415)
              | hBOOL(hAPP(U_1416,bool,hAPP(U_1416,fun(U_1416,bool),ord_less(U_1416),U_1414),U_1415)) ) )
          | hBOOL(hAPP(U_1416,bool,hAPP(U_1416,fun(U_1416,bool),ord_less(U_1416),U_1415),U_1414)) )
      | ~ linorder(U_1416) ),
    inference(variable_rename,[status(thm)],[f_379_1]) ).

fof(f_379_3,plain,
    ( ! [U_1414,U_1415,U_1416] :
        ( ~ hBOOL(hAPP(U_1416,bool,hAPP(U_1416,fun(U_1416,bool),ord_less(U_1416),U_1414),U_1415))
        | ti(U_1416,U_1414) != ti(U_1416,U_1415)
        | ~ sP71(U_1414,U_1415,U_1416) )
    & ! [U_1414,U_1415,U_1416] :
        ( ti(U_1416,U_1414) = ti(U_1416,U_1415)
        | hBOOL(hAPP(U_1416,bool,hAPP(U_1416,fun(U_1416,bool),ord_less(U_1416),U_1414),U_1415))
        | ~ sP71(U_1414,U_1415,U_1416) )
    & ! [U_1414,U_1415,U_1416] :
        ( sP71(U_1414,U_1415,U_1416)
        | hBOOL(hAPP(U_1416,bool,hAPP(U_1416,fun(U_1416,bool),ord_less(U_1416),U_1415),U_1414))
        | ~ linorder(U_1416) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP71])],[f_379_2]) ).

cnf(f_379_4,plain,
    ( sP71(U_1414,U_1415,U_1416)
    | hBOOL(hAPP(U_1416,bool,hAPP(U_1416,fun(U_1416,bool),ord_less(U_1416),U_1415),U_1414))
    | ~ linorder(U_1416) ),
    inference(clausify,[status(thm)],[f_379_3]) ).

cnf(f_379_5,plain,
    ( ti(U_1416,U_1414) = ti(U_1416,U_1415)
    | hBOOL(hAPP(U_1416,bool,hAPP(U_1416,fun(U_1416,bool),ord_less(U_1416),U_1414),U_1415))
    | ~ sP71(U_1414,U_1415,U_1416) ),
    inference(clausify,[status(thm)],[f_379_3]) ).

cnf(f_379_6,plain,
    ( ~ hBOOL(hAPP(U_1416,bool,hAPP(U_1416,fun(U_1416,bool),ord_less(U_1416),U_1414),U_1415))
    | ti(U_1416,U_1414) != ti(U_1416,U_1415)
    | ~ sP71(U_1414,U_1415,U_1416) ),
    inference(clausify,[status(thm)],[f_379_3]) ).

fof(f_380_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_309_linorder__neqE]) ).

fof(f_380_2,plain,
    ! [U_1419] :
      ( ! [U_1418,U_1417] :
          ( hBOOL(hAPP(U_1419,bool,hAPP(U_1419,fun(U_1419,bool),ord_less(U_1419),U_1417),U_1418))
          | hBOOL(hAPP(U_1419,bool,hAPP(U_1419,fun(U_1419,bool),ord_less(U_1419),U_1418),U_1417))
          | ti(U_1419,U_1418) = ti(U_1419,U_1417) )
      | ~ linorder(U_1419) ),
    inference(variable_rename,[status(thm)],[f_380_1]) ).

fof(f_380_3,plain,
    ! [U_1418,U_1419,U_1417] :
      ( hBOOL(hAPP(U_1419,bool,hAPP(U_1419,fun(U_1419,bool),ord_less(U_1419),U_1417),U_1418))
      | hBOOL(hAPP(U_1419,bool,hAPP(U_1419,fun(U_1419,bool),ord_less(U_1419),U_1418),U_1417))
      | ti(U_1419,U_1418) = ti(U_1419,U_1417)
      | ~ linorder(U_1419) ),
    inference(definitional_conversion,[status(esa)],[f_380_2]) ).

cnf(f_380_4,plain,
    ( hBOOL(hAPP(U_1419,bool,hAPP(U_1419,fun(U_1419,bool),ord_less(U_1419),U_1417),U_1418))
    | hBOOL(hAPP(U_1419,bool,hAPP(U_1419,fun(U_1419,bool),ord_less(U_1419),U_1418),U_1417))
    | ti(U_1419,U_1418) = ti(U_1419,U_1417)
    | ~ linorder(U_1419) ),
    inference(clausify,[status(thm)],[f_380_3]) ).

fof(f_381_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_310_less__imp__neq]) ).

fof(f_381_2,plain,
    ! [U_1422] :
      ( ! [U_1421,U_1420] :
          ( ti(U_1422,U_1421) != ti(U_1422,U_1420)
          | ~ hBOOL(hAPP(U_1422,bool,hAPP(U_1422,fun(U_1422,bool),ord_less(U_1422),U_1421),U_1420)) )
      | ~ order(U_1422) ),
    inference(variable_rename,[status(thm)],[f_381_1]) ).

fof(f_381_3,plain,
    ! [U_1421,U_1420,U_1422] :
      ( ti(U_1422,U_1421) != ti(U_1422,U_1420)
      | ~ hBOOL(hAPP(U_1422,bool,hAPP(U_1422,fun(U_1422,bool),ord_less(U_1422),U_1421),U_1420))
      | ~ order(U_1422) ),
    inference(definitional_conversion,[status(esa)],[f_381_2]) ).

cnf(f_381_4,plain,
    ( ti(U_1422,U_1421) != ti(U_1422,U_1420)
    | ~ hBOOL(hAPP(U_1422,bool,hAPP(U_1422,fun(U_1422,bool),ord_less(U_1422),U_1421),U_1420))
    | ~ order(U_1422) ),
    inference(clausify,[status(thm)],[f_381_3]) ).

fof(f_382_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_311_order__less__not__sym]) ).

fof(f_382_2,plain,
    ! [U_1425] :
      ( ! [U_1424,U_1423] :
          ( ~ hBOOL(hAPP(U_1425,bool,hAPP(U_1425,fun(U_1425,bool),ord_less(U_1425),U_1423),U_1424))
          | ~ hBOOL(hAPP(U_1425,bool,hAPP(U_1425,fun(U_1425,bool),ord_less(U_1425),U_1424),U_1423)) )
      | ~ preorder(U_1425) ),
    inference(variable_rename,[status(thm)],[f_382_1]) ).

fof(f_382_3,plain,
    ! [U_1424,U_1425,U_1423] :
      ( ~ hBOOL(hAPP(U_1425,bool,hAPP(U_1425,fun(U_1425,bool),ord_less(U_1425),U_1423),U_1424))
      | ~ hBOOL(hAPP(U_1425,bool,hAPP(U_1425,fun(U_1425,bool),ord_less(U_1425),U_1424),U_1423))
      | ~ preorder(U_1425) ),
    inference(definitional_conversion,[status(esa)],[f_382_2]) ).

cnf(f_382_4,plain,
    ( ~ hBOOL(hAPP(U_1425,bool,hAPP(U_1425,fun(U_1425,bool),ord_less(U_1425),U_1423),U_1424))
    | ~ hBOOL(hAPP(U_1425,bool,hAPP(U_1425,fun(U_1425,bool),ord_less(U_1425),U_1424),U_1423))
    | ~ preorder(U_1425) ),
    inference(clausify,[status(thm)],[f_382_3]) ).

fof(f_383_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_312_order__less__imp__not__less]) ).

fof(f_383_2,plain,
    ! [U_1428] :
      ( ! [U_1427,U_1426] :
          ( ~ hBOOL(hAPP(U_1428,bool,hAPP(U_1428,fun(U_1428,bool),ord_less(U_1428),U_1426),U_1427))
          | ~ hBOOL(hAPP(U_1428,bool,hAPP(U_1428,fun(U_1428,bool),ord_less(U_1428),U_1427),U_1426)) )
      | ~ preorder(U_1428) ),
    inference(variable_rename,[status(thm)],[f_383_1]) ).

fof(f_383_3,plain,
    ! [U_1426,U_1428,U_1427] :
      ( ~ hBOOL(hAPP(U_1428,bool,hAPP(U_1428,fun(U_1428,bool),ord_less(U_1428),U_1426),U_1427))
      | ~ hBOOL(hAPP(U_1428,bool,hAPP(U_1428,fun(U_1428,bool),ord_less(U_1428),U_1427),U_1426))
      | ~ preorder(U_1428) ),
    inference(definitional_conversion,[status(esa)],[f_383_2]) ).

cnf(f_383_4,plain,
    ( ~ hBOOL(hAPP(U_1428,bool,hAPP(U_1428,fun(U_1428,bool),ord_less(U_1428),U_1426),U_1427))
    | ~ hBOOL(hAPP(U_1428,bool,hAPP(U_1428,fun(U_1428,bool),ord_less(U_1428),U_1427),U_1426))
    | ~ preorder(U_1428) ),
    inference(clausify,[status(thm)],[f_383_3]) ).

fof(f_384_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_313_order__less__imp__not__eq]) ).

fof(f_384_2,plain,
    ! [U_1431] :
      ( ! [U_1430,U_1429] :
          ( ti(U_1431,U_1430) != ti(U_1431,U_1429)
          | ~ hBOOL(hAPP(U_1431,bool,hAPP(U_1431,fun(U_1431,bool),ord_less(U_1431),U_1430),U_1429)) )
      | ~ order(U_1431) ),
    inference(variable_rename,[status(thm)],[f_384_1]) ).

fof(f_384_3,plain,
    ! [U_1430,U_1429,U_1431] :
      ( ti(U_1431,U_1430) != ti(U_1431,U_1429)
      | ~ hBOOL(hAPP(U_1431,bool,hAPP(U_1431,fun(U_1431,bool),ord_less(U_1431),U_1430),U_1429))
      | ~ order(U_1431) ),
    inference(definitional_conversion,[status(esa)],[f_384_2]) ).

cnf(f_384_4,plain,
    ( ti(U_1431,U_1430) != ti(U_1431,U_1429)
    | ~ hBOOL(hAPP(U_1431,bool,hAPP(U_1431,fun(U_1431,bool),ord_less(U_1431),U_1430),U_1429))
    | ~ order(U_1431) ),
    inference(clausify,[status(thm)],[f_384_3]) ).

fof(f_385_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_314_order__less__imp__not__eq2]) ).

fof(f_385_2,plain,
    ! [U_1434] :
      ( ! [U_1433,U_1432] :
          ( ti(U_1434,U_1432) != ti(U_1434,U_1433)
          | ~ hBOOL(hAPP(U_1434,bool,hAPP(U_1434,fun(U_1434,bool),ord_less(U_1434),U_1433),U_1432)) )
      | ~ order(U_1434) ),
    inference(variable_rename,[status(thm)],[f_385_1]) ).

fof(f_385_3,plain,
    ! [U_1432,U_1433,U_1434] :
      ( ti(U_1434,U_1432) != ti(U_1434,U_1433)
      | ~ hBOOL(hAPP(U_1434,bool,hAPP(U_1434,fun(U_1434,bool),ord_less(U_1434),U_1433),U_1432))
      | ~ order(U_1434) ),
    inference(definitional_conversion,[status(esa)],[f_385_2]) ).

cnf(f_385_4,plain,
    ( ti(U_1434,U_1432) != ti(U_1434,U_1433)
    | ~ hBOOL(hAPP(U_1434,bool,hAPP(U_1434,fun(U_1434,bool),ord_less(U_1434),U_1433),U_1432))
    | ~ order(U_1434) ),
    inference(clausify,[status(thm)],[f_385_3]) ).

fof(f_386_1,plain,
    ! [X_b] :
      ( ! [Pa,X_1,Y_2] :
          ( hBOOL(Pa)
          | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_1))
          | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2)) )
      | ~ preorder(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_315_order__less__imp__triv]) ).

fof(f_386_2,plain,
    ! [U_1438] :
      ( ! [U_1437,U_1436,U_1435] :
          ( hBOOL(U_1437)
          | ~ hBOOL(hAPP(U_1438,bool,hAPP(U_1438,fun(U_1438,bool),ord_less(U_1438),U_1435),U_1436))
          | ~ hBOOL(hAPP(U_1438,bool,hAPP(U_1438,fun(U_1438,bool),ord_less(U_1438),U_1436),U_1435)) )
      | ~ preorder(U_1438) ),
    inference(variable_rename,[status(thm)],[f_386_1]) ).

fof(f_386_3,plain,
    ! [U_1436,U_1437,U_1435,U_1438] :
      ( hBOOL(U_1437)
      | ~ hBOOL(hAPP(U_1438,bool,hAPP(U_1438,fun(U_1438,bool),ord_less(U_1438),U_1435),U_1436))
      | ~ hBOOL(hAPP(U_1438,bool,hAPP(U_1438,fun(U_1438,bool),ord_less(U_1438),U_1436),U_1435))
      | ~ preorder(U_1438) ),
    inference(definitional_conversion,[status(esa)],[f_386_2]) ).

cnf(f_386_4,plain,
    ( hBOOL(U_1437)
    | ~ hBOOL(hAPP(U_1438,bool,hAPP(U_1438,fun(U_1438,bool),ord_less(U_1438),U_1435),U_1436))
    | ~ hBOOL(hAPP(U_1438,bool,hAPP(U_1438,fun(U_1438,bool),ord_less(U_1438),U_1436),U_1435))
    | ~ preorder(U_1438) ),
    inference(clausify,[status(thm)],[f_386_3]) ).

fof(f_387_1,plain,
    ! [X_a] :
      ( ! [A_1,B] :
          ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) )
      | ~ preorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_316_order__less__asym_H]) ).

fof(f_387_2,plain,
    ! [U_1441] :
      ( ! [U_1440,U_1439] :
          ( ~ hBOOL(hAPP(U_1441,bool,hAPP(U_1441,fun(U_1441,bool),ord_less(U_1441),U_1439),U_1440))
          | ~ hBOOL(hAPP(U_1441,bool,hAPP(U_1441,fun(U_1441,bool),ord_less(U_1441),U_1440),U_1439)) )
      | ~ preorder(U_1441) ),
    inference(variable_rename,[status(thm)],[f_387_1]) ).

fof(f_387_3,plain,
    ! [U_1440,U_1441,U_1439] :
      ( ~ hBOOL(hAPP(U_1441,bool,hAPP(U_1441,fun(U_1441,bool),ord_less(U_1441),U_1439),U_1440))
      | ~ hBOOL(hAPP(U_1441,bool,hAPP(U_1441,fun(U_1441,bool),ord_less(U_1441),U_1440),U_1439))
      | ~ preorder(U_1441) ),
    inference(definitional_conversion,[status(esa)],[f_387_2]) ).

cnf(f_387_4,plain,
    ( ~ hBOOL(hAPP(U_1441,bool,hAPP(U_1441,fun(U_1441,bool),ord_less(U_1441),U_1439),U_1440))
    | ~ hBOOL(hAPP(U_1441,bool,hAPP(U_1441,fun(U_1441,bool),ord_less(U_1441),U_1440),U_1439))
    | ~ preorder(U_1441) ),
    inference(clausify,[status(thm)],[f_387_3]) ).

fof(f_388_1,plain,
    ! [X_a] :
      ( ! [B,A_1] :
          ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)) )
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_317_xt1_I9_J]) ).

fof(f_388_2,plain,
    ! [U_1444] :
      ( ! [U_1443,U_1442] :
          ( ~ hBOOL(hAPP(U_1444,bool,hAPP(U_1444,fun(U_1444,bool),ord_less(U_1444),U_1442),U_1443))
          | ~ hBOOL(hAPP(U_1444,bool,hAPP(U_1444,fun(U_1444,bool),ord_less(U_1444),U_1443),U_1442)) )
      | ~ order(U_1444) ),
    inference(variable_rename,[status(thm)],[f_388_1]) ).

fof(f_388_3,plain,
    ! [U_1443,U_1442,U_1444] :
      ( ~ hBOOL(hAPP(U_1444,bool,hAPP(U_1444,fun(U_1444,bool),ord_less(U_1444),U_1442),U_1443))
      | ~ hBOOL(hAPP(U_1444,bool,hAPP(U_1444,fun(U_1444,bool),ord_less(U_1444),U_1443),U_1442))
      | ~ order(U_1444) ),
    inference(definitional_conversion,[status(esa)],[f_388_2]) ).

cnf(f_388_4,plain,
    ( ~ hBOOL(hAPP(U_1444,bool,hAPP(U_1444,fun(U_1444,bool),ord_less(U_1444),U_1442),U_1443))
    | ~ hBOOL(hAPP(U_1444,bool,hAPP(U_1444,fun(U_1444,bool),ord_less(U_1444),U_1443),U_1442))
    | ~ order(U_1444) ),
    inference(clausify,[status(thm)],[f_388_3]) ).

fof(f_389_1,plain,
    ! [X_a] :
      ( ! [C,A_1,B] :
          ( 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),C))
          | A_1 != B )
      | ~ ord(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_318_ord__eq__less__trans]) ).

fof(f_389_2,plain,
    ! [U_1448] :
      ( ! [U_1447,U_1446,U_1445] :
          ( hBOOL(hAPP(U_1448,bool,hAPP(U_1448,fun(U_1448,bool),ord_less(U_1448),U_1446),U_1447))
          | ~ hBOOL(hAPP(U_1448,bool,hAPP(U_1448,fun(U_1448,bool),ord_less(U_1448),U_1445),U_1447))
          | U_1446 != U_1445 )
      | ~ ord(U_1448) ),
    inference(variable_rename,[status(thm)],[f_389_1]) ).

fof(f_389_3,plain,
    ! [U_1448,U_1445,U_1446,U_1447] :
      ( hBOOL(hAPP(U_1448,bool,hAPP(U_1448,fun(U_1448,bool),ord_less(U_1448),U_1446),U_1447))
      | ~ hBOOL(hAPP(U_1448,bool,hAPP(U_1448,fun(U_1448,bool),ord_less(U_1448),U_1445),U_1447))
      | U_1446 != U_1445
      | ~ ord(U_1448) ),
    inference(definitional_conversion,[status(esa)],[f_389_2]) ).

cnf(f_389_4,plain,
    ( hBOOL(hAPP(U_1448,bool,hAPP(U_1448,fun(U_1448,bool),ord_less(U_1448),U_1446),U_1447))
    | ~ hBOOL(hAPP(U_1448,bool,hAPP(U_1448,fun(U_1448,bool),ord_less(U_1448),U_1445),U_1447))
    | U_1446 != U_1445
    | ~ ord(U_1448) ),
    inference(clausify,[status(thm)],[f_389_3]) ).

fof(f_390_1,plain,
    ! [X_a] :
      ( ! [C,A_1,B] :
          ( 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))
          | ti(X_a,A_1) != ti(X_a,B) )
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_319_xt1_I1_J]) ).

fof(f_390_2,plain,
    ! [U_1452] :
      ( ! [U_1451,U_1450,U_1449] :
          ( hBOOL(hAPP(U_1452,bool,hAPP(U_1452,fun(U_1452,bool),ord_less(U_1452),U_1451),U_1450))
          | ~ hBOOL(hAPP(U_1452,bool,hAPP(U_1452,fun(U_1452,bool),ord_less(U_1452),U_1451),U_1449))
          | ti(U_1452,U_1450) != ti(U_1452,U_1449) )
      | ~ order(U_1452) ),
    inference(variable_rename,[status(thm)],[f_390_1]) ).

fof(f_390_3,plain,
    ! [U_1450,U_1452,U_1451,U_1449] :
      ( hBOOL(hAPP(U_1452,bool,hAPP(U_1452,fun(U_1452,bool),ord_less(U_1452),U_1451),U_1450))
      | ~ hBOOL(hAPP(U_1452,bool,hAPP(U_1452,fun(U_1452,bool),ord_less(U_1452),U_1451),U_1449))
      | ti(U_1452,U_1450) != ti(U_1452,U_1449)
      | ~ order(U_1452) ),
    inference(definitional_conversion,[status(esa)],[f_390_2]) ).

cnf(f_390_4,plain,
    ( hBOOL(hAPP(U_1452,bool,hAPP(U_1452,fun(U_1452,bool),ord_less(U_1452),U_1451),U_1450))
    | ~ hBOOL(hAPP(U_1452,bool,hAPP(U_1452,fun(U_1452,bool),ord_less(U_1452),U_1451),U_1449))
    | ti(U_1452,U_1450) != ti(U_1452,U_1449)
    | ~ order(U_1452) ),
    inference(clausify,[status(thm)],[f_390_3]) ).

fof(f_391_1,plain,
    ! [X_a] :
      ( ! [C,A_1,B] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),C))
          | B != C
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) )
      | ~ ord(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_320_ord__less__eq__trans]) ).

fof(f_391_2,plain,
    ! [U_1456] :
      ( ! [U_1455,U_1454,U_1453] :
          ( hBOOL(hAPP(U_1456,bool,hAPP(U_1456,fun(U_1456,bool),ord_less(U_1456),U_1454),U_1455))
          | U_1453 != U_1455
          | ~ hBOOL(hAPP(U_1456,bool,hAPP(U_1456,fun(U_1456,bool),ord_less(U_1456),U_1454),U_1453)) )
      | ~ ord(U_1456) ),
    inference(variable_rename,[status(thm)],[f_391_1]) ).

fof(f_391_3,plain,
    ! [U_1456,U_1455,U_1454,U_1453] :
      ( hBOOL(hAPP(U_1456,bool,hAPP(U_1456,fun(U_1456,bool),ord_less(U_1456),U_1454),U_1455))
      | U_1453 != U_1455
      | ~ hBOOL(hAPP(U_1456,bool,hAPP(U_1456,fun(U_1456,bool),ord_less(U_1456),U_1454),U_1453))
      | ~ ord(U_1456) ),
    inference(definitional_conversion,[status(esa)],[f_391_2]) ).

cnf(f_391_4,plain,
    ( hBOOL(hAPP(U_1456,bool,hAPP(U_1456,fun(U_1456,bool),ord_less(U_1456),U_1454),U_1455))
    | U_1453 != U_1455
    | ~ hBOOL(hAPP(U_1456,bool,hAPP(U_1456,fun(U_1456,bool),ord_less(U_1456),U_1454),U_1453))
    | ~ ord(U_1456) ),
    inference(clausify,[status(thm)],[f_391_3]) ).

fof(f_392_1,plain,
    ! [X_a] :
      ( ! [C,B,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) != ti(X_a,C)
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)) )
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_321_xt1_I2_J]) ).

fof(f_392_2,plain,
    ! [U_1460] :
      ( ! [U_1459,U_1458,U_1457] :
          ( hBOOL(hAPP(U_1460,bool,hAPP(U_1460,fun(U_1460,bool),ord_less(U_1460),U_1459),U_1457))
          | ti(U_1460,U_1458) != ti(U_1460,U_1459)
          | ~ hBOOL(hAPP(U_1460,bool,hAPP(U_1460,fun(U_1460,bool),ord_less(U_1460),U_1458),U_1457)) )
      | ~ order(U_1460) ),
    inference(variable_rename,[status(thm)],[f_392_1]) ).

fof(f_392_3,plain,
    ! [U_1459,U_1458,U_1457,U_1460] :
      ( hBOOL(hAPP(U_1460,bool,hAPP(U_1460,fun(U_1460,bool),ord_less(U_1460),U_1459),U_1457))
      | ti(U_1460,U_1458) != ti(U_1460,U_1459)
      | ~ hBOOL(hAPP(U_1460,bool,hAPP(U_1460,fun(U_1460,bool),ord_less(U_1460),U_1458),U_1457))
      | ~ order(U_1460) ),
    inference(definitional_conversion,[status(esa)],[f_392_2]) ).

cnf(f_392_4,plain,
    ( hBOOL(hAPP(U_1460,bool,hAPP(U_1460,fun(U_1460,bool),ord_less(U_1460),U_1459),U_1457))
    | ti(U_1460,U_1458) != ti(U_1460,U_1459)
    | ~ hBOOL(hAPP(U_1460,bool,hAPP(U_1460,fun(U_1460,bool),ord_less(U_1460),U_1458),U_1457))
    | ~ order(U_1460) ),
    inference(clausify,[status(thm)],[f_392_3]) ).

fof(f_393_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_322_order__less__trans]) ).

fof(f_393_2,plain,
    ! [U_1464] :
      ( ! [U_1463,U_1462,U_1461] :
          ( hBOOL(hAPP(U_1464,bool,hAPP(U_1464,fun(U_1464,bool),ord_less(U_1464),U_1462),U_1463))
          | ~ hBOOL(hAPP(U_1464,bool,hAPP(U_1464,fun(U_1464,bool),ord_less(U_1464),U_1461),U_1463))
          | ~ hBOOL(hAPP(U_1464,bool,hAPP(U_1464,fun(U_1464,bool),ord_less(U_1464),U_1462),U_1461)) )
      | ~ preorder(U_1464) ),
    inference(variable_rename,[status(thm)],[f_393_1]) ).

fof(f_393_3,plain,
    ! [U_1464,U_1462,U_1461,U_1463] :
      ( hBOOL(hAPP(U_1464,bool,hAPP(U_1464,fun(U_1464,bool),ord_less(U_1464),U_1462),U_1463))
      | ~ hBOOL(hAPP(U_1464,bool,hAPP(U_1464,fun(U_1464,bool),ord_less(U_1464),U_1461),U_1463))
      | ~ hBOOL(hAPP(U_1464,bool,hAPP(U_1464,fun(U_1464,bool),ord_less(U_1464),U_1462),U_1461))
      | ~ preorder(U_1464) ),
    inference(definitional_conversion,[status(esa)],[f_393_2]) ).

cnf(f_393_4,plain,
    ( hBOOL(hAPP(U_1464,bool,hAPP(U_1464,fun(U_1464,bool),ord_less(U_1464),U_1462),U_1463))
    | ~ hBOOL(hAPP(U_1464,bool,hAPP(U_1464,fun(U_1464,bool),ord_less(U_1464),U_1461),U_1463))
    | ~ hBOOL(hAPP(U_1464,bool,hAPP(U_1464,fun(U_1464,bool),ord_less(U_1464),U_1462),U_1461))
    | ~ preorder(U_1464) ),
    inference(clausify,[status(thm)],[f_393_3]) ).

fof(f_394_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_323_xt1_I10_J]) ).

fof(f_394_2,plain,
    ! [U_1468] :
      ( ! [U_1467,U_1466,U_1465] :
          ( hBOOL(hAPP(U_1468,bool,hAPP(U_1468,fun(U_1468,bool),ord_less(U_1468),U_1467),U_1465))
          | ~ hBOOL(hAPP(U_1468,bool,hAPP(U_1468,fun(U_1468,bool),ord_less(U_1468),U_1467),U_1466))
          | ~ hBOOL(hAPP(U_1468,bool,hAPP(U_1468,fun(U_1468,bool),ord_less(U_1468),U_1466),U_1465)) )
      | ~ order(U_1468) ),
    inference(variable_rename,[status(thm)],[f_394_1]) ).

fof(f_394_3,plain,
    ! [U_1466,U_1465,U_1468,U_1467] :
      ( hBOOL(hAPP(U_1468,bool,hAPP(U_1468,fun(U_1468,bool),ord_less(U_1468),U_1467),U_1465))
      | ~ hBOOL(hAPP(U_1468,bool,hAPP(U_1468,fun(U_1468,bool),ord_less(U_1468),U_1467),U_1466))
      | ~ hBOOL(hAPP(U_1468,bool,hAPP(U_1468,fun(U_1468,bool),ord_less(U_1468),U_1466),U_1465))
      | ~ order(U_1468) ),
    inference(definitional_conversion,[status(esa)],[f_394_2]) ).

cnf(f_394_4,plain,
    ( hBOOL(hAPP(U_1468,bool,hAPP(U_1468,fun(U_1468,bool),ord_less(U_1468),U_1467),U_1465))
    | ~ hBOOL(hAPP(U_1468,bool,hAPP(U_1468,fun(U_1468,bool),ord_less(U_1468),U_1467),U_1466))
    | ~ hBOOL(hAPP(U_1468,bool,hAPP(U_1468,fun(U_1468,bool),ord_less(U_1468),U_1466),U_1465))
    | ~ order(U_1468) ),
    inference(clausify,[status(thm)],[f_394_3]) ).

fof(f_395_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_324_order__less__asym]) ).

fof(f_395_2,plain,
    ! [U_1471] :
      ( ! [U_1470,U_1469] :
          ( ~ hBOOL(hAPP(U_1471,bool,hAPP(U_1471,fun(U_1471,bool),ord_less(U_1471),U_1469),U_1470))
          | ~ hBOOL(hAPP(U_1471,bool,hAPP(U_1471,fun(U_1471,bool),ord_less(U_1471),U_1470),U_1469)) )
      | ~ preorder(U_1471) ),
    inference(variable_rename,[status(thm)],[f_395_1]) ).

fof(f_395_3,plain,
    ! [U_1469,U_1471,U_1470] :
      ( ~ hBOOL(hAPP(U_1471,bool,hAPP(U_1471,fun(U_1471,bool),ord_less(U_1471),U_1469),U_1470))
      | ~ hBOOL(hAPP(U_1471,bool,hAPP(U_1471,fun(U_1471,bool),ord_less(U_1471),U_1470),U_1469))
      | ~ preorder(U_1471) ),
    inference(definitional_conversion,[status(esa)],[f_395_2]) ).

cnf(f_395_4,plain,
    ( ~ hBOOL(hAPP(U_1471,bool,hAPP(U_1471,fun(U_1471,bool),ord_less(U_1471),U_1469),U_1470))
    | ~ hBOOL(hAPP(U_1471,bool,hAPP(U_1471,fun(U_1471,bool),ord_less(U_1471),U_1470),U_1469))
    | ~ preorder(U_1471) ),
    inference(clausify,[status(thm)],[f_395_3]) ).

fof(f_396_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_325_linorder__cases]) ).

fof(f_396_2,plain,
    ! [U_1474] :
      ( ! [U_1473,U_1472] :
          ( hBOOL(hAPP(U_1474,bool,hAPP(U_1474,fun(U_1474,bool),ord_less(U_1474),U_1472),U_1473))
          | ti(U_1474,U_1473) = ti(U_1474,U_1472)
          | hBOOL(hAPP(U_1474,bool,hAPP(U_1474,fun(U_1474,bool),ord_less(U_1474),U_1473),U_1472)) )
      | ~ linorder(U_1474) ),
    inference(variable_rename,[status(thm)],[f_396_1]) ).

fof(f_396_3,plain,
    ! [U_1472,U_1473,U_1474] :
      ( hBOOL(hAPP(U_1474,bool,hAPP(U_1474,fun(U_1474,bool),ord_less(U_1474),U_1472),U_1473))
      | ti(U_1474,U_1473) = ti(U_1474,U_1472)
      | hBOOL(hAPP(U_1474,bool,hAPP(U_1474,fun(U_1474,bool),ord_less(U_1474),U_1473),U_1472))
      | ~ linorder(U_1474) ),
    inference(definitional_conversion,[status(esa)],[f_396_2]) ).

cnf(f_396_4,plain,
    ( hBOOL(hAPP(U_1474,bool,hAPP(U_1474,fun(U_1474,bool),ord_less(U_1474),U_1472),U_1473))
    | ti(U_1474,U_1473) = ti(U_1474,U_1472)
    | hBOOL(hAPP(U_1474,bool,hAPP(U_1474,fun(U_1474,bool),ord_less(U_1474),U_1473),U_1472))
    | ~ linorder(U_1474) ),
    inference(clausify,[status(thm)],[f_396_3]) ).

fof(f_397_1,plain,
    ! [X_b] :
      ( ! [X_1,Y_2] :
          ( ( ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2))
            | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_2),X_1)) )
          & ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_2),X_1))
            | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2)) ) )
      | ~ linorder(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_326_linorder__not__less]) ).

fof(f_397_2,plain,
    ! [U_1477] :
      ( ! [U_1476,U_1475] :
          ( ( ~ hBOOL(hAPP(U_1477,bool,hAPP(U_1477,fun(U_1477,bool),ord_less(U_1477),U_1476),U_1475))
            | ~ hBOOL(hAPP(U_1477,bool,hAPP(U_1477,fun(U_1477,bool),ord_less_eq(U_1477),U_1475),U_1476)) )
          & ( hBOOL(hAPP(U_1477,bool,hAPP(U_1477,fun(U_1477,bool),ord_less_eq(U_1477),U_1475),U_1476))
            | hBOOL(hAPP(U_1477,bool,hAPP(U_1477,fun(U_1477,bool),ord_less(U_1477),U_1476),U_1475)) ) )
      | ~ linorder(U_1477) ),
    inference(variable_rename,[status(thm)],[f_397_1]) ).

fof(f_397_3,plain,
    ! [U_1477] :
      ( ( ! [U_1481,U_1479] :
            ( ~ hBOOL(hAPP(U_1477,bool,hAPP(U_1477,fun(U_1477,bool),ord_less(U_1477),U_1481),U_1479))
            | ~ hBOOL(hAPP(U_1477,bool,hAPP(U_1477,fun(U_1477,bool),ord_less_eq(U_1477),U_1479),U_1481)) )
        & ! [U_1480,U_1478] :
            ( hBOOL(hAPP(U_1477,bool,hAPP(U_1477,fun(U_1477,bool),ord_less_eq(U_1477),U_1478),U_1480))
            | hBOOL(hAPP(U_1477,bool,hAPP(U_1477,fun(U_1477,bool),ord_less(U_1477),U_1480),U_1478)) ) )
      | ~ linorder(U_1477) ),
    inference(miniscope,[status(thm)],[f_397_2]) ).

fof(f_397_4,plain,
    ( ! [U_1481,U_1477,U_1479,U_1478,U_1480] :
        ( ~ hBOOL(hAPP(U_1477,bool,hAPP(U_1477,fun(U_1477,bool),ord_less(U_1477),U_1481),U_1479))
        | ~ hBOOL(hAPP(U_1477,bool,hAPP(U_1477,fun(U_1477,bool),ord_less_eq(U_1477),U_1479),U_1481))
        | ~ sP72(U_1481,U_1477,U_1479,U_1478,U_1480) )
    & ! [U_1481,U_1477,U_1479,U_1478,U_1480] :
        ( hBOOL(hAPP(U_1477,bool,hAPP(U_1477,fun(U_1477,bool),ord_less_eq(U_1477),U_1478),U_1480))
        | hBOOL(hAPP(U_1477,bool,hAPP(U_1477,fun(U_1477,bool),ord_less(U_1477),U_1480),U_1478))
        | ~ sP72(U_1481,U_1477,U_1479,U_1478,U_1480) )
    & ! [U_1481,U_1477,U_1479,U_1478,U_1480] :
        ( sP72(U_1481,U_1477,U_1479,U_1478,U_1480)
        | ~ linorder(U_1477) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP72])],[f_397_3]) ).

cnf(f_397_5,plain,
    ( sP72(U_1481,U_1477,U_1479,U_1478,U_1480)
    | ~ linorder(U_1477) ),
    inference(clausify,[status(thm)],[f_397_4]) ).

cnf(f_397_6,plain,
    ( hBOOL(hAPP(U_1477,bool,hAPP(U_1477,fun(U_1477,bool),ord_less_eq(U_1477),U_1478),U_1480))
    | hBOOL(hAPP(U_1477,bool,hAPP(U_1477,fun(U_1477,bool),ord_less(U_1477),U_1480),U_1478))
    | ~ sP72(U_1481,U_1477,U_1479,U_1478,U_1480) ),
    inference(clausify,[status(thm)],[f_397_4]) ).

cnf(f_397_7,plain,
    ( ~ hBOOL(hAPP(U_1477,bool,hAPP(U_1477,fun(U_1477,bool),ord_less(U_1477),U_1481),U_1479))
    | ~ hBOOL(hAPP(U_1477,bool,hAPP(U_1477,fun(U_1477,bool),ord_less_eq(U_1477),U_1479),U_1481))
    | ~ sP72(U_1481,U_1477,U_1479,U_1478,U_1480) ),
    inference(clausify,[status(thm)],[f_397_4]) ).

fof(f_398_1,plain,
    ! [X_b] :
      ( ! [X_1,Y_2] :
          ( ( ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2))
            | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_1)) )
          & ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_1))
            | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2)) ) )
      | ~ linorder(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_327_linorder__not__le]) ).

fof(f_398_2,plain,
    ! [U_1484] :
      ( ! [U_1483,U_1482] :
          ( ( ~ hBOOL(hAPP(U_1484,bool,hAPP(U_1484,fun(U_1484,bool),ord_less_eq(U_1484),U_1483),U_1482))
            | ~ hBOOL(hAPP(U_1484,bool,hAPP(U_1484,fun(U_1484,bool),ord_less(U_1484),U_1482),U_1483)) )
          & ( hBOOL(hAPP(U_1484,bool,hAPP(U_1484,fun(U_1484,bool),ord_less(U_1484),U_1482),U_1483))
            | hBOOL(hAPP(U_1484,bool,hAPP(U_1484,fun(U_1484,bool),ord_less_eq(U_1484),U_1483),U_1482)) ) )
      | ~ linorder(U_1484) ),
    inference(variable_rename,[status(thm)],[f_398_1]) ).

fof(f_398_3,plain,
    ! [U_1484] :
      ( ( ! [U_1488,U_1486] :
            ( ~ hBOOL(hAPP(U_1484,bool,hAPP(U_1484,fun(U_1484,bool),ord_less_eq(U_1484),U_1488),U_1486))
            | ~ hBOOL(hAPP(U_1484,bool,hAPP(U_1484,fun(U_1484,bool),ord_less(U_1484),U_1486),U_1488)) )
        & ! [U_1487,U_1485] :
            ( hBOOL(hAPP(U_1484,bool,hAPP(U_1484,fun(U_1484,bool),ord_less(U_1484),U_1485),U_1487))
            | hBOOL(hAPP(U_1484,bool,hAPP(U_1484,fun(U_1484,bool),ord_less_eq(U_1484),U_1487),U_1485)) ) )
      | ~ linorder(U_1484) ),
    inference(miniscope,[status(thm)],[f_398_2]) ).

fof(f_398_4,plain,
    ( ! [U_1488,U_1484,U_1486,U_1485,U_1487] :
        ( ~ hBOOL(hAPP(U_1484,bool,hAPP(U_1484,fun(U_1484,bool),ord_less_eq(U_1484),U_1488),U_1486))
        | ~ hBOOL(hAPP(U_1484,bool,hAPP(U_1484,fun(U_1484,bool),ord_less(U_1484),U_1486),U_1488))
        | ~ sP73(U_1488,U_1484,U_1486,U_1485,U_1487) )
    & ! [U_1488,U_1484,U_1486,U_1485,U_1487] :
        ( hBOOL(hAPP(U_1484,bool,hAPP(U_1484,fun(U_1484,bool),ord_less(U_1484),U_1485),U_1487))
        | hBOOL(hAPP(U_1484,bool,hAPP(U_1484,fun(U_1484,bool),ord_less_eq(U_1484),U_1487),U_1485))
        | ~ sP73(U_1488,U_1484,U_1486,U_1485,U_1487) )
    & ! [U_1488,U_1484,U_1486,U_1485,U_1487] :
        ( sP73(U_1488,U_1484,U_1486,U_1485,U_1487)
        | ~ linorder(U_1484) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP73])],[f_398_3]) ).

cnf(f_398_5,plain,
    ( sP73(U_1488,U_1484,U_1486,U_1485,U_1487)
    | ~ linorder(U_1484) ),
    inference(clausify,[status(thm)],[f_398_4]) ).

cnf(f_398_6,plain,
    ( hBOOL(hAPP(U_1484,bool,hAPP(U_1484,fun(U_1484,bool),ord_less(U_1484),U_1485),U_1487))
    | hBOOL(hAPP(U_1484,bool,hAPP(U_1484,fun(U_1484,bool),ord_less_eq(U_1484),U_1487),U_1485))
    | ~ sP73(U_1488,U_1484,U_1486,U_1485,U_1487) ),
    inference(clausify,[status(thm)],[f_398_4]) ).

cnf(f_398_7,plain,
    ( ~ hBOOL(hAPP(U_1484,bool,hAPP(U_1484,fun(U_1484,bool),ord_less_eq(U_1484),U_1488),U_1486))
    | ~ hBOOL(hAPP(U_1484,bool,hAPP(U_1484,fun(U_1484,bool),ord_less(U_1484),U_1486),U_1488))
    | ~ sP73(U_1488,U_1484,U_1486,U_1485,U_1487) ),
    inference(clausify,[status(thm)],[f_398_4]) ).

fof(f_399_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_328_linorder__le__less__linear]) ).

fof(f_399_2,plain,
    ! [U_1491] :
      ( ! [U_1490,U_1489] :
          ( hBOOL(hAPP(U_1491,bool,hAPP(U_1491,fun(U_1491,bool),ord_less(U_1491),U_1489),U_1490))
          | hBOOL(hAPP(U_1491,bool,hAPP(U_1491,fun(U_1491,bool),ord_less_eq(U_1491),U_1490),U_1489)) )
      | ~ linorder(U_1491) ),
    inference(variable_rename,[status(thm)],[f_399_1]) ).

fof(f_399_3,plain,
    ! [U_1489,U_1490,U_1491] :
      ( hBOOL(hAPP(U_1491,bool,hAPP(U_1491,fun(U_1491,bool),ord_less(U_1491),U_1489),U_1490))
      | hBOOL(hAPP(U_1491,bool,hAPP(U_1491,fun(U_1491,bool),ord_less_eq(U_1491),U_1490),U_1489))
      | ~ linorder(U_1491) ),
    inference(definitional_conversion,[status(esa)],[f_399_2]) ).

cnf(f_399_4,plain,
    ( hBOOL(hAPP(U_1491,bool,hAPP(U_1491,fun(U_1491,bool),ord_less(U_1491),U_1489),U_1490))
    | hBOOL(hAPP(U_1491,bool,hAPP(U_1491,fun(U_1491,bool),ord_less_eq(U_1491),U_1490),U_1489))
    | ~ linorder(U_1491) ),
    inference(clausify,[status(thm)],[f_399_3]) ).

fof(f_400_1,plain,
    ! [X_b] :
      ( ! [X_1,Y_2] :
          ( ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2))
            | ti(X_b,X_1) = ti(X_b,Y_2)
            | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2)) )
          & ( ( ti(X_b,X_1) != ti(X_b,Y_2)
              & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2)) )
            | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2)) ) )
      | ~ order(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_329_order__less__le]) ).

fof(f_400_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_1493),U_1492))
            | ti(U_1494,U_1493) = ti(U_1494,U_1492)
            | ~ hBOOL(hAPP(U_1494,bool,hAPP(U_1494,fun(U_1494,bool),ord_less_eq(U_1494),U_1493),U_1492)) )
          & ( ( ti(U_1494,U_1493) != ti(U_1494,U_1492)
              & hBOOL(hAPP(U_1494,bool,hAPP(U_1494,fun(U_1494,bool),ord_less_eq(U_1494),U_1493),U_1492)) )
            | ~ hBOOL(hAPP(U_1494,bool,hAPP(U_1494,fun(U_1494,bool),ord_less(U_1494),U_1493),U_1492)) ) )
      | ~ order(U_1494) ),
    inference(variable_rename,[status(thm)],[f_400_1]) ).

fof(f_400_3,plain,
    ! [U_1494] :
      ( ( ! [U_1498,U_1496] :
            ( hBOOL(hAPP(U_1494,bool,hAPP(U_1494,fun(U_1494,bool),ord_less(U_1494),U_1498),U_1496))
            | ti(U_1494,U_1498) = ti(U_1494,U_1496)
            | ~ hBOOL(hAPP(U_1494,bool,hAPP(U_1494,fun(U_1494,bool),ord_less_eq(U_1494),U_1498),U_1496)) )
        & ! [U_1497,U_1495] :
            ( ( ti(U_1494,U_1497) != ti(U_1494,U_1495)
              & hBOOL(hAPP(U_1494,bool,hAPP(U_1494,fun(U_1494,bool),ord_less_eq(U_1494),U_1497),U_1495)) )
            | ~ hBOOL(hAPP(U_1494,bool,hAPP(U_1494,fun(U_1494,bool),ord_less(U_1494),U_1497),U_1495)) ) )
      | ~ order(U_1494) ),
    inference(miniscope,[status(thm)],[f_400_2]) ).

fof(f_400_4,plain,
    ( ! [U_1494,U_1495,U_1497] :
        ( ti(U_1494,U_1497) != ti(U_1494,U_1495)
        | ~ sP74(U_1494,U_1495,U_1497) )
    & ! [U_1494,U_1495,U_1497] :
        ( hBOOL(hAPP(U_1494,bool,hAPP(U_1494,fun(U_1494,bool),ord_less_eq(U_1494),U_1497),U_1495))
        | ~ sP74(U_1494,U_1495,U_1497) )
    & ! [U_1498,U_1494,U_1496,U_1495,U_1497] :
        ( hBOOL(hAPP(U_1494,bool,hAPP(U_1494,fun(U_1494,bool),ord_less(U_1494),U_1498),U_1496))
        | ti(U_1494,U_1498) = ti(U_1494,U_1496)
        | ~ hBOOL(hAPP(U_1494,bool,hAPP(U_1494,fun(U_1494,bool),ord_less_eq(U_1494),U_1498),U_1496))
        | ~ sP75(U_1498,U_1494,U_1496,U_1495,U_1497) )
    & ! [U_1498,U_1494,U_1496,U_1495,U_1497] :
        ( sP74(U_1494,U_1495,U_1497)
        | ~ hBOOL(hAPP(U_1494,bool,hAPP(U_1494,fun(U_1494,bool),ord_less(U_1494),U_1497),U_1495))
        | ~ sP75(U_1498,U_1494,U_1496,U_1495,U_1497) )
    & ! [U_1498,U_1494,U_1496,U_1495,U_1497] :
        ( sP75(U_1498,U_1494,U_1496,U_1495,U_1497)
        | ~ order(U_1494) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP74,sP75])],[f_400_3]) ).

cnf(f_400_5,plain,
    ( sP75(U_1498,U_1494,U_1496,U_1495,U_1497)
    | ~ order(U_1494) ),
    inference(clausify,[status(thm)],[f_400_4]) ).

cnf(f_400_6,plain,
    ( sP74(U_1494,U_1495,U_1497)
    | ~ hBOOL(hAPP(U_1494,bool,hAPP(U_1494,fun(U_1494,bool),ord_less(U_1494),U_1497),U_1495))
    | ~ sP75(U_1498,U_1494,U_1496,U_1495,U_1497) ),
    inference(clausify,[status(thm)],[f_400_4]) ).

cnf(f_400_7,plain,
    ( hBOOL(hAPP(U_1494,bool,hAPP(U_1494,fun(U_1494,bool),ord_less(U_1494),U_1498),U_1496))
    | ti(U_1494,U_1498) = ti(U_1494,U_1496)
    | ~ hBOOL(hAPP(U_1494,bool,hAPP(U_1494,fun(U_1494,bool),ord_less_eq(U_1494),U_1498),U_1496))
    | ~ sP75(U_1498,U_1494,U_1496,U_1495,U_1497) ),
    inference(clausify,[status(thm)],[f_400_4]) ).

cnf(f_400_8,plain,
    ( hBOOL(hAPP(U_1494,bool,hAPP(U_1494,fun(U_1494,bool),ord_less_eq(U_1494),U_1497),U_1495))
    | ~ sP74(U_1494,U_1495,U_1497) ),
    inference(clausify,[status(thm)],[f_400_4]) ).

cnf(f_400_9,plain,
    ( ti(U_1494,U_1497) != ti(U_1494,U_1495)
    | ~ sP74(U_1494,U_1495,U_1497) ),
    inference(clausify,[status(thm)],[f_400_4]) ).

fof(f_401_1,plain,
    ! [X_b] :
      ( ! [X_1,Y_2] :
          ( ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2))
            | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_2),X_1))
            | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2)) )
          & ( ( ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_2),X_1))
              & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2)) )
            | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2)) ) )
      | ~ preorder(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_330_less__le__not__le]) ).

fof(f_401_2,plain,
    ! [U_1501] :
      ( ! [U_1500,U_1499] :
          ( ( hBOOL(hAPP(U_1501,bool,hAPP(U_1501,fun(U_1501,bool),ord_less(U_1501),U_1500),U_1499))
            | hBOOL(hAPP(U_1501,bool,hAPP(U_1501,fun(U_1501,bool),ord_less_eq(U_1501),U_1499),U_1500))
            | ~ hBOOL(hAPP(U_1501,bool,hAPP(U_1501,fun(U_1501,bool),ord_less_eq(U_1501),U_1500),U_1499)) )
          & ( ( ~ hBOOL(hAPP(U_1501,bool,hAPP(U_1501,fun(U_1501,bool),ord_less_eq(U_1501),U_1499),U_1500))
              & hBOOL(hAPP(U_1501,bool,hAPP(U_1501,fun(U_1501,bool),ord_less_eq(U_1501),U_1500),U_1499)) )
            | ~ hBOOL(hAPP(U_1501,bool,hAPP(U_1501,fun(U_1501,bool),ord_less(U_1501),U_1500),U_1499)) ) )
      | ~ preorder(U_1501) ),
    inference(variable_rename,[status(thm)],[f_401_1]) ).

fof(f_401_3,plain,
    ! [U_1501] :
      ( ( ! [U_1505,U_1503] :
            ( hBOOL(hAPP(U_1501,bool,hAPP(U_1501,fun(U_1501,bool),ord_less(U_1501),U_1505),U_1503))
            | hBOOL(hAPP(U_1501,bool,hAPP(U_1501,fun(U_1501,bool),ord_less_eq(U_1501),U_1503),U_1505))
            | ~ hBOOL(hAPP(U_1501,bool,hAPP(U_1501,fun(U_1501,bool),ord_less_eq(U_1501),U_1505),U_1503)) )
        & ! [U_1504,U_1502] :
            ( ( ~ hBOOL(hAPP(U_1501,bool,hAPP(U_1501,fun(U_1501,bool),ord_less_eq(U_1501),U_1502),U_1504))
              & hBOOL(hAPP(U_1501,bool,hAPP(U_1501,fun(U_1501,bool),ord_less_eq(U_1501),U_1504),U_1502)) )
            | ~ hBOOL(hAPP(U_1501,bool,hAPP(U_1501,fun(U_1501,bool),ord_less(U_1501),U_1504),U_1502)) ) )
      | ~ preorder(U_1501) ),
    inference(miniscope,[status(thm)],[f_401_2]) ).

fof(f_401_4,plain,
    ( ! [U_1502,U_1501,U_1504] :
        ( ~ hBOOL(hAPP(U_1501,bool,hAPP(U_1501,fun(U_1501,bool),ord_less_eq(U_1501),U_1502),U_1504))
        | ~ sP76(U_1502,U_1501,U_1504) )
    & ! [U_1502,U_1501,U_1504] :
        ( hBOOL(hAPP(U_1501,bool,hAPP(U_1501,fun(U_1501,bool),ord_less_eq(U_1501),U_1504),U_1502))
        | ~ sP76(U_1502,U_1501,U_1504) )
    & ! [U_1503,U_1502,U_1501,U_1505,U_1504] :
        ( hBOOL(hAPP(U_1501,bool,hAPP(U_1501,fun(U_1501,bool),ord_less(U_1501),U_1505),U_1503))
        | hBOOL(hAPP(U_1501,bool,hAPP(U_1501,fun(U_1501,bool),ord_less_eq(U_1501),U_1503),U_1505))
        | ~ hBOOL(hAPP(U_1501,bool,hAPP(U_1501,fun(U_1501,bool),ord_less_eq(U_1501),U_1505),U_1503))
        | ~ sP77(U_1503,U_1502,U_1501,U_1505,U_1504) )
    & ! [U_1503,U_1502,U_1501,U_1505,U_1504] :
        ( sP76(U_1502,U_1501,U_1504)
        | ~ hBOOL(hAPP(U_1501,bool,hAPP(U_1501,fun(U_1501,bool),ord_less(U_1501),U_1504),U_1502))
        | ~ sP77(U_1503,U_1502,U_1501,U_1505,U_1504) )
    & ! [U_1503,U_1502,U_1501,U_1505,U_1504] :
        ( sP77(U_1503,U_1502,U_1501,U_1505,U_1504)
        | ~ preorder(U_1501) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP76,sP77])],[f_401_3]) ).

cnf(f_401_5,plain,
    ( sP77(U_1503,U_1502,U_1501,U_1505,U_1504)
    | ~ preorder(U_1501) ),
    inference(clausify,[status(thm)],[f_401_4]) ).

cnf(f_401_6,plain,
    ( sP76(U_1502,U_1501,U_1504)
    | ~ hBOOL(hAPP(U_1501,bool,hAPP(U_1501,fun(U_1501,bool),ord_less(U_1501),U_1504),U_1502))
    | ~ sP77(U_1503,U_1502,U_1501,U_1505,U_1504) ),
    inference(clausify,[status(thm)],[f_401_4]) ).

cnf(f_401_7,plain,
    ( hBOOL(hAPP(U_1501,bool,hAPP(U_1501,fun(U_1501,bool),ord_less(U_1501),U_1505),U_1503))
    | hBOOL(hAPP(U_1501,bool,hAPP(U_1501,fun(U_1501,bool),ord_less_eq(U_1501),U_1503),U_1505))
    | ~ hBOOL(hAPP(U_1501,bool,hAPP(U_1501,fun(U_1501,bool),ord_less_eq(U_1501),U_1505),U_1503))
    | ~ sP77(U_1503,U_1502,U_1501,U_1505,U_1504) ),
    inference(clausify,[status(thm)],[f_401_4]) ).

cnf(f_401_8,plain,
    ( hBOOL(hAPP(U_1501,bool,hAPP(U_1501,fun(U_1501,bool),ord_less_eq(U_1501),U_1504),U_1502))
    | ~ sP76(U_1502,U_1501,U_1504) ),
    inference(clausify,[status(thm)],[f_401_4]) ).

cnf(f_401_9,plain,
    ( ~ hBOOL(hAPP(U_1501,bool,hAPP(U_1501,fun(U_1501,bool),ord_less_eq(U_1501),U_1502),U_1504))
    | ~ sP76(U_1502,U_1501,U_1504) ),
    inference(clausify,[status(thm)],[f_401_4]) ).

fof(f_402_1,plain,
    ! [X_b] :
      ( ! [X_1,Y_2] :
          ( ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2))
            | ( ti(X_b,X_1) != ti(X_b,Y_2)
              & ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2)) ) )
          & ( ti(X_b,X_1) = ti(X_b,Y_2)
            | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2))
            | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2)) ) )
      | ~ order(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_331_order__le__less]) ).

fof(f_402_2,plain,
    ! [U_1508] :
      ( ! [U_1507,U_1506] :
          ( ( hBOOL(hAPP(U_1508,bool,hAPP(U_1508,fun(U_1508,bool),ord_less_eq(U_1508),U_1507),U_1506))
            | ( ti(U_1508,U_1507) != ti(U_1508,U_1506)
              & ~ hBOOL(hAPP(U_1508,bool,hAPP(U_1508,fun(U_1508,bool),ord_less(U_1508),U_1507),U_1506)) ) )
          & ( ti(U_1508,U_1507) = ti(U_1508,U_1506)
            | hBOOL(hAPP(U_1508,bool,hAPP(U_1508,fun(U_1508,bool),ord_less(U_1508),U_1507),U_1506))
            | ~ hBOOL(hAPP(U_1508,bool,hAPP(U_1508,fun(U_1508,bool),ord_less_eq(U_1508),U_1507),U_1506)) ) )
      | ~ order(U_1508) ),
    inference(variable_rename,[status(thm)],[f_402_1]) ).

fof(f_402_3,plain,
    ! [U_1508] :
      ( ( ! [U_1512,U_1510] :
            ( hBOOL(hAPP(U_1508,bool,hAPP(U_1508,fun(U_1508,bool),ord_less_eq(U_1508),U_1512),U_1510))
            | ( ti(U_1508,U_1512) != ti(U_1508,U_1510)
              & ~ hBOOL(hAPP(U_1508,bool,hAPP(U_1508,fun(U_1508,bool),ord_less(U_1508),U_1512),U_1510)) ) )
        & ! [U_1511,U_1509] :
            ( ti(U_1508,U_1511) = ti(U_1508,U_1509)
            | hBOOL(hAPP(U_1508,bool,hAPP(U_1508,fun(U_1508,bool),ord_less(U_1508),U_1511),U_1509))
            | ~ hBOOL(hAPP(U_1508,bool,hAPP(U_1508,fun(U_1508,bool),ord_less_eq(U_1508),U_1511),U_1509)) ) )
      | ~ order(U_1508) ),
    inference(miniscope,[status(thm)],[f_402_2]) ).

fof(f_402_4,plain,
    ( ! [U_1510,U_1508,U_1512] :
        ( ti(U_1508,U_1512) != ti(U_1508,U_1510)
        | ~ sP78(U_1510,U_1508,U_1512) )
    & ! [U_1510,U_1508,U_1512] :
        ( ~ hBOOL(hAPP(U_1508,bool,hAPP(U_1508,fun(U_1508,bool),ord_less(U_1508),U_1512),U_1510))
        | ~ sP78(U_1510,U_1508,U_1512) )
    & ! [U_1509,U_1510,U_1508,U_1511,U_1512] :
        ( hBOOL(hAPP(U_1508,bool,hAPP(U_1508,fun(U_1508,bool),ord_less_eq(U_1508),U_1512),U_1510))
        | sP78(U_1510,U_1508,U_1512)
        | ~ sP79(U_1509,U_1510,U_1508,U_1511,U_1512) )
    & ! [U_1509,U_1510,U_1508,U_1511,U_1512] :
        ( ti(U_1508,U_1511) = ti(U_1508,U_1509)
        | hBOOL(hAPP(U_1508,bool,hAPP(U_1508,fun(U_1508,bool),ord_less(U_1508),U_1511),U_1509))
        | ~ hBOOL(hAPP(U_1508,bool,hAPP(U_1508,fun(U_1508,bool),ord_less_eq(U_1508),U_1511),U_1509))
        | ~ sP79(U_1509,U_1510,U_1508,U_1511,U_1512) )
    & ! [U_1509,U_1510,U_1508,U_1511,U_1512] :
        ( sP79(U_1509,U_1510,U_1508,U_1511,U_1512)
        | ~ order(U_1508) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP78,sP79])],[f_402_3]) ).

cnf(f_402_5,plain,
    ( sP79(U_1509,U_1510,U_1508,U_1511,U_1512)
    | ~ order(U_1508) ),
    inference(clausify,[status(thm)],[f_402_4]) ).

cnf(f_402_6,plain,
    ( ti(U_1508,U_1511) = ti(U_1508,U_1509)
    | hBOOL(hAPP(U_1508,bool,hAPP(U_1508,fun(U_1508,bool),ord_less(U_1508),U_1511),U_1509))
    | ~ hBOOL(hAPP(U_1508,bool,hAPP(U_1508,fun(U_1508,bool),ord_less_eq(U_1508),U_1511),U_1509))
    | ~ sP79(U_1509,U_1510,U_1508,U_1511,U_1512) ),
    inference(clausify,[status(thm)],[f_402_4]) ).

cnf(f_402_7,plain,
    ( hBOOL(hAPP(U_1508,bool,hAPP(U_1508,fun(U_1508,bool),ord_less_eq(U_1508),U_1512),U_1510))
    | sP78(U_1510,U_1508,U_1512)
    | ~ sP79(U_1509,U_1510,U_1508,U_1511,U_1512) ),
    inference(clausify,[status(thm)],[f_402_4]) ).

cnf(f_402_8,plain,
    ( ~ hBOOL(hAPP(U_1508,bool,hAPP(U_1508,fun(U_1508,bool),ord_less(U_1508),U_1512),U_1510))
    | ~ sP78(U_1510,U_1508,U_1512) ),
    inference(clausify,[status(thm)],[f_402_4]) ).

cnf(f_402_9,plain,
    ( ti(U_1508,U_1512) != ti(U_1508,U_1510)
    | ~ sP78(U_1510,U_1508,U_1512) ),
    inference(clausify,[status(thm)],[f_402_4]) ).

fof(f_403_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_332_leI]) ).

fof(f_403_2,plain,
    ! [U_1515] :
      ( ! [U_1514,U_1513] :
          ( hBOOL(hAPP(U_1515,bool,hAPP(U_1515,fun(U_1515,bool),ord_less_eq(U_1515),U_1513),U_1514))
          | hBOOL(hAPP(U_1515,bool,hAPP(U_1515,fun(U_1515,bool),ord_less(U_1515),U_1514),U_1513)) )
      | ~ linorder(U_1515) ),
    inference(variable_rename,[status(thm)],[f_403_1]) ).

fof(f_403_3,plain,
    ! [U_1514,U_1515,U_1513] :
      ( hBOOL(hAPP(U_1515,bool,hAPP(U_1515,fun(U_1515,bool),ord_less_eq(U_1515),U_1513),U_1514))
      | hBOOL(hAPP(U_1515,bool,hAPP(U_1515,fun(U_1515,bool),ord_less(U_1515),U_1514),U_1513))
      | ~ linorder(U_1515) ),
    inference(definitional_conversion,[status(esa)],[f_403_2]) ).

cnf(f_403_4,plain,
    ( hBOOL(hAPP(U_1515,bool,hAPP(U_1515,fun(U_1515,bool),ord_less_eq(U_1515),U_1513),U_1514))
    | hBOOL(hAPP(U_1515,bool,hAPP(U_1515,fun(U_1515,bool),ord_less(U_1515),U_1514),U_1513))
    | ~ linorder(U_1515) ),
    inference(clausify,[status(thm)],[f_403_3]) ).

fof(f_404_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_333_not__leE]) ).

fof(f_404_2,plain,
    ! [U_1518] :
      ( ! [U_1517,U_1516] :
          ( hBOOL(hAPP(U_1518,bool,hAPP(U_1518,fun(U_1518,bool),ord_less(U_1518),U_1516),U_1517))
          | hBOOL(hAPP(U_1518,bool,hAPP(U_1518,fun(U_1518,bool),ord_less_eq(U_1518),U_1517),U_1516)) )
      | ~ linorder(U_1518) ),
    inference(variable_rename,[status(thm)],[f_404_1]) ).

fof(f_404_3,plain,
    ! [U_1517,U_1516,U_1518] :
      ( hBOOL(hAPP(U_1518,bool,hAPP(U_1518,fun(U_1518,bool),ord_less(U_1518),U_1516),U_1517))
      | hBOOL(hAPP(U_1518,bool,hAPP(U_1518,fun(U_1518,bool),ord_less_eq(U_1518),U_1517),U_1516))
      | ~ linorder(U_1518) ),
    inference(definitional_conversion,[status(esa)],[f_404_2]) ).

cnf(f_404_4,plain,
    ( hBOOL(hAPP(U_1518,bool,hAPP(U_1518,fun(U_1518,bool),ord_less(U_1518),U_1516),U_1517))
    | hBOOL(hAPP(U_1518,bool,hAPP(U_1518,fun(U_1518,bool),ord_less_eq(U_1518),U_1517),U_1516))
    | ~ linorder(U_1518) ),
    inference(clausify,[status(thm)],[f_404_3]) ).

fof(f_405_1,plain,
    ! [X_b] :
      ( ! [X_1,Y_2] :
          ( ( ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2))
              | ti(X_b,X_1) != ti(X_b,Y_2) )
            & ( ti(X_b,X_1) = ti(X_b,Y_2)
              | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2)) ) )
          | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2)) )
      | ~ linorder(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_334_linorder__antisym__conv1]) ).

fof(f_405_2,plain,
    ! [U_1521] :
      ( ! [U_1520,U_1519] :
          ( ( ( hBOOL(hAPP(U_1521,bool,hAPP(U_1521,fun(U_1521,bool),ord_less_eq(U_1521),U_1520),U_1519))
              | ti(U_1521,U_1520) != ti(U_1521,U_1519) )
            & ( ti(U_1521,U_1520) = ti(U_1521,U_1519)
              | ~ hBOOL(hAPP(U_1521,bool,hAPP(U_1521,fun(U_1521,bool),ord_less_eq(U_1521),U_1520),U_1519)) ) )
          | hBOOL(hAPP(U_1521,bool,hAPP(U_1521,fun(U_1521,bool),ord_less(U_1521),U_1520),U_1519)) )
      | ~ linorder(U_1521) ),
    inference(variable_rename,[status(thm)],[f_405_1]) ).

fof(f_405_3,plain,
    ( ! [U_1519,U_1520,U_1521] :
        ( hBOOL(hAPP(U_1521,bool,hAPP(U_1521,fun(U_1521,bool),ord_less_eq(U_1521),U_1520),U_1519))
        | ti(U_1521,U_1520) != ti(U_1521,U_1519)
        | ~ sP80(U_1519,U_1520,U_1521) )
    & ! [U_1519,U_1520,U_1521] :
        ( ti(U_1521,U_1520) = ti(U_1521,U_1519)
        | ~ hBOOL(hAPP(U_1521,bool,hAPP(U_1521,fun(U_1521,bool),ord_less_eq(U_1521),U_1520),U_1519))
        | ~ sP80(U_1519,U_1520,U_1521) )
    & ! [U_1519,U_1520,U_1521] :
        ( sP80(U_1519,U_1520,U_1521)
        | hBOOL(hAPP(U_1521,bool,hAPP(U_1521,fun(U_1521,bool),ord_less(U_1521),U_1520),U_1519))
        | ~ linorder(U_1521) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP80])],[f_405_2]) ).

cnf(f_405_4,plain,
    ( sP80(U_1519,U_1520,U_1521)
    | hBOOL(hAPP(U_1521,bool,hAPP(U_1521,fun(U_1521,bool),ord_less(U_1521),U_1520),U_1519))
    | ~ linorder(U_1521) ),
    inference(clausify,[status(thm)],[f_405_3]) ).

cnf(f_405_5,plain,
    ( ti(U_1521,U_1520) = ti(U_1521,U_1519)
    | ~ hBOOL(hAPP(U_1521,bool,hAPP(U_1521,fun(U_1521,bool),ord_less_eq(U_1521),U_1520),U_1519))
    | ~ sP80(U_1519,U_1520,U_1521) ),
    inference(clausify,[status(thm)],[f_405_3]) ).

cnf(f_405_6,plain,
    ( hBOOL(hAPP(U_1521,bool,hAPP(U_1521,fun(U_1521,bool),ord_less_eq(U_1521),U_1520),U_1519))
    | ti(U_1521,U_1520) != ti(U_1521,U_1519)
    | ~ sP80(U_1519,U_1520,U_1521) ),
    inference(clausify,[status(thm)],[f_405_3]) ).

fof(f_406_1,plain,
    ! [X_a] :
      ( ! [A_1,B] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B))
          | ti(X_a,A_1) = ti(X_a,B) )
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_335_order__neq__le__trans]) ).

fof(f_406_2,plain,
    ! [U_1524] :
      ( ! [U_1523,U_1522] :
          ( hBOOL(hAPP(U_1524,bool,hAPP(U_1524,fun(U_1524,bool),ord_less(U_1524),U_1523),U_1522))
          | ~ hBOOL(hAPP(U_1524,bool,hAPP(U_1524,fun(U_1524,bool),ord_less_eq(U_1524),U_1523),U_1522))
          | ti(U_1524,U_1523) = ti(U_1524,U_1522) )
      | ~ order(U_1524) ),
    inference(variable_rename,[status(thm)],[f_406_1]) ).

fof(f_406_3,plain,
    ! [U_1522,U_1523,U_1524] :
      ( hBOOL(hAPP(U_1524,bool,hAPP(U_1524,fun(U_1524,bool),ord_less(U_1524),U_1523),U_1522))
      | ~ hBOOL(hAPP(U_1524,bool,hAPP(U_1524,fun(U_1524,bool),ord_less_eq(U_1524),U_1523),U_1522))
      | ti(U_1524,U_1523) = ti(U_1524,U_1522)
      | ~ order(U_1524) ),
    inference(definitional_conversion,[status(esa)],[f_406_2]) ).

cnf(f_406_4,plain,
    ( hBOOL(hAPP(U_1524,bool,hAPP(U_1524,fun(U_1524,bool),ord_less(U_1524),U_1523),U_1522))
    | ~ hBOOL(hAPP(U_1524,bool,hAPP(U_1524,fun(U_1524,bool),ord_less_eq(U_1524),U_1523),U_1522))
    | ti(U_1524,U_1523) = ti(U_1524,U_1522)
    | ~ order(U_1524) ),
    inference(clausify,[status(thm)],[f_406_3]) ).

fof(f_407_1,plain,
    ! [X_a] :
      ( ! [A_1,B] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1))
          | ti(X_a,A_1) = ti(X_a,B) )
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_336_xt1_I12_J]) ).

fof(f_407_2,plain,
    ! [U_1527] :
      ( ! [U_1526,U_1525] :
          ( hBOOL(hAPP(U_1527,bool,hAPP(U_1527,fun(U_1527,bool),ord_less(U_1527),U_1525),U_1526))
          | ~ hBOOL(hAPP(U_1527,bool,hAPP(U_1527,fun(U_1527,bool),ord_less_eq(U_1527),U_1525),U_1526))
          | ti(U_1527,U_1526) = ti(U_1527,U_1525) )
      | ~ order(U_1527) ),
    inference(variable_rename,[status(thm)],[f_407_1]) ).

fof(f_407_3,plain,
    ! [U_1526,U_1525,U_1527] :
      ( hBOOL(hAPP(U_1527,bool,hAPP(U_1527,fun(U_1527,bool),ord_less(U_1527),U_1525),U_1526))
      | ~ hBOOL(hAPP(U_1527,bool,hAPP(U_1527,fun(U_1527,bool),ord_less_eq(U_1527),U_1525),U_1526))
      | ti(U_1527,U_1526) = ti(U_1527,U_1525)
      | ~ order(U_1527) ),
    inference(definitional_conversion,[status(esa)],[f_407_2]) ).

cnf(f_407_4,plain,
    ( hBOOL(hAPP(U_1527,bool,hAPP(U_1527,fun(U_1527,bool),ord_less(U_1527),U_1525),U_1526))
    | ~ hBOOL(hAPP(U_1527,bool,hAPP(U_1527,fun(U_1527,bool),ord_less_eq(U_1527),U_1525),U_1526))
    | ti(U_1527,U_1526) = ti(U_1527,U_1525)
    | ~ order(U_1527) ),
    inference(clausify,[status(thm)],[f_407_3]) ).

fof(f_408_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_337_leD]) ).

fof(f_408_2,plain,
    ! [U_1530] :
      ( ! [U_1529,U_1528] :
          ( ~ hBOOL(hAPP(U_1530,bool,hAPP(U_1530,fun(U_1530,bool),ord_less(U_1530),U_1528),U_1529))
          | ~ hBOOL(hAPP(U_1530,bool,hAPP(U_1530,fun(U_1530,bool),ord_less_eq(U_1530),U_1529),U_1528)) )
      | ~ linorder(U_1530) ),
    inference(variable_rename,[status(thm)],[f_408_1]) ).

fof(f_408_3,plain,
    ! [U_1528,U_1530,U_1529] :
      ( ~ hBOOL(hAPP(U_1530,bool,hAPP(U_1530,fun(U_1530,bool),ord_less(U_1530),U_1528),U_1529))
      | ~ hBOOL(hAPP(U_1530,bool,hAPP(U_1530,fun(U_1530,bool),ord_less_eq(U_1530),U_1529),U_1528))
      | ~ linorder(U_1530) ),
    inference(definitional_conversion,[status(esa)],[f_408_2]) ).

cnf(f_408_4,plain,
    ( ~ hBOOL(hAPP(U_1530,bool,hAPP(U_1530,fun(U_1530,bool),ord_less(U_1530),U_1528),U_1529))
    | ~ hBOOL(hAPP(U_1530,bool,hAPP(U_1530,fun(U_1530,bool),ord_less_eq(U_1530),U_1529),U_1528))
    | ~ linorder(U_1530) ),
    inference(clausify,[status(thm)],[f_408_3]) ).

fof(f_409_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_338_order__less__imp__le]) ).

fof(f_409_2,plain,
    ! [U_1533] :
      ( ! [U_1532,U_1531] :
          ( hBOOL(hAPP(U_1533,bool,hAPP(U_1533,fun(U_1533,bool),ord_less_eq(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_1531)) )
      | ~ preorder(U_1533) ),
    inference(variable_rename,[status(thm)],[f_409_1]) ).

fof(f_409_3,plain,
    ! [U_1533,U_1531,U_1532] :
      ( hBOOL(hAPP(U_1533,bool,hAPP(U_1533,fun(U_1533,bool),ord_less_eq(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_1531))
      | ~ preorder(U_1533) ),
    inference(definitional_conversion,[status(esa)],[f_409_2]) ).

cnf(f_409_4,plain,
    ( hBOOL(hAPP(U_1533,bool,hAPP(U_1533,fun(U_1533,bool),ord_less_eq(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_1531))
    | ~ preorder(U_1533) ),
    inference(clausify,[status(thm)],[f_409_3]) ).

fof(f_410_1,plain,
    ! [X_b] :
      ( ! [X_1,Y_2] :
          ( ( ( ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2))
              | ti(X_b,X_1) != ti(X_b,Y_2) )
            & ( ti(X_b,X_1) = ti(X_b,Y_2)
              | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2)) ) )
          | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2)) )
      | ~ linorder(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_339_linorder__antisym__conv2]) ).

fof(f_410_2,plain,
    ! [U_1536] :
      ( ! [U_1535,U_1534] :
          ( ( ( ~ hBOOL(hAPP(U_1536,bool,hAPP(U_1536,fun(U_1536,bool),ord_less(U_1536),U_1535),U_1534))
              | ti(U_1536,U_1535) != ti(U_1536,U_1534) )
            & ( ti(U_1536,U_1535) = ti(U_1536,U_1534)
              | hBOOL(hAPP(U_1536,bool,hAPP(U_1536,fun(U_1536,bool),ord_less(U_1536),U_1535),U_1534)) ) )
          | ~ hBOOL(hAPP(U_1536,bool,hAPP(U_1536,fun(U_1536,bool),ord_less_eq(U_1536),U_1535),U_1534)) )
      | ~ linorder(U_1536) ),
    inference(variable_rename,[status(thm)],[f_410_1]) ).

fof(f_410_3,plain,
    ( ! [U_1534,U_1535,U_1536] :
        ( ~ hBOOL(hAPP(U_1536,bool,hAPP(U_1536,fun(U_1536,bool),ord_less(U_1536),U_1535),U_1534))
        | ti(U_1536,U_1535) != ti(U_1536,U_1534)
        | ~ sP81(U_1534,U_1535,U_1536) )
    & ! [U_1534,U_1535,U_1536] :
        ( ti(U_1536,U_1535) = ti(U_1536,U_1534)
        | hBOOL(hAPP(U_1536,bool,hAPP(U_1536,fun(U_1536,bool),ord_less(U_1536),U_1535),U_1534))
        | ~ sP81(U_1534,U_1535,U_1536) )
    & ! [U_1534,U_1535,U_1536] :
        ( sP81(U_1534,U_1535,U_1536)
        | ~ hBOOL(hAPP(U_1536,bool,hAPP(U_1536,fun(U_1536,bool),ord_less_eq(U_1536),U_1535),U_1534))
        | ~ linorder(U_1536) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP81])],[f_410_2]) ).

cnf(f_410_4,plain,
    ( sP81(U_1534,U_1535,U_1536)
    | ~ hBOOL(hAPP(U_1536,bool,hAPP(U_1536,fun(U_1536,bool),ord_less_eq(U_1536),U_1535),U_1534))
    | ~ linorder(U_1536) ),
    inference(clausify,[status(thm)],[f_410_3]) ).

cnf(f_410_5,plain,
    ( ti(U_1536,U_1535) = ti(U_1536,U_1534)
    | hBOOL(hAPP(U_1536,bool,hAPP(U_1536,fun(U_1536,bool),ord_less(U_1536),U_1535),U_1534))
    | ~ sP81(U_1534,U_1535,U_1536) ),
    inference(clausify,[status(thm)],[f_410_3]) ).

cnf(f_410_6,plain,
    ( ~ hBOOL(hAPP(U_1536,bool,hAPP(U_1536,fun(U_1536,bool),ord_less(U_1536),U_1535),U_1534))
    | ti(U_1536,U_1535) != ti(U_1536,U_1534)
    | ~ sP81(U_1534,U_1535,U_1536) ),
    inference(clausify,[status(thm)],[f_410_3]) ).

fof(f_411_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_340_order__le__imp__less__or__eq]) ).

fof(f_411_2,plain,
    ! [U_1539] :
      ( ! [U_1538,U_1537] :
          ( ti(U_1539,U_1538) = ti(U_1539,U_1537)
          | hBOOL(hAPP(U_1539,bool,hAPP(U_1539,fun(U_1539,bool),ord_less(U_1539),U_1538),U_1537))
          | ~ hBOOL(hAPP(U_1539,bool,hAPP(U_1539,fun(U_1539,bool),ord_less_eq(U_1539),U_1538),U_1537)) )
      | ~ order(U_1539) ),
    inference(variable_rename,[status(thm)],[f_411_1]) ).

fof(f_411_3,plain,
    ! [U_1538,U_1537,U_1539] :
      ( ti(U_1539,U_1538) = ti(U_1539,U_1537)
      | hBOOL(hAPP(U_1539,bool,hAPP(U_1539,fun(U_1539,bool),ord_less(U_1539),U_1538),U_1537))
      | ~ hBOOL(hAPP(U_1539,bool,hAPP(U_1539,fun(U_1539,bool),ord_less_eq(U_1539),U_1538),U_1537))
      | ~ order(U_1539) ),
    inference(definitional_conversion,[status(esa)],[f_411_2]) ).

cnf(f_411_4,plain,
    ( ti(U_1539,U_1538) = ti(U_1539,U_1537)
    | hBOOL(hAPP(U_1539,bool,hAPP(U_1539,fun(U_1539,bool),ord_less(U_1539),U_1538),U_1537))
    | ~ hBOOL(hAPP(U_1539,bool,hAPP(U_1539,fun(U_1539,bool),ord_less_eq(U_1539),U_1538),U_1537))
    | ~ order(U_1539) ),
    inference(clausify,[status(thm)],[f_411_3]) ).

fof(f_412_1,plain,
    ! [X_a] :
      ( ! [A_1,B] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))
          | ti(X_a,A_1) = ti(X_a,B)
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) )
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_341_order__le__neq__trans]) ).

fof(f_412_2,plain,
    ! [U_1542] :
      ( ! [U_1541,U_1540] :
          ( hBOOL(hAPP(U_1542,bool,hAPP(U_1542,fun(U_1542,bool),ord_less(U_1542),U_1541),U_1540))
          | ti(U_1542,U_1541) = ti(U_1542,U_1540)
          | ~ hBOOL(hAPP(U_1542,bool,hAPP(U_1542,fun(U_1542,bool),ord_less_eq(U_1542),U_1541),U_1540)) )
      | ~ order(U_1542) ),
    inference(variable_rename,[status(thm)],[f_412_1]) ).

fof(f_412_3,plain,
    ! [U_1542,U_1541,U_1540] :
      ( hBOOL(hAPP(U_1542,bool,hAPP(U_1542,fun(U_1542,bool),ord_less(U_1542),U_1541),U_1540))
      | ti(U_1542,U_1541) = ti(U_1542,U_1540)
      | ~ hBOOL(hAPP(U_1542,bool,hAPP(U_1542,fun(U_1542,bool),ord_less_eq(U_1542),U_1541),U_1540))
      | ~ order(U_1542) ),
    inference(definitional_conversion,[status(esa)],[f_412_2]) ).

cnf(f_412_4,plain,
    ( hBOOL(hAPP(U_1542,bool,hAPP(U_1542,fun(U_1542,bool),ord_less(U_1542),U_1541),U_1540))
    | ti(U_1542,U_1541) = ti(U_1542,U_1540)
    | ~ hBOOL(hAPP(U_1542,bool,hAPP(U_1542,fun(U_1542,bool),ord_less_eq(U_1542),U_1541),U_1540))
    | ~ order(U_1542) ),
    inference(clausify,[status(thm)],[f_412_3]) ).

fof(f_413_1,plain,
    ! [X_a] :
      ( ! [B,A_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1))
          | ti(X_a,A_1) = ti(X_a,B)
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1)) )
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_342_xt1_I11_J]) ).

fof(f_413_2,plain,
    ! [U_1545] :
      ( ! [U_1544,U_1543] :
          ( hBOOL(hAPP(U_1545,bool,hAPP(U_1545,fun(U_1545,bool),ord_less(U_1545),U_1544),U_1543))
          | ti(U_1545,U_1543) = ti(U_1545,U_1544)
          | ~ hBOOL(hAPP(U_1545,bool,hAPP(U_1545,fun(U_1545,bool),ord_less_eq(U_1545),U_1544),U_1543)) )
      | ~ order(U_1545) ),
    inference(variable_rename,[status(thm)],[f_413_1]) ).

fof(f_413_3,plain,
    ! [U_1544,U_1543,U_1545] :
      ( hBOOL(hAPP(U_1545,bool,hAPP(U_1545,fun(U_1545,bool),ord_less(U_1545),U_1544),U_1543))
      | ti(U_1545,U_1543) = ti(U_1545,U_1544)
      | ~ hBOOL(hAPP(U_1545,bool,hAPP(U_1545,fun(U_1545,bool),ord_less_eq(U_1545),U_1544),U_1543))
      | ~ order(U_1545) ),
    inference(definitional_conversion,[status(esa)],[f_413_2]) ).

cnf(f_413_4,plain,
    ( hBOOL(hAPP(U_1545,bool,hAPP(U_1545,fun(U_1545,bool),ord_less(U_1545),U_1544),U_1543))
    | ti(U_1545,U_1543) = ti(U_1545,U_1544)
    | ~ hBOOL(hAPP(U_1545,bool,hAPP(U_1545,fun(U_1545,bool),ord_less_eq(U_1545),U_1544),U_1543))
    | ~ order(U_1545) ),
    inference(clausify,[status(thm)],[f_413_3]) ).

fof(f_414_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_343_order__less__le__trans]) ).

fof(f_414_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_1547),U_1548))
          | ~ hBOOL(hAPP(U_1549,bool,hAPP(U_1549,fun(U_1549,bool),ord_less_eq(U_1549),U_1546),U_1548))
          | ~ hBOOL(hAPP(U_1549,bool,hAPP(U_1549,fun(U_1549,bool),ord_less(U_1549),U_1547),U_1546)) )
      | ~ preorder(U_1549) ),
    inference(variable_rename,[status(thm)],[f_414_1]) ).

fof(f_414_3,plain,
    ! [U_1546,U_1548,U_1547,U_1549] :
      ( hBOOL(hAPP(U_1549,bool,hAPP(U_1549,fun(U_1549,bool),ord_less(U_1549),U_1547),U_1548))
      | ~ hBOOL(hAPP(U_1549,bool,hAPP(U_1549,fun(U_1549,bool),ord_less_eq(U_1549),U_1546),U_1548))
      | ~ hBOOL(hAPP(U_1549,bool,hAPP(U_1549,fun(U_1549,bool),ord_less(U_1549),U_1547),U_1546))
      | ~ preorder(U_1549) ),
    inference(definitional_conversion,[status(esa)],[f_414_2]) ).

cnf(f_414_4,plain,
    ( hBOOL(hAPP(U_1549,bool,hAPP(U_1549,fun(U_1549,bool),ord_less(U_1549),U_1547),U_1548))
    | ~ hBOOL(hAPP(U_1549,bool,hAPP(U_1549,fun(U_1549,bool),ord_less_eq(U_1549),U_1546),U_1548))
    | ~ hBOOL(hAPP(U_1549,bool,hAPP(U_1549,fun(U_1549,bool),ord_less(U_1549),U_1547),U_1546))
    | ~ preorder(U_1549) ),
    inference(clausify,[status(thm)],[f_414_3]) ).

fof(f_415_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_344_xt1_I7_J]) ).

fof(f_415_2,plain,
    ! [U_1553] :
      ( ! [U_1552,U_1551,U_1550] :
          ( hBOOL(hAPP(U_1553,bool,hAPP(U_1553,fun(U_1553,bool),ord_less(U_1553),U_1552),U_1550))
          | ~ hBOOL(hAPP(U_1553,bool,hAPP(U_1553,fun(U_1553,bool),ord_less_eq(U_1553),U_1552),U_1551))
          | ~ hBOOL(hAPP(U_1553,bool,hAPP(U_1553,fun(U_1553,bool),ord_less(U_1553),U_1551),U_1550)) )
      | ~ order(U_1553) ),
    inference(variable_rename,[status(thm)],[f_415_1]) ).

fof(f_415_3,plain,
    ! [U_1552,U_1553,U_1550,U_1551] :
      ( hBOOL(hAPP(U_1553,bool,hAPP(U_1553,fun(U_1553,bool),ord_less(U_1553),U_1552),U_1550))
      | ~ hBOOL(hAPP(U_1553,bool,hAPP(U_1553,fun(U_1553,bool),ord_less_eq(U_1553),U_1552),U_1551))
      | ~ hBOOL(hAPP(U_1553,bool,hAPP(U_1553,fun(U_1553,bool),ord_less(U_1553),U_1551),U_1550))
      | ~ order(U_1553) ),
    inference(definitional_conversion,[status(esa)],[f_415_2]) ).

cnf(f_415_4,plain,
    ( hBOOL(hAPP(U_1553,bool,hAPP(U_1553,fun(U_1553,bool),ord_less(U_1553),U_1552),U_1550))
    | ~ hBOOL(hAPP(U_1553,bool,hAPP(U_1553,fun(U_1553,bool),ord_less_eq(U_1553),U_1552),U_1551))
    | ~ hBOOL(hAPP(U_1553,bool,hAPP(U_1553,fun(U_1553,bool),ord_less(U_1553),U_1551),U_1550))
    | ~ order(U_1553) ),
    inference(clausify,[status(thm)],[f_415_3]) ).

fof(f_416_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_345_order__le__less__trans]) ).

fof(f_416_2,plain,
    ! [U_1557] :
      ( ! [U_1556,U_1555,U_1554] :
          ( hBOOL(hAPP(U_1557,bool,hAPP(U_1557,fun(U_1557,bool),ord_less(U_1557),U_1555),U_1556))
          | ~ hBOOL(hAPP(U_1557,bool,hAPP(U_1557,fun(U_1557,bool),ord_less(U_1557),U_1554),U_1556))
          | ~ hBOOL(hAPP(U_1557,bool,hAPP(U_1557,fun(U_1557,bool),ord_less_eq(U_1557),U_1555),U_1554)) )
      | ~ preorder(U_1557) ),
    inference(variable_rename,[status(thm)],[f_416_1]) ).

fof(f_416_3,plain,
    ! [U_1557,U_1555,U_1554,U_1556] :
      ( hBOOL(hAPP(U_1557,bool,hAPP(U_1557,fun(U_1557,bool),ord_less(U_1557),U_1555),U_1556))
      | ~ hBOOL(hAPP(U_1557,bool,hAPP(U_1557,fun(U_1557,bool),ord_less(U_1557),U_1554),U_1556))
      | ~ hBOOL(hAPP(U_1557,bool,hAPP(U_1557,fun(U_1557,bool),ord_less_eq(U_1557),U_1555),U_1554))
      | ~ preorder(U_1557) ),
    inference(definitional_conversion,[status(esa)],[f_416_2]) ).

cnf(f_416_4,plain,
    ( hBOOL(hAPP(U_1557,bool,hAPP(U_1557,fun(U_1557,bool),ord_less(U_1557),U_1555),U_1556))
    | ~ hBOOL(hAPP(U_1557,bool,hAPP(U_1557,fun(U_1557,bool),ord_less(U_1557),U_1554),U_1556))
    | ~ hBOOL(hAPP(U_1557,bool,hAPP(U_1557,fun(U_1557,bool),ord_less_eq(U_1557),U_1555),U_1554))
    | ~ preorder(U_1557) ),
    inference(clausify,[status(thm)],[f_416_3]) ).

fof(f_417_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_346_xt1_I8_J]) ).

fof(f_417_2,plain,
    ! [U_1561] :
      ( ! [U_1560,U_1559,U_1558] :
          ( hBOOL(hAPP(U_1561,bool,hAPP(U_1561,fun(U_1561,bool),ord_less(U_1561),U_1560),U_1558))
          | ~ hBOOL(hAPP(U_1561,bool,hAPP(U_1561,fun(U_1561,bool),ord_less(U_1561),U_1560),U_1559))
          | ~ hBOOL(hAPP(U_1561,bool,hAPP(U_1561,fun(U_1561,bool),ord_less_eq(U_1561),U_1559),U_1558)) )
      | ~ order(U_1561) ),
    inference(variable_rename,[status(thm)],[f_417_1]) ).

fof(f_417_3,plain,
    ! [U_1558,U_1561,U_1560,U_1559] :
      ( hBOOL(hAPP(U_1561,bool,hAPP(U_1561,fun(U_1561,bool),ord_less(U_1561),U_1560),U_1558))
      | ~ hBOOL(hAPP(U_1561,bool,hAPP(U_1561,fun(U_1561,bool),ord_less(U_1561),U_1560),U_1559))
      | ~ hBOOL(hAPP(U_1561,bool,hAPP(U_1561,fun(U_1561,bool),ord_less_eq(U_1561),U_1559),U_1558))
      | ~ order(U_1561) ),
    inference(definitional_conversion,[status(esa)],[f_417_2]) ).

cnf(f_417_4,plain,
    ( hBOOL(hAPP(U_1561,bool,hAPP(U_1561,fun(U_1561,bool),ord_less(U_1561),U_1560),U_1558))
    | ~ hBOOL(hAPP(U_1561,bool,hAPP(U_1561,fun(U_1561,bool),ord_less(U_1561),U_1560),U_1559))
    | ~ hBOOL(hAPP(U_1561,bool,hAPP(U_1561,fun(U_1561,bool),ord_less_eq(U_1561),U_1559),U_1558))
    | ~ order(U_1561) ),
    inference(clausify,[status(thm)],[f_417_3]) ).

fof(f_418_1,plain,
    ! [X_b] :
      ( ! [A_2,C_1,B_3] :
          ( ( 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_3),C_1)))
            | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_3)) )
          & ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_3))
            | ~ 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_3),C_1))) ) )
      | ~ ordere236663937imp_le(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_347_add__less__cancel__right]) ).

fof(f_418_2,plain,
    ! [U_1565] :
      ( ! [U_1564,U_1563,U_1562] :
          ( ( hBOOL(hAPP(U_1565,bool,hAPP(U_1565,fun(U_1565,bool),ord_less(U_1565),hAPP(U_1565,U_1565,hAPP(U_1565,fun(U_1565,U_1565),plus_plus(U_1565),U_1564),U_1563)),hAPP(U_1565,U_1565,hAPP(U_1565,fun(U_1565,U_1565),plus_plus(U_1565),U_1562),U_1563)))
            | ~ hBOOL(hAPP(U_1565,bool,hAPP(U_1565,fun(U_1565,bool),ord_less(U_1565),U_1564),U_1562)) )
          & ( hBOOL(hAPP(U_1565,bool,hAPP(U_1565,fun(U_1565,bool),ord_less(U_1565),U_1564),U_1562))
            | ~ hBOOL(hAPP(U_1565,bool,hAPP(U_1565,fun(U_1565,bool),ord_less(U_1565),hAPP(U_1565,U_1565,hAPP(U_1565,fun(U_1565,U_1565),plus_plus(U_1565),U_1564),U_1563)),hAPP(U_1565,U_1565,hAPP(U_1565,fun(U_1565,U_1565),plus_plus(U_1565),U_1562),U_1563))) ) )
      | ~ ordere236663937imp_le(U_1565) ),
    inference(variable_rename,[status(thm)],[f_418_1]) ).

fof(f_418_3,plain,
    ! [U_1565] :
      ( ( ! [U_1571,U_1569,U_1567] :
            ( hBOOL(hAPP(U_1565,bool,hAPP(U_1565,fun(U_1565,bool),ord_less(U_1565),hAPP(U_1565,U_1565,hAPP(U_1565,fun(U_1565,U_1565),plus_plus(U_1565),U_1571),U_1569)),hAPP(U_1565,U_1565,hAPP(U_1565,fun(U_1565,U_1565),plus_plus(U_1565),U_1567),U_1569)))
            | ~ hBOOL(hAPP(U_1565,bool,hAPP(U_1565,fun(U_1565,bool),ord_less(U_1565),U_1571),U_1567)) )
        & ! [U_1570,U_1568,U_1566] :
            ( hBOOL(hAPP(U_1565,bool,hAPP(U_1565,fun(U_1565,bool),ord_less(U_1565),U_1570),U_1566))
            | ~ hBOOL(hAPP(U_1565,bool,hAPP(U_1565,fun(U_1565,bool),ord_less(U_1565),hAPP(U_1565,U_1565,hAPP(U_1565,fun(U_1565,U_1565),plus_plus(U_1565),U_1570),U_1568)),hAPP(U_1565,U_1565,hAPP(U_1565,fun(U_1565,U_1565),plus_plus(U_1565),U_1566),U_1568))) ) )
      | ~ ordere236663937imp_le(U_1565) ),
    inference(miniscope,[status(thm)],[f_418_2]) ).

fof(f_418_4,plain,
    ( ! [U_1568,U_1565,U_1566,U_1567,U_1570,U_1571,U_1569] :
        ( hBOOL(hAPP(U_1565,bool,hAPP(U_1565,fun(U_1565,bool),ord_less(U_1565),hAPP(U_1565,U_1565,hAPP(U_1565,fun(U_1565,U_1565),plus_plus(U_1565),U_1571),U_1569)),hAPP(U_1565,U_1565,hAPP(U_1565,fun(U_1565,U_1565),plus_plus(U_1565),U_1567),U_1569)))
        | ~ hBOOL(hAPP(U_1565,bool,hAPP(U_1565,fun(U_1565,bool),ord_less(U_1565),U_1571),U_1567))
        | ~ sP82(U_1568,U_1565,U_1566,U_1567,U_1570,U_1571,U_1569) )
    & ! [U_1568,U_1565,U_1566,U_1567,U_1570,U_1571,U_1569] :
        ( hBOOL(hAPP(U_1565,bool,hAPP(U_1565,fun(U_1565,bool),ord_less(U_1565),U_1570),U_1566))
        | ~ hBOOL(hAPP(U_1565,bool,hAPP(U_1565,fun(U_1565,bool),ord_less(U_1565),hAPP(U_1565,U_1565,hAPP(U_1565,fun(U_1565,U_1565),plus_plus(U_1565),U_1570),U_1568)),hAPP(U_1565,U_1565,hAPP(U_1565,fun(U_1565,U_1565),plus_plus(U_1565),U_1566),U_1568)))
        | ~ sP82(U_1568,U_1565,U_1566,U_1567,U_1570,U_1571,U_1569) )
    & ! [U_1568,U_1565,U_1566,U_1567,U_1570,U_1571,U_1569] :
        ( sP82(U_1568,U_1565,U_1566,U_1567,U_1570,U_1571,U_1569)
        | ~ ordere236663937imp_le(U_1565) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP82])],[f_418_3]) ).

cnf(f_418_5,plain,
    ( sP82(U_1568,U_1565,U_1566,U_1567,U_1570,U_1571,U_1569)
    | ~ ordere236663937imp_le(U_1565) ),
    inference(clausify,[status(thm)],[f_418_4]) ).

cnf(f_418_6,plain,
    ( hBOOL(hAPP(U_1565,bool,hAPP(U_1565,fun(U_1565,bool),ord_less(U_1565),U_1570),U_1566))
    | ~ hBOOL(hAPP(U_1565,bool,hAPP(U_1565,fun(U_1565,bool),ord_less(U_1565),hAPP(U_1565,U_1565,hAPP(U_1565,fun(U_1565,U_1565),plus_plus(U_1565),U_1570),U_1568)),hAPP(U_1565,U_1565,hAPP(U_1565,fun(U_1565,U_1565),plus_plus(U_1565),U_1566),U_1568)))
    | ~ sP82(U_1568,U_1565,U_1566,U_1567,U_1570,U_1571,U_1569) ),
    inference(clausify,[status(thm)],[f_418_4]) ).

cnf(f_418_7,plain,
    ( hBOOL(hAPP(U_1565,bool,hAPP(U_1565,fun(U_1565,bool),ord_less(U_1565),hAPP(U_1565,U_1565,hAPP(U_1565,fun(U_1565,U_1565),plus_plus(U_1565),U_1571),U_1569)),hAPP(U_1565,U_1565,hAPP(U_1565,fun(U_1565,U_1565),plus_plus(U_1565),U_1567),U_1569)))
    | ~ hBOOL(hAPP(U_1565,bool,hAPP(U_1565,fun(U_1565,bool),ord_less(U_1565),U_1571),U_1567))
    | ~ sP82(U_1568,U_1565,U_1566,U_1567,U_1570,U_1571,U_1569) ),
    inference(clausify,[status(thm)],[f_418_4]) ).

fof(f_419_1,plain,
    ! [X_b] :
      ( ! [C_1,A_2,B_3] :
          ( ( 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_3)))
            | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_3)) )
          & ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_3))
            | ~ 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_3))) ) )
      | ~ ordere236663937imp_le(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_348_add__less__cancel__left]) ).

fof(f_419_2,plain,
    ! [U_1575] :
      ( ! [U_1574,U_1573,U_1572] :
          ( ( hBOOL(hAPP(U_1575,bool,hAPP(U_1575,fun(U_1575,bool),ord_less(U_1575),hAPP(U_1575,U_1575,hAPP(U_1575,fun(U_1575,U_1575),plus_plus(U_1575),U_1574),U_1573)),hAPP(U_1575,U_1575,hAPP(U_1575,fun(U_1575,U_1575),plus_plus(U_1575),U_1574),U_1572)))
            | ~ hBOOL(hAPP(U_1575,bool,hAPP(U_1575,fun(U_1575,bool),ord_less(U_1575),U_1573),U_1572)) )
          & ( hBOOL(hAPP(U_1575,bool,hAPP(U_1575,fun(U_1575,bool),ord_less(U_1575),U_1573),U_1572))
            | ~ hBOOL(hAPP(U_1575,bool,hAPP(U_1575,fun(U_1575,bool),ord_less(U_1575),hAPP(U_1575,U_1575,hAPP(U_1575,fun(U_1575,U_1575),plus_plus(U_1575),U_1574),U_1573)),hAPP(U_1575,U_1575,hAPP(U_1575,fun(U_1575,U_1575),plus_plus(U_1575),U_1574),U_1572))) ) )
      | ~ ordere236663937imp_le(U_1575) ),
    inference(variable_rename,[status(thm)],[f_419_1]) ).

fof(f_419_3,plain,
    ! [U_1575] :
      ( ( ! [U_1581,U_1579,U_1577] :
            ( hBOOL(hAPP(U_1575,bool,hAPP(U_1575,fun(U_1575,bool),ord_less(U_1575),hAPP(U_1575,U_1575,hAPP(U_1575,fun(U_1575,U_1575),plus_plus(U_1575),U_1581),U_1579)),hAPP(U_1575,U_1575,hAPP(U_1575,fun(U_1575,U_1575),plus_plus(U_1575),U_1581),U_1577)))
            | ~ hBOOL(hAPP(U_1575,bool,hAPP(U_1575,fun(U_1575,bool),ord_less(U_1575),U_1579),U_1577)) )
        & ! [U_1580,U_1578,U_1576] :
            ( hBOOL(hAPP(U_1575,bool,hAPP(U_1575,fun(U_1575,bool),ord_less(U_1575),U_1578),U_1576))
            | ~ hBOOL(hAPP(U_1575,bool,hAPP(U_1575,fun(U_1575,bool),ord_less(U_1575),hAPP(U_1575,U_1575,hAPP(U_1575,fun(U_1575,U_1575),plus_plus(U_1575),U_1580),U_1578)),hAPP(U_1575,U_1575,hAPP(U_1575,fun(U_1575,U_1575),plus_plus(U_1575),U_1580),U_1576))) ) )
      | ~ ordere236663937imp_le(U_1575) ),
    inference(miniscope,[status(thm)],[f_419_2]) ).

fof(f_419_4,plain,
    ( ! [U_1575,U_1576,U_1578,U_1577,U_1580,U_1579,U_1581] :
        ( hBOOL(hAPP(U_1575,bool,hAPP(U_1575,fun(U_1575,bool),ord_less(U_1575),hAPP(U_1575,U_1575,hAPP(U_1575,fun(U_1575,U_1575),plus_plus(U_1575),U_1581),U_1579)),hAPP(U_1575,U_1575,hAPP(U_1575,fun(U_1575,U_1575),plus_plus(U_1575),U_1581),U_1577)))
        | ~ hBOOL(hAPP(U_1575,bool,hAPP(U_1575,fun(U_1575,bool),ord_less(U_1575),U_1579),U_1577))
        | ~ sP83(U_1575,U_1576,U_1578,U_1577,U_1580,U_1579,U_1581) )
    & ! [U_1575,U_1576,U_1578,U_1577,U_1580,U_1579,U_1581] :
        ( hBOOL(hAPP(U_1575,bool,hAPP(U_1575,fun(U_1575,bool),ord_less(U_1575),U_1578),U_1576))
        | ~ hBOOL(hAPP(U_1575,bool,hAPP(U_1575,fun(U_1575,bool),ord_less(U_1575),hAPP(U_1575,U_1575,hAPP(U_1575,fun(U_1575,U_1575),plus_plus(U_1575),U_1580),U_1578)),hAPP(U_1575,U_1575,hAPP(U_1575,fun(U_1575,U_1575),plus_plus(U_1575),U_1580),U_1576)))
        | ~ sP83(U_1575,U_1576,U_1578,U_1577,U_1580,U_1579,U_1581) )
    & ! [U_1575,U_1576,U_1578,U_1577,U_1580,U_1579,U_1581] :
        ( sP83(U_1575,U_1576,U_1578,U_1577,U_1580,U_1579,U_1581)
        | ~ ordere236663937imp_le(U_1575) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP83])],[f_419_3]) ).

cnf(f_419_5,plain,
    ( sP83(U_1575,U_1576,U_1578,U_1577,U_1580,U_1579,U_1581)
    | ~ ordere236663937imp_le(U_1575) ),
    inference(clausify,[status(thm)],[f_419_4]) ).

cnf(f_419_6,plain,
    ( hBOOL(hAPP(U_1575,bool,hAPP(U_1575,fun(U_1575,bool),ord_less(U_1575),U_1578),U_1576))
    | ~ hBOOL(hAPP(U_1575,bool,hAPP(U_1575,fun(U_1575,bool),ord_less(U_1575),hAPP(U_1575,U_1575,hAPP(U_1575,fun(U_1575,U_1575),plus_plus(U_1575),U_1580),U_1578)),hAPP(U_1575,U_1575,hAPP(U_1575,fun(U_1575,U_1575),plus_plus(U_1575),U_1580),U_1576)))
    | ~ sP83(U_1575,U_1576,U_1578,U_1577,U_1580,U_1579,U_1581) ),
    inference(clausify,[status(thm)],[f_419_4]) ).

cnf(f_419_7,plain,
    ( hBOOL(hAPP(U_1575,bool,hAPP(U_1575,fun(U_1575,bool),ord_less(U_1575),hAPP(U_1575,U_1575,hAPP(U_1575,fun(U_1575,U_1575),plus_plus(U_1575),U_1581),U_1579)),hAPP(U_1575,U_1575,hAPP(U_1575,fun(U_1575,U_1575),plus_plus(U_1575),U_1581),U_1577)))
    | ~ hBOOL(hAPP(U_1575,bool,hAPP(U_1575,fun(U_1575,bool),ord_less(U_1575),U_1579),U_1577))
    | ~ sP83(U_1575,U_1576,U_1578,U_1577,U_1580,U_1579,U_1581) ),
    inference(clausify,[status(thm)],[f_419_4]) ).

fof(f_420_1,plain,
    ! [X_a] :
      ( ! [C,A_1,B] :
          ( 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),C)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) )
      | ~ ordere223160158up_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_349_add__strict__right__mono]) ).

fof(f_420_2,plain,
    ! [U_1585] :
      ( ! [U_1584,U_1583,U_1582] :
          ( hBOOL(hAPP(U_1585,bool,hAPP(U_1585,fun(U_1585,bool),ord_less(U_1585),hAPP(U_1585,U_1585,hAPP(U_1585,fun(U_1585,U_1585),plus_plus(U_1585),U_1583),U_1584)),hAPP(U_1585,U_1585,hAPP(U_1585,fun(U_1585,U_1585),plus_plus(U_1585),U_1582),U_1584)))
          | ~ hBOOL(hAPP(U_1585,bool,hAPP(U_1585,fun(U_1585,bool),ord_less(U_1585),U_1583),U_1582)) )
      | ~ ordere223160158up_add(U_1585) ),
    inference(variable_rename,[status(thm)],[f_420_1]) ).

fof(f_420_3,plain,
    ! [U_1583,U_1584,U_1585,U_1582] :
      ( hBOOL(hAPP(U_1585,bool,hAPP(U_1585,fun(U_1585,bool),ord_less(U_1585),hAPP(U_1585,U_1585,hAPP(U_1585,fun(U_1585,U_1585),plus_plus(U_1585),U_1583),U_1584)),hAPP(U_1585,U_1585,hAPP(U_1585,fun(U_1585,U_1585),plus_plus(U_1585),U_1582),U_1584)))
      | ~ hBOOL(hAPP(U_1585,bool,hAPP(U_1585,fun(U_1585,bool),ord_less(U_1585),U_1583),U_1582))
      | ~ ordere223160158up_add(U_1585) ),
    inference(definitional_conversion,[status(esa)],[f_420_2]) ).

cnf(f_420_4,plain,
    ( hBOOL(hAPP(U_1585,bool,hAPP(U_1585,fun(U_1585,bool),ord_less(U_1585),hAPP(U_1585,U_1585,hAPP(U_1585,fun(U_1585,U_1585),plus_plus(U_1585),U_1583),U_1584)),hAPP(U_1585,U_1585,hAPP(U_1585,fun(U_1585,U_1585),plus_plus(U_1585),U_1582),U_1584)))
    | ~ hBOOL(hAPP(U_1585,bool,hAPP(U_1585,fun(U_1585,bool),ord_less(U_1585),U_1583),U_1582))
    | ~ ordere223160158up_add(U_1585) ),
    inference(clausify,[status(thm)],[f_420_3]) ).

fof(f_421_1,plain,
    ! [X_a] :
      ( ! [C,A_1,B] :
          ( 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)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) )
      | ~ ordere223160158up_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_350_add__strict__left__mono]) ).

fof(f_421_2,plain,
    ! [U_1589] :
      ( ! [U_1588,U_1587,U_1586] :
          ( hBOOL(hAPP(U_1589,bool,hAPP(U_1589,fun(U_1589,bool),ord_less(U_1589),hAPP(U_1589,U_1589,hAPP(U_1589,fun(U_1589,U_1589),plus_plus(U_1589),U_1588),U_1587)),hAPP(U_1589,U_1589,hAPP(U_1589,fun(U_1589,U_1589),plus_plus(U_1589),U_1588),U_1586)))
          | ~ hBOOL(hAPP(U_1589,bool,hAPP(U_1589,fun(U_1589,bool),ord_less(U_1589),U_1587),U_1586)) )
      | ~ ordere223160158up_add(U_1589) ),
    inference(variable_rename,[status(thm)],[f_421_1]) ).

fof(f_421_3,plain,
    ! [U_1587,U_1586,U_1589,U_1588] :
      ( hBOOL(hAPP(U_1589,bool,hAPP(U_1589,fun(U_1589,bool),ord_less(U_1589),hAPP(U_1589,U_1589,hAPP(U_1589,fun(U_1589,U_1589),plus_plus(U_1589),U_1588),U_1587)),hAPP(U_1589,U_1589,hAPP(U_1589,fun(U_1589,U_1589),plus_plus(U_1589),U_1588),U_1586)))
      | ~ hBOOL(hAPP(U_1589,bool,hAPP(U_1589,fun(U_1589,bool),ord_less(U_1589),U_1587),U_1586))
      | ~ ordere223160158up_add(U_1589) ),
    inference(definitional_conversion,[status(esa)],[f_421_2]) ).

cnf(f_421_4,plain,
    ( hBOOL(hAPP(U_1589,bool,hAPP(U_1589,fun(U_1589,bool),ord_less(U_1589),hAPP(U_1589,U_1589,hAPP(U_1589,fun(U_1589,U_1589),plus_plus(U_1589),U_1588),U_1587)),hAPP(U_1589,U_1589,hAPP(U_1589,fun(U_1589,U_1589),plus_plus(U_1589),U_1588),U_1586)))
    | ~ hBOOL(hAPP(U_1589,bool,hAPP(U_1589,fun(U_1589,bool),ord_less(U_1589),U_1587),U_1586))
    | ~ ordere223160158up_add(U_1589) ),
    inference(clausify,[status(thm)],[f_421_3]) ).

fof(f_422_1,plain,
    ! [X_a] :
      ( ! [C,D,A_1,B] :
          ( 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),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)) )
      | ~ ordere223160158up_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_351_add__strict__mono]) ).

fof(f_422_2,plain,
    ! [U_1594] :
      ( ! [U_1593,U_1592,U_1591,U_1590] :
          ( hBOOL(hAPP(U_1594,bool,hAPP(U_1594,fun(U_1594,bool),ord_less(U_1594),hAPP(U_1594,U_1594,hAPP(U_1594,fun(U_1594,U_1594),plus_plus(U_1594),U_1591),U_1593)),hAPP(U_1594,U_1594,hAPP(U_1594,fun(U_1594,U_1594),plus_plus(U_1594),U_1590),U_1592)))
          | ~ hBOOL(hAPP(U_1594,bool,hAPP(U_1594,fun(U_1594,bool),ord_less(U_1594),U_1593),U_1592))
          | ~ hBOOL(hAPP(U_1594,bool,hAPP(U_1594,fun(U_1594,bool),ord_less(U_1594),U_1591),U_1590)) )
      | ~ ordere223160158up_add(U_1594) ),
    inference(variable_rename,[status(thm)],[f_422_1]) ).

fof(f_422_3,plain,
    ! [U_1594,U_1591,U_1590,U_1592,U_1593] :
      ( hBOOL(hAPP(U_1594,bool,hAPP(U_1594,fun(U_1594,bool),ord_less(U_1594),hAPP(U_1594,U_1594,hAPP(U_1594,fun(U_1594,U_1594),plus_plus(U_1594),U_1591),U_1593)),hAPP(U_1594,U_1594,hAPP(U_1594,fun(U_1594,U_1594),plus_plus(U_1594),U_1590),U_1592)))
      | ~ hBOOL(hAPP(U_1594,bool,hAPP(U_1594,fun(U_1594,bool),ord_less(U_1594),U_1593),U_1592))
      | ~ hBOOL(hAPP(U_1594,bool,hAPP(U_1594,fun(U_1594,bool),ord_less(U_1594),U_1591),U_1590))
      | ~ ordere223160158up_add(U_1594) ),
    inference(definitional_conversion,[status(esa)],[f_422_2]) ).

cnf(f_422_4,plain,
    ( hBOOL(hAPP(U_1594,bool,hAPP(U_1594,fun(U_1594,bool),ord_less(U_1594),hAPP(U_1594,U_1594,hAPP(U_1594,fun(U_1594,U_1594),plus_plus(U_1594),U_1591),U_1593)),hAPP(U_1594,U_1594,hAPP(U_1594,fun(U_1594,U_1594),plus_plus(U_1594),U_1590),U_1592)))
    | ~ hBOOL(hAPP(U_1594,bool,hAPP(U_1594,fun(U_1594,bool),ord_less(U_1594),U_1593),U_1592))
    | ~ hBOOL(hAPP(U_1594,bool,hAPP(U_1594,fun(U_1594,bool),ord_less(U_1594),U_1591),U_1590))
    | ~ ordere223160158up_add(U_1594) ),
    inference(clausify,[status(thm)],[f_422_3]) ).

fof(f_423_1,plain,
    ! [X_a] :
      ( ! [A_1,C,B] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))
          | ~ 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),C))) )
      | ~ ordere236663937imp_le(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_352_add__less__imp__less__right]) ).

fof(f_423_2,plain,
    ! [U_1598] :
      ( ! [U_1597,U_1596,U_1595] :
          ( hBOOL(hAPP(U_1598,bool,hAPP(U_1598,fun(U_1598,bool),ord_less(U_1598),U_1597),U_1595))
          | ~ hBOOL(hAPP(U_1598,bool,hAPP(U_1598,fun(U_1598,bool),ord_less(U_1598),hAPP(U_1598,U_1598,hAPP(U_1598,fun(U_1598,U_1598),plus_plus(U_1598),U_1597),U_1596)),hAPP(U_1598,U_1598,hAPP(U_1598,fun(U_1598,U_1598),plus_plus(U_1598),U_1595),U_1596))) )
      | ~ ordere236663937imp_le(U_1598) ),
    inference(variable_rename,[status(thm)],[f_423_1]) ).

fof(f_423_3,plain,
    ! [U_1596,U_1598,U_1595,U_1597] :
      ( hBOOL(hAPP(U_1598,bool,hAPP(U_1598,fun(U_1598,bool),ord_less(U_1598),U_1597),U_1595))
      | ~ hBOOL(hAPP(U_1598,bool,hAPP(U_1598,fun(U_1598,bool),ord_less(U_1598),hAPP(U_1598,U_1598,hAPP(U_1598,fun(U_1598,U_1598),plus_plus(U_1598),U_1597),U_1596)),hAPP(U_1598,U_1598,hAPP(U_1598,fun(U_1598,U_1598),plus_plus(U_1598),U_1595),U_1596)))
      | ~ ordere236663937imp_le(U_1598) ),
    inference(definitional_conversion,[status(esa)],[f_423_2]) ).

cnf(f_423_4,plain,
    ( hBOOL(hAPP(U_1598,bool,hAPP(U_1598,fun(U_1598,bool),ord_less(U_1598),U_1597),U_1595))
    | ~ hBOOL(hAPP(U_1598,bool,hAPP(U_1598,fun(U_1598,bool),ord_less(U_1598),hAPP(U_1598,U_1598,hAPP(U_1598,fun(U_1598,U_1598),plus_plus(U_1598),U_1597),U_1596)),hAPP(U_1598,U_1598,hAPP(U_1598,fun(U_1598,U_1598),plus_plus(U_1598),U_1595),U_1596)))
    | ~ ordere236663937imp_le(U_1598) ),
    inference(clausify,[status(thm)],[f_423_3]) ).

fof(f_424_1,plain,
    ! [X_a] :
      ( ! [C,A_1,B] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))
          | ~ 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))) )
      | ~ ordere236663937imp_le(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_353_add__less__imp__less__left]) ).

fof(f_424_2,plain,
    ! [U_1602] :
      ( ! [U_1601,U_1600,U_1599] :
          ( hBOOL(hAPP(U_1602,bool,hAPP(U_1602,fun(U_1602,bool),ord_less(U_1602),U_1600),U_1599))
          | ~ hBOOL(hAPP(U_1602,bool,hAPP(U_1602,fun(U_1602,bool),ord_less(U_1602),hAPP(U_1602,U_1602,hAPP(U_1602,fun(U_1602,U_1602),plus_plus(U_1602),U_1601),U_1600)),hAPP(U_1602,U_1602,hAPP(U_1602,fun(U_1602,U_1602),plus_plus(U_1602),U_1601),U_1599))) )
      | ~ ordere236663937imp_le(U_1602) ),
    inference(variable_rename,[status(thm)],[f_424_1]) ).

fof(f_424_3,plain,
    ! [U_1599,U_1602,U_1600,U_1601] :
      ( hBOOL(hAPP(U_1602,bool,hAPP(U_1602,fun(U_1602,bool),ord_less(U_1602),U_1600),U_1599))
      | ~ hBOOL(hAPP(U_1602,bool,hAPP(U_1602,fun(U_1602,bool),ord_less(U_1602),hAPP(U_1602,U_1602,hAPP(U_1602,fun(U_1602,U_1602),plus_plus(U_1602),U_1601),U_1600)),hAPP(U_1602,U_1602,hAPP(U_1602,fun(U_1602,U_1602),plus_plus(U_1602),U_1601),U_1599)))
      | ~ ordere236663937imp_le(U_1602) ),
    inference(definitional_conversion,[status(esa)],[f_424_2]) ).

cnf(f_424_4,plain,
    ( hBOOL(hAPP(U_1602,bool,hAPP(U_1602,fun(U_1602,bool),ord_less(U_1602),U_1600),U_1599))
    | ~ hBOOL(hAPP(U_1602,bool,hAPP(U_1602,fun(U_1602,bool),ord_less(U_1602),hAPP(U_1602,U_1602,hAPP(U_1602,fun(U_1602,U_1602),plus_plus(U_1602),U_1601),U_1600)),hAPP(U_1602,U_1602,hAPP(U_1602,fun(U_1602,U_1602),plus_plus(U_1602),U_1601),U_1599)))
    | ~ ordere236663937imp_le(U_1602) ),
    inference(clausify,[status(thm)],[f_424_3]) ).

fof(f_425_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_354_not__less__bot]) ).

fof(f_425_2,plain,
    ! [U_1604] :
      ( ! [U_1603] : ~ hBOOL(hAPP(U_1604,bool,hAPP(U_1604,fun(U_1604,bool),ord_less(U_1604),U_1603),bot_bot(U_1604)))
      | ~ bot(U_1604) ),
    inference(variable_rename,[status(thm)],[f_425_1]) ).

fof(f_425_3,plain,
    ! [U_1604,U_1603] :
      ( ~ hBOOL(hAPP(U_1604,bool,hAPP(U_1604,fun(U_1604,bool),ord_less(U_1604),U_1603),bot_bot(U_1604)))
      | ~ bot(U_1604) ),
    inference(definitional_conversion,[status(esa)],[f_425_2]) ).

cnf(f_425_4,plain,
    ( ~ hBOOL(hAPP(U_1604,bool,hAPP(U_1604,fun(U_1604,bool),ord_less(U_1604),U_1603),bot_bot(U_1604)))
    | ~ bot(U_1604) ),
    inference(clausify,[status(thm)],[f_425_3]) ).

fof(f_426_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_355_bot__less]) ).

fof(f_426_2,plain,
    ! [U_1606] :
      ( ! [U_1605] :
          ( ( ti(U_1606,U_1605) != bot_bot(U_1606)
            | ~ hBOOL(hAPP(U_1606,bool,hAPP(U_1606,fun(U_1606,bool),ord_less(U_1606),bot_bot(U_1606)),U_1605)) )
          & ( hBOOL(hAPP(U_1606,bool,hAPP(U_1606,fun(U_1606,bool),ord_less(U_1606),bot_bot(U_1606)),U_1605))
            | ti(U_1606,U_1605) = bot_bot(U_1606) ) )
      | ~ bot(U_1606) ),
    inference(variable_rename,[status(thm)],[f_426_1]) ).

fof(f_426_3,plain,
    ! [U_1606] :
      ( ( ! [U_1608] :
            ( ti(U_1606,U_1608) != bot_bot(U_1606)
            | ~ hBOOL(hAPP(U_1606,bool,hAPP(U_1606,fun(U_1606,bool),ord_less(U_1606),bot_bot(U_1606)),U_1608)) )
        & ! [U_1607] :
            ( hBOOL(hAPP(U_1606,bool,hAPP(U_1606,fun(U_1606,bool),ord_less(U_1606),bot_bot(U_1606)),U_1607))
            | ti(U_1606,U_1607) = bot_bot(U_1606) ) )
      | ~ bot(U_1606) ),
    inference(miniscope,[status(thm)],[f_426_2]) ).

fof(f_426_4,plain,
    ( ! [U_1606,U_1607,U_1608] :
        ( ti(U_1606,U_1608) != bot_bot(U_1606)
        | ~ hBOOL(hAPP(U_1606,bool,hAPP(U_1606,fun(U_1606,bool),ord_less(U_1606),bot_bot(U_1606)),U_1608))
        | ~ sP84(U_1606,U_1607,U_1608) )
    & ! [U_1606,U_1607,U_1608] :
        ( hBOOL(hAPP(U_1606,bool,hAPP(U_1606,fun(U_1606,bool),ord_less(U_1606),bot_bot(U_1606)),U_1607))
        | ti(U_1606,U_1607) = bot_bot(U_1606)
        | ~ sP84(U_1606,U_1607,U_1608) )
    & ! [U_1606,U_1607,U_1608] :
        ( sP84(U_1606,U_1607,U_1608)
        | ~ bot(U_1606) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP84])],[f_426_3]) ).

cnf(f_426_5,plain,
    ( sP84(U_1606,U_1607,U_1608)
    | ~ bot(U_1606) ),
    inference(clausify,[status(thm)],[f_426_4]) ).

cnf(f_426_6,plain,
    ( hBOOL(hAPP(U_1606,bool,hAPP(U_1606,fun(U_1606,bool),ord_less(U_1606),bot_bot(U_1606)),U_1607))
    | ti(U_1606,U_1607) = bot_bot(U_1606)
    | ~ sP84(U_1606,U_1607,U_1608) ),
    inference(clausify,[status(thm)],[f_426_4]) ).

cnf(f_426_7,plain,
    ( ti(U_1606,U_1608) != bot_bot(U_1606)
    | ~ hBOOL(hAPP(U_1606,bool,hAPP(U_1606,fun(U_1606,bool),ord_less(U_1606),bot_bot(U_1606)),U_1608))
    | ~ sP84(U_1606,U_1607,U_1608) ),
    inference(clausify,[status(thm)],[f_426_4]) ).

fof(f_427_1,plain,
    ! [X_b] :
      ( ! [A_2,B_3,C_1,D_1] :
          ( ( ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_3))
              | ~ 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_3)) ) )
          | hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3) != 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_356_diff__eq__diff__less]) ).

fof(f_427_2,plain,
    ! [U_1613] :
      ( ! [U_1612,U_1611,U_1610,U_1609] :
          ( ( ( hBOOL(hAPP(U_1613,bool,hAPP(U_1613,fun(U_1613,bool),ord_less(U_1613),U_1612),U_1611))
              | ~ hBOOL(hAPP(U_1613,bool,hAPP(U_1613,fun(U_1613,bool),ord_less(U_1613),U_1610),U_1609)) )
            & ( hBOOL(hAPP(U_1613,bool,hAPP(U_1613,fun(U_1613,bool),ord_less(U_1613),U_1610),U_1609))
              | ~ hBOOL(hAPP(U_1613,bool,hAPP(U_1613,fun(U_1613,bool),ord_less(U_1613),U_1612),U_1611)) ) )
          | hAPP(U_1613,U_1613,hAPP(U_1613,fun(U_1613,U_1613),minus_minus(U_1613),U_1612),U_1611) != hAPP(U_1613,U_1613,hAPP(U_1613,fun(U_1613,U_1613),minus_minus(U_1613),U_1610),U_1609) )
      | ~ ordered_ab_group_add(U_1613) ),
    inference(variable_rename,[status(thm)],[f_427_1]) ).

fof(f_427_3,plain,
    ( ! [U_1611,U_1613,U_1612,U_1609,U_1610] :
        ( hBOOL(hAPP(U_1613,bool,hAPP(U_1613,fun(U_1613,bool),ord_less(U_1613),U_1612),U_1611))
        | ~ hBOOL(hAPP(U_1613,bool,hAPP(U_1613,fun(U_1613,bool),ord_less(U_1613),U_1610),U_1609))
        | ~ sP85(U_1611,U_1613,U_1612,U_1609,U_1610) )
    & ! [U_1611,U_1613,U_1612,U_1609,U_1610] :
        ( hBOOL(hAPP(U_1613,bool,hAPP(U_1613,fun(U_1613,bool),ord_less(U_1613),U_1610),U_1609))
        | ~ hBOOL(hAPP(U_1613,bool,hAPP(U_1613,fun(U_1613,bool),ord_less(U_1613),U_1612),U_1611))
        | ~ sP85(U_1611,U_1613,U_1612,U_1609,U_1610) )
    & ! [U_1611,U_1613,U_1612,U_1609,U_1610] :
        ( sP85(U_1611,U_1613,U_1612,U_1609,U_1610)
        | hAPP(U_1613,U_1613,hAPP(U_1613,fun(U_1613,U_1613),minus_minus(U_1613),U_1612),U_1611) != hAPP(U_1613,U_1613,hAPP(U_1613,fun(U_1613,U_1613),minus_minus(U_1613),U_1610),U_1609)
        | ~ ordered_ab_group_add(U_1613) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP85])],[f_427_2]) ).

cnf(f_427_4,plain,
    ( sP85(U_1611,U_1613,U_1612,U_1609,U_1610)
    | hAPP(U_1613,U_1613,hAPP(U_1613,fun(U_1613,U_1613),minus_minus(U_1613),U_1612),U_1611) != hAPP(U_1613,U_1613,hAPP(U_1613,fun(U_1613,U_1613),minus_minus(U_1613),U_1610),U_1609)
    | ~ ordered_ab_group_add(U_1613) ),
    inference(clausify,[status(thm)],[f_427_3]) ).

cnf(f_427_5,plain,
    ( hBOOL(hAPP(U_1613,bool,hAPP(U_1613,fun(U_1613,bool),ord_less(U_1613),U_1610),U_1609))
    | ~ hBOOL(hAPP(U_1613,bool,hAPP(U_1613,fun(U_1613,bool),ord_less(U_1613),U_1612),U_1611))
    | ~ sP85(U_1611,U_1613,U_1612,U_1609,U_1610) ),
    inference(clausify,[status(thm)],[f_427_3]) ).

cnf(f_427_6,plain,
    ( hBOOL(hAPP(U_1613,bool,hAPP(U_1613,fun(U_1613,bool),ord_less(U_1613),U_1612),U_1611))
    | ~ hBOOL(hAPP(U_1613,bool,hAPP(U_1613,fun(U_1613,bool),ord_less(U_1613),U_1610),U_1609))
    | ~ sP85(U_1611,U_1613,U_1612,U_1609,U_1610) ),
    inference(clausify,[status(thm)],[f_427_3]) ).

fof(f_428_1,plain,
    ! [M,Na] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,M))) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,M)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_357_not__less__eq]) ).

fof(f_428_2,plain,
    ! [U_1615,U_1614] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1615),U_1614))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1614),hAPP(nat,nat,suc,U_1615))) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1614),hAPP(nat,nat,suc,U_1615)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1615),U_1614)) ) ),
    inference(variable_rename,[status(thm)],[f_428_1]) ).

fof(f_428_3,plain,
    ( ! [U_1619,U_1617] :
        ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1619),U_1617))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1617),hAPP(nat,nat,suc,U_1619))) )
    & ! [U_1618,U_1616] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1616),hAPP(nat,nat,suc,U_1618)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1618),U_1616)) ) ),
    inference(miniscope,[status(thm)],[f_428_2]) ).

fof(f_428_4,plain,
    ( ! [U_1617,U_1619] :
        ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1619),U_1617))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1617),hAPP(nat,nat,suc,U_1619))) )
    & ! [U_1616,U_1618] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1616),hAPP(nat,nat,suc,U_1618)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1618),U_1616)) ) ),
    inference(definitional_conversion,[status(esa)],[f_428_3]) ).

cnf(f_428_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1616),hAPP(nat,nat,suc,U_1618)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1618),U_1616)) ),
    inference(clausify,[status(thm)],[f_428_4]) ).

cnf(f_428_6,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1619),U_1617))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1617),hAPP(nat,nat,suc,U_1619))) ),
    inference(clausify,[status(thm)],[f_428_4]) ).

fof(f_429_1,plain,
    ! [M,Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,Na)))
        | ( M != Na
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)) ) )
      & ( M = Na
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_358_less__Suc__eq]) ).

fof(f_429_2,plain,
    ! [U_1621,U_1620] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1621),hAPP(nat,nat,suc,U_1620)))
        | ( U_1621 != U_1620
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1621),U_1620)) ) )
      & ( U_1621 = U_1620
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1621),U_1620))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1621),hAPP(nat,nat,suc,U_1620))) ) ),
    inference(variable_rename,[status(thm)],[f_429_1]) ).

fof(f_429_3,plain,
    ( ! [U_1625,U_1623] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1625),hAPP(nat,nat,suc,U_1623)))
        | ( U_1625 != U_1623
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1625),U_1623)) ) )
    & ! [U_1624,U_1622] :
        ( U_1624 = U_1622
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1624),U_1622))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1624),hAPP(nat,nat,suc,U_1622))) ) ),
    inference(miniscope,[status(thm)],[f_429_2]) ).

fof(f_429_4,plain,
    ( ! [U_1625,U_1623] :
        ( U_1625 != U_1623
        | ~ sP86(U_1625,U_1623) )
    & ! [U_1625,U_1623] :
        ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1625),U_1623))
        | ~ sP86(U_1625,U_1623) )
    & ! [U_1625,U_1623] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1625),hAPP(nat,nat,suc,U_1623)))
        | sP86(U_1625,U_1623) )
    & ! [U_1622,U_1624] :
        ( U_1624 = U_1622
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1624),U_1622))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1624),hAPP(nat,nat,suc,U_1622))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP86])],[f_429_3]) ).

cnf(f_429_5,plain,
    ( U_1624 = U_1622
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1624),U_1622))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1624),hAPP(nat,nat,suc,U_1622))) ),
    inference(clausify,[status(thm)],[f_429_4]) ).

cnf(f_429_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1625),hAPP(nat,nat,suc,U_1623)))
    | sP86(U_1625,U_1623) ),
    inference(clausify,[status(thm)],[f_429_4]) ).

cnf(f_429_7,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1625),U_1623))
    | ~ sP86(U_1625,U_1623) ),
    inference(clausify,[status(thm)],[f_429_4]) ).

cnf(f_429_8,plain,
    ( U_1625 != U_1623
    | ~ sP86(U_1625,U_1623) ),
    inference(clausify,[status(thm)],[f_429_4]) ).

fof(f_430_1,plain,
    ! [M,Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,Na)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_359_Suc__less__eq]) ).

fof(f_430_2,plain,
    ! [U_1627,U_1626] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1627)),hAPP(nat,nat,suc,U_1626)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1627),U_1626)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1627),U_1626))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1627)),hAPP(nat,nat,suc,U_1626))) ) ),
    inference(variable_rename,[status(thm)],[f_430_1]) ).

fof(f_430_3,plain,
    ( ! [U_1631,U_1629] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1631)),hAPP(nat,nat,suc,U_1629)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1631),U_1629)) )
    & ! [U_1630,U_1628] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1630),U_1628))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1630)),hAPP(nat,nat,suc,U_1628))) ) ),
    inference(miniscope,[status(thm)],[f_430_2]) ).

fof(f_430_4,plain,
    ( ! [U_1629,U_1631] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1631)),hAPP(nat,nat,suc,U_1629)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1631),U_1629)) )
    & ! [U_1630,U_1628] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1630),U_1628))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1630)),hAPP(nat,nat,suc,U_1628))) ) ),
    inference(definitional_conversion,[status(esa)],[f_430_3]) ).

cnf(f_430_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1630),U_1628))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1630)),hAPP(nat,nat,suc,U_1628))) ),
    inference(clausify,[status(thm)],[f_430_4]) ).

cnf(f_430_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1631)),hAPP(nat,nat,suc,U_1629)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1631),U_1629)) ),
    inference(clausify,[status(thm)],[f_430_4]) ).

fof(f_431_1,plain,
    ! [Na,M] :
      ( ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,M)))
          | Na != M )
        & ( Na = M
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,M))) ) )
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M)) ),
    inference(fof_nnf,[status(thm)],[fact_360_not__less__less__Suc__eq]) ).

fof(f_431_2,plain,
    ! [U_1633,U_1632] :
      ( ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1633),hAPP(nat,nat,suc,U_1632)))
          | U_1633 != U_1632 )
        & ( U_1633 = U_1632
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1633),hAPP(nat,nat,suc,U_1632))) ) )
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1633),U_1632)) ),
    inference(variable_rename,[status(thm)],[f_431_1]) ).

fof(f_431_3,plain,
    ( ! [U_1633,U_1632] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1633),hAPP(nat,nat,suc,U_1632)))
        | U_1633 != U_1632
        | ~ sP87(U_1633,U_1632) )
    & ! [U_1633,U_1632] :
        ( U_1633 = U_1632
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1633),hAPP(nat,nat,suc,U_1632)))
        | ~ sP87(U_1633,U_1632) )
    & ! [U_1633,U_1632] :
        ( sP87(U_1633,U_1632)
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1633),U_1632)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP87])],[f_431_2]) ).

cnf(f_431_4,plain,
    ( sP87(U_1633,U_1632)
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1633),U_1632)) ),
    inference(clausify,[status(thm)],[f_431_3]) ).

cnf(f_431_5,plain,
    ( U_1633 = U_1632
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1633),hAPP(nat,nat,suc,U_1632)))
    | ~ sP87(U_1633,U_1632) ),
    inference(clausify,[status(thm)],[f_431_3]) ).

cnf(f_431_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1633),hAPP(nat,nat,suc,U_1632)))
    | U_1633 != U_1632
    | ~ sP87(U_1633,U_1632) ),
    inference(clausify,[status(thm)],[f_431_3]) ).

fof(f_432_1,plain,
    ! [N,M_1] :
      ( M_1 = N
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,suc,M_1)))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M_1)) ),
    inference(fof_nnf,[status(thm)],[fact_361_less__antisym]) ).

fof(f_432_2,plain,
    ! [U_1635,U_1634] :
      ( U_1634 = U_1635
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1635),hAPP(nat,nat,suc,U_1634)))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1635),U_1634)) ),
    inference(variable_rename,[status(thm)],[f_432_1]) ).

fof(f_432_3,plain,
    ! [U_1635,U_1634] :
      ( U_1634 = U_1635
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1635),hAPP(nat,nat,suc,U_1634)))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1635),U_1634)) ),
    inference(definitional_conversion,[status(esa)],[f_432_2]) ).

cnf(f_432_4,plain,
    ( U_1634 = U_1635
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1635),hAPP(nat,nat,suc,U_1634)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1635),U_1634)) ),
    inference(clausify,[status(thm)],[f_432_3]) ).

fof(f_433_1,plain,
    ! [M_1,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)) ),
    inference(fof_nnf,[status(thm)],[fact_362_less__SucI]) ).

fof(f_433_2,plain,
    ! [U_1637,U_1636] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1637),hAPP(nat,nat,suc,U_1636)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1637),U_1636)) ),
    inference(variable_rename,[status(thm)],[f_433_1]) ).

fof(f_433_3,plain,
    ! [U_1637,U_1636] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1637),hAPP(nat,nat,suc,U_1636)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1637),U_1636)) ),
    inference(definitional_conversion,[status(esa)],[f_433_2]) ).

cnf(f_433_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1637),hAPP(nat,nat,suc,U_1636)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1637),U_1636)) ),
    inference(clausify,[status(thm)],[f_433_3]) ).

fof(f_434_1,plain,
    ! [M_1,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_1)),N))
      | hAPP(nat,nat,suc,M_1) = N
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)) ),
    inference(fof_nnf,[status(thm)],[fact_363_Suc__lessI]) ).

fof(f_434_2,plain,
    ! [U_1639,U_1638] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1639)),U_1638))
      | hAPP(nat,nat,suc,U_1639) = U_1638
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1639),U_1638)) ),
    inference(variable_rename,[status(thm)],[f_434_1]) ).

fof(f_434_3,plain,
    ! [U_1638,U_1639] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1639)),U_1638))
      | hAPP(nat,nat,suc,U_1639) = U_1638
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1639),U_1638)) ),
    inference(definitional_conversion,[status(esa)],[f_434_2]) ).

cnf(f_434_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1639)),U_1638))
    | hAPP(nat,nat,suc,U_1639) = U_1638
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1639),U_1638)) ),
    inference(clausify,[status(thm)],[f_434_3]) ).

fof(f_435_1,plain,
    ! [K_1,I_2,J] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,I_2)),K_1))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J),K_1))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J)) ),
    inference(fof_nnf,[status(thm)],[fact_364_less__trans__Suc]) ).

fof(f_435_2,plain,
    ! [U_1642,U_1641,U_1640] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1641)),U_1642))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1640),U_1642))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1641),U_1640)) ),
    inference(variable_rename,[status(thm)],[f_435_1]) ).

fof(f_435_3,plain,
    ! [U_1640,U_1641,U_1642] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1641)),U_1642))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1640),U_1642))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1641),U_1640)) ),
    inference(definitional_conversion,[status(esa)],[f_435_2]) ).

cnf(f_435_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1641)),U_1642))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1640),U_1642))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1641),U_1640)) ),
    inference(clausify,[status(thm)],[f_435_3]) ).

fof(f_436_1,plain,
    ! [M_1,N] :
      ( M_1 = N
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N))) ),
    inference(fof_nnf,[status(thm)],[fact_365_less__SucE]) ).

fof(f_436_2,plain,
    ! [U_1644,U_1643] :
      ( U_1644 = U_1643
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1644),U_1643))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1644),hAPP(nat,nat,suc,U_1643))) ),
    inference(variable_rename,[status(thm)],[f_436_1]) ).

fof(f_436_3,plain,
    ! [U_1643,U_1644] :
      ( U_1644 = U_1643
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1644),U_1643))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1644),hAPP(nat,nat,suc,U_1643))) ),
    inference(definitional_conversion,[status(esa)],[f_436_2]) ).

cnf(f_436_4,plain,
    ( U_1644 = U_1643
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1644),U_1643))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1644),hAPP(nat,nat,suc,U_1643))) ),
    inference(clausify,[status(thm)],[f_436_3]) ).

fof(f_437_1,plain,
    ! [M_1,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_1)),N)) ),
    inference(fof_nnf,[status(thm)],[fact_366_Suc__lessD]) ).

fof(f_437_2,plain,
    ! [U_1646,U_1645] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1646),U_1645))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1646)),U_1645)) ),
    inference(variable_rename,[status(thm)],[f_437_1]) ).

fof(f_437_3,plain,
    ! [U_1645,U_1646] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1646),U_1645))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1646)),U_1645)) ),
    inference(definitional_conversion,[status(esa)],[f_437_2]) ).

cnf(f_437_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1646),U_1645))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1646)),U_1645)) ),
    inference(clausify,[status(thm)],[f_437_3]) ).

fof(f_438_1,plain,
    ! [M_1,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_1)),hAPP(nat,nat,suc,N))) ),
    inference(fof_nnf,[status(thm)],[fact_367_Suc__less__SucD]) ).

fof(f_438_2,plain,
    ! [U_1648,U_1647] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1648),U_1647))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1648)),hAPP(nat,nat,suc,U_1647))) ),
    inference(variable_rename,[status(thm)],[f_438_1]) ).

fof(f_438_3,plain,
    ! [U_1647,U_1648] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1648),U_1647))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1648)),hAPP(nat,nat,suc,U_1647))) ),
    inference(definitional_conversion,[status(esa)],[f_438_2]) ).

cnf(f_438_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1648),U_1647))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1648)),hAPP(nat,nat,suc,U_1647))) ),
    inference(clausify,[status(thm)],[f_438_3]) ).

fof(f_439_1,plain,
    ! [I_2,J] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),J)),I_2)),
    inference(fof_nnf,[status(thm)],[fact_368_not__add__less1]) ).

fof(f_439_2,plain,
    ! [U_1650,U_1649] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1650),U_1649)),U_1650)),
    inference(variable_rename,[status(thm)],[f_439_1]) ).

fof(f_439_3,plain,
    ! [U_1649,U_1650] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1650),U_1649)),U_1650)),
    inference(definitional_conversion,[status(esa)],[f_439_2]) ).

cnf(f_439_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_1650),U_1649)),U_1650)),
    inference(clausify,[status(thm)],[f_439_3]) ).

fof(f_440_1,plain,
    ! [J,I_2] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),I_2)),I_2)),
    inference(fof_nnf,[status(thm)],[fact_369_not__add__less2]) ).

fof(f_440_2,plain,
    ! [U_1652,U_1651] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1652),U_1651)),U_1651)),
    inference(variable_rename,[status(thm)],[f_440_1]) ).

fof(f_440_3,plain,
    ! [U_1651,U_1652] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1652),U_1651)),U_1651)),
    inference(definitional_conversion,[status(esa)],[f_440_2]) ).

cnf(f_440_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_1652),U_1651)),U_1651)),
    inference(clausify,[status(thm)],[f_440_3]) ).

fof(f_441_1,plain,
    ! [K,M,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),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),Na)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),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),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_370_nat__add__left__cancel__less]) ).

fof(f_441_2,plain,
    ! [U_1655,U_1654,U_1653] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1655),U_1654)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1655),U_1653)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1654),U_1653)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1654),U_1653))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1655),U_1654)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1655),U_1653))) ) ),
    inference(variable_rename,[status(thm)],[f_441_1]) ).

fof(f_441_3,plain,
    ( ! [U_1661,U_1659,U_1657] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1661),U_1659)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1661),U_1657)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1659),U_1657)) )
    & ! [U_1660,U_1658,U_1656] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1658),U_1656))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1660),U_1658)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1660),U_1656))) ) ),
    inference(miniscope,[status(thm)],[f_441_2]) ).

fof(f_441_4,plain,
    ( ! [U_1657,U_1659,U_1661] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1661),U_1659)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1661),U_1657)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1659),U_1657)) )
    & ! [U_1656,U_1658,U_1660] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1658),U_1656))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1660),U_1658)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1660),U_1656))) ) ),
    inference(definitional_conversion,[status(esa)],[f_441_3]) ).

cnf(f_441_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1658),U_1656))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1660),U_1658)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1660),U_1656))) ),
    inference(clausify,[status(thm)],[f_441_4]) ).

cnf(f_441_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_1661),U_1659)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1661),U_1657)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1659),U_1657)) ),
    inference(clausify,[status(thm)],[f_441_4]) ).

fof(f_442_1,plain,
    ! [M_1,I_2,J] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),M_1)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J)) ),
    inference(fof_nnf,[status(thm)],[fact_371_trans__less__add1]) ).

fof(f_442_2,plain,
    ! [U_1664,U_1663,U_1662] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1663),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1662),U_1664)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1663),U_1662)) ),
    inference(variable_rename,[status(thm)],[f_442_1]) ).

fof(f_442_3,plain,
    ! [U_1662,U_1663,U_1664] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1663),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1662),U_1664)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1663),U_1662)) ),
    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_1663),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1662),U_1664)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1663),U_1662)) ),
    inference(clausify,[status(thm)],[f_442_3]) ).

fof(f_443_1,plain,
    ! [M_1,I_2,J] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),J)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J)) ),
    inference(fof_nnf,[status(thm)],[fact_372_trans__less__add2]) ).

fof(f_443_2,plain,
    ! [U_1667,U_1666,U_1665] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1666),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1667),U_1665)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1666),U_1665)) ),
    inference(variable_rename,[status(thm)],[f_443_1]) ).

fof(f_443_3,plain,
    ! [U_1666,U_1665,U_1667] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1666),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1667),U_1665)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1666),U_1665)) ),
    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_1666),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1667),U_1665)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1666),U_1665)) ),
    inference(clausify,[status(thm)],[f_443_3]) ).

fof(f_444_1,plain,
    ! [K_1,I_2,J] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),K_1)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J)) ),
    inference(fof_nnf,[status(thm)],[fact_373_add__less__mono1]) ).

fof(f_444_2,plain,
    ! [U_1670,U_1669,U_1668] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1669),U_1670)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1668),U_1670)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1669),U_1668)) ),
    inference(variable_rename,[status(thm)],[f_444_1]) ).

fof(f_444_3,plain,
    ! [U_1668,U_1669,U_1670] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1669),U_1670)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1668),U_1670)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1669),U_1668)) ),
    inference(definitional_conversion,[status(esa)],[f_444_2]) ).

cnf(f_444_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_1669),U_1670)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1668),U_1670)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1669),U_1668)) ),
    inference(clausify,[status(thm)],[f_444_3]) ).

fof(f_445_1,plain,
    ! [K_1,L_1,I_2,J] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),L_1)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_1),L_1))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J)) ),
    inference(fof_nnf,[status(thm)],[fact_374_add__less__mono]) ).

fof(f_445_2,plain,
    ! [U_1674,U_1673,U_1672,U_1671] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1672),U_1674)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1671),U_1673)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1674),U_1673))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1672),U_1671)) ),
    inference(variable_rename,[status(thm)],[f_445_1]) ).

fof(f_445_3,plain,
    ! [U_1672,U_1671,U_1673,U_1674] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1672),U_1674)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1671),U_1673)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1674),U_1673))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1672),U_1671)) ),
    inference(definitional_conversion,[status(esa)],[f_445_2]) ).

cnf(f_445_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_1672),U_1674)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1671),U_1673)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1674),U_1673))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1672),U_1671)) ),
    inference(clausify,[status(thm)],[f_445_3]) ).

fof(f_446_1,plain,
    ! [M_1,N,K_1,L_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N))
      | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),L_1) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_1),L_1)) ),
    inference(fof_nnf,[status(thm)],[fact_375_less__add__eq__less]) ).

fof(f_446_2,plain,
    ! [U_1678,U_1677,U_1676,U_1675] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1678),U_1677))
      | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1678),U_1675) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1676),U_1677)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1676),U_1675)) ),
    inference(variable_rename,[status(thm)],[f_446_1]) ).

fof(f_446_3,plain,
    ! [U_1677,U_1676,U_1675,U_1678] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1678),U_1677))
      | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1678),U_1675) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1676),U_1677)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1676),U_1675)) ),
    inference(definitional_conversion,[status(esa)],[f_446_2]) ).

cnf(f_446_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1678),U_1677))
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1678),U_1675) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1676),U_1677)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1676),U_1675)) ),
    inference(clausify,[status(thm)],[f_446_3]) ).

fof(f_447_1,plain,
    ! [I_2,J,K_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),K_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_2),J)),K_1)) ),
    inference(fof_nnf,[status(thm)],[fact_376_add__lessD1]) ).

fof(f_447_2,plain,
    ! [U_1681,U_1680,U_1679] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1681),U_1679))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1681),U_1680)),U_1679)) ),
    inference(variable_rename,[status(thm)],[f_447_1]) ).

fof(f_447_3,plain,
    ! [U_1679,U_1680,U_1681] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1681),U_1679))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1681),U_1680)),U_1679)) ),
    inference(definitional_conversion,[status(esa)],[f_447_2]) ).

cnf(f_447_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1681),U_1679))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1681),U_1680)),U_1679)) ),
    inference(clausify,[status(thm)],[f_447_3]) ).

fof(f_448_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_377_termination__basic__simps_I1_J]) ).

fof(f_448_2,plain,
    ! [U_1684,U_1683,U_1682] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1683),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1682),U_1684)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1683),U_1682)) ),
    inference(variable_rename,[status(thm)],[f_448_1]) ).

fof(f_448_3,plain,
    ! [U_1683,U_1682,U_1684] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1683),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1682),U_1684)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1683),U_1682)) ),
    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_1683),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1682),U_1684)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1683),U_1682)) ),
    inference(clausify,[status(thm)],[f_448_3]) ).

fof(f_449_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_378_termination__basic__simps_I2_J]) ).

fof(f_449_2,plain,
    ! [U_1687,U_1686,U_1685] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1686),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1687),U_1685)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1686),U_1685)) ),
    inference(variable_rename,[status(thm)],[f_449_1]) ).

fof(f_449_3,plain,
    ! [U_1686,U_1685,U_1687] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1686),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1687),U_1685)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1686),U_1685)) ),
    inference(definitional_conversion,[status(esa)],[f_449_2]) ).

cnf(f_449_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1686),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1687),U_1685)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1686),U_1685)) ),
    inference(clausify,[status(thm)],[f_449_3]) ).

fof(f_450_1,plain,
    ! [M,Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))
        | M = Na
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)) )
      & ( ( M != Na
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)) )
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_379_nat__less__le]) ).

fof(f_450_2,plain,
    ! [U_1689,U_1688] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1689),U_1688))
        | U_1689 = U_1688
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1689),U_1688)) )
      & ( ( U_1689 != U_1688
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1689),U_1688)) )
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1689),U_1688)) ) ),
    inference(variable_rename,[status(thm)],[f_450_1]) ).

fof(f_450_3,plain,
    ( ! [U_1693,U_1691] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1693),U_1691))
        | U_1693 = U_1691
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1693),U_1691)) )
    & ! [U_1692,U_1690] :
        ( ( U_1692 != U_1690
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1692),U_1690)) )
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1692),U_1690)) ) ),
    inference(miniscope,[status(thm)],[f_450_2]) ).

fof(f_450_4,plain,
    ( ! [U_1690,U_1692] :
        ( U_1692 != U_1690
        | ~ sP88(U_1690,U_1692) )
    & ! [U_1690,U_1692] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1692),U_1690))
        | ~ sP88(U_1690,U_1692) )
    & ! [U_1693,U_1691] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1693),U_1691))
        | U_1693 = U_1691
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1693),U_1691)) )
    & ! [U_1690,U_1692] :
        ( sP88(U_1690,U_1692)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1692),U_1690)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP88])],[f_450_3]) ).

cnf(f_450_5,plain,
    ( sP88(U_1690,U_1692)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1692),U_1690)) ),
    inference(clausify,[status(thm)],[f_450_4]) ).

cnf(f_450_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1693),U_1691))
    | U_1693 = U_1691
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1693),U_1691)) ),
    inference(clausify,[status(thm)],[f_450_4]) ).

cnf(f_450_7,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1692),U_1690))
    | ~ sP88(U_1690,U_1692) ),
    inference(clausify,[status(thm)],[f_450_4]) ).

cnf(f_450_8,plain,
    ( U_1692 != U_1690
    | ~ sP88(U_1690,U_1692) ),
    inference(clausify,[status(thm)],[f_450_4]) ).

fof(f_451_1,plain,
    ! [M,Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na))
        | ( M != Na
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)) ) )
      & ( M = Na
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_380_le__eq__less__or__eq]) ).

fof(f_451_2,plain,
    ! [U_1695,U_1694] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1695),U_1694))
        | ( U_1695 != U_1694
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1695),U_1694)) ) )
      & ( U_1695 = U_1694
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1695),U_1694))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1695),U_1694)) ) ),
    inference(variable_rename,[status(thm)],[f_451_1]) ).

fof(f_451_3,plain,
    ( ! [U_1699,U_1697] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1699),U_1697))
        | ( U_1699 != U_1697
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1699),U_1697)) ) )
    & ! [U_1698,U_1696] :
        ( U_1698 = U_1696
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1698),U_1696))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1698),U_1696)) ) ),
    inference(miniscope,[status(thm)],[f_451_2]) ).

fof(f_451_4,plain,
    ( ! [U_1697,U_1699] :
        ( U_1699 != U_1697
        | ~ sP89(U_1697,U_1699) )
    & ! [U_1697,U_1699] :
        ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1699),U_1697))
        | ~ sP89(U_1697,U_1699) )
    & ! [U_1697,U_1699] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1699),U_1697))
        | sP89(U_1697,U_1699) )
    & ! [U_1696,U_1698] :
        ( U_1698 = U_1696
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1698),U_1696))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1698),U_1696)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP89])],[f_451_3]) ).

cnf(f_451_5,plain,
    ( U_1698 = U_1696
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1698),U_1696))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1698),U_1696)) ),
    inference(clausify,[status(thm)],[f_451_4]) ).

cnf(f_451_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1699),U_1697))
    | sP89(U_1697,U_1699) ),
    inference(clausify,[status(thm)],[f_451_4]) ).

cnf(f_451_7,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1699),U_1697))
    | ~ sP89(U_1697,U_1699) ),
    inference(clausify,[status(thm)],[f_451_4]) ).

cnf(f_451_8,plain,
    ( U_1699 != U_1697
    | ~ sP89(U_1697,U_1699) ),
    inference(clausify,[status(thm)],[f_451_4]) ).

fof(f_452_1,plain,
    ! [M_1,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)) ),
    inference(fof_nnf,[status(thm)],[fact_381_less__imp__le__nat]) ).

fof(f_452_2,plain,
    ! [U_1701,U_1700] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1701),U_1700))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1701),U_1700)) ),
    inference(variable_rename,[status(thm)],[f_452_1]) ).

fof(f_452_3,plain,
    ! [U_1701,U_1700] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1701),U_1700))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1701),U_1700)) ),
    inference(definitional_conversion,[status(esa)],[f_452_2]) ).

cnf(f_452_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1701),U_1700))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1701),U_1700)) ),
    inference(clausify,[status(thm)],[f_452_3]) ).

fof(f_453_1,plain,
    ! [M_1,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N))
      | M_1 = N
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)) ),
    inference(fof_nnf,[status(thm)],[fact_382_le__neq__implies__less]) ).

fof(f_453_2,plain,
    ! [U_1703,U_1702] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1703),U_1702))
      | U_1703 = U_1702
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1703),U_1702)) ),
    inference(variable_rename,[status(thm)],[f_453_1]) ).

fof(f_453_3,plain,
    ! [U_1703,U_1702] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1703),U_1702))
      | U_1703 = U_1702
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1703),U_1702)) ),
    inference(definitional_conversion,[status(esa)],[f_453_2]) ).

cnf(f_453_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1703),U_1702))
    | U_1703 = U_1702
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1703),U_1702)) ),
    inference(clausify,[status(thm)],[f_453_3]) ).

fof(f_454_1,plain,
    ! [M_1,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N))
      | ( M_1 != N
        & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)) ) ),
    inference(fof_nnf,[status(thm)],[fact_383_less__or__eq__imp__le]) ).

fof(f_454_2,plain,
    ! [U_1705,U_1704] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1705),U_1704))
      | ( 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_454_1]) ).

fof(f_454_3,plain,
    ( ! [U_1705,U_1704] :
        ( U_1705 != U_1704
        | ~ sP90(U_1705,U_1704) )
    & ! [U_1705,U_1704] :
        ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1705),U_1704))
        | ~ sP90(U_1705,U_1704) )
    & ! [U_1705,U_1704] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1705),U_1704))
        | sP90(U_1705,U_1704) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP90])],[f_454_2]) ).

cnf(f_454_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1705),U_1704))
    | sP90(U_1705,U_1704) ),
    inference(clausify,[status(thm)],[f_454_3]) ).

cnf(f_454_5,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1705),U_1704))
    | ~ sP90(U_1705,U_1704) ),
    inference(clausify,[status(thm)],[f_454_3]) ).

cnf(f_454_6,plain,
    ( U_1705 != U_1704
    | ~ sP90(U_1705,U_1704) ),
    inference(clausify,[status(thm)],[f_454_3]) ).

fof(f_455_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_384_termination__basic__simps_I5_J]) ).

fof(f_455_2,plain,
    ! [U_1707,U_1706] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1707),U_1706))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1707),U_1706)) ),
    inference(variable_rename,[status(thm)],[f_455_1]) ).

fof(f_455_3,plain,
    ! [U_1706,U_1707] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1707),U_1706))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1707),U_1706)) ),
    inference(definitional_conversion,[status(esa)],[f_455_2]) ).

cnf(f_455_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1707),U_1706))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1707),U_1706)) ),
    inference(clausify,[status(thm)],[f_455_3]) ).

fof(f_456_1,plain,
    ! [N,J,K_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),N)),K_1))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J),K_1)) ),
    inference(fof_nnf,[status(thm)],[fact_385_less__imp__diff__less]) ).

fof(f_456_2,plain,
    ! [U_1710,U_1709,U_1708] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1709),U_1710)),U_1708))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1709),U_1708)) ),
    inference(variable_rename,[status(thm)],[f_456_1]) ).

fof(f_456_3,plain,
    ! [U_1709,U_1708,U_1710] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1709),U_1710)),U_1708))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1709),U_1708)) ),
    inference(definitional_conversion,[status(esa)],[f_456_2]) ).

cnf(f_456_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_1709),U_1710)),U_1708))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1709),U_1708)) ),
    inference(clausify,[status(thm)],[f_456_3]) ).

fof(f_457_1,plain,
    ! [L_1,M_1,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_1),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L_1),M_1)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),L_1))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)) ),
    inference(fof_nnf,[status(thm)],[fact_386_diff__less__mono2]) ).

fof(f_457_2,plain,
    ! [U_1713,U_1712,U_1711] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1713),U_1711)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1713),U_1712)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1712),U_1713))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1712),U_1711)) ),
    inference(variable_rename,[status(thm)],[f_457_1]) ).

fof(f_457_3,plain,
    ! [U_1711,U_1712,U_1713] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1713),U_1711)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1713),U_1712)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1712),U_1713))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1712),U_1711)) ),
    inference(definitional_conversion,[status(esa)],[f_457_2]) ).

cnf(f_457_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_1713),U_1711)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1713),U_1712)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1712),U_1713))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1712),U_1711)) ),
    inference(clausify,[status(thm)],[f_457_3]) ).

fof(f_458_1,plain,
    ! [N_2] :
      ( ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),N_2))
        | ! [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_2)) ) )
      & ( ? [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_2)) )
        | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),N_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_387_finite__nat__set__iff__bounded]) ).

fof(f_458_2,plain,
    ! [U_1718] :
      ( ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_1718))
        | ! [U_1717] :
          ? [U_1716] :
            ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1716),U_1717))
            & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_1716),U_1718)) ) )
      & ( ? [U_1715] :
          ! [U_1714] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1714),U_1715))
            | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_1714),U_1718)) )
        | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_1718)) ) ),
    inference(variable_rename,[status(thm)],[f_458_1]) ).

fof(f_458_3,plain,
    ( ! [U_1720] :
        ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_1720))
        | ! [U_1717] :
          ? [U_1716] :
            ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1716),U_1717))
            & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_1716),U_1720)) ) )
    & ! [U_1719] :
        ( ? [U_1715] :
          ! [U_1714] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1714),U_1715))
            | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_1714),U_1719)) )
        | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_1719)) ) ),
    inference(miniscope,[status(thm)],[f_458_2]) ).

fof(f_458_4,plain,
    ( ! [U_1720] :
        ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_1720))
        | ! [U_1717] :
          ? [U_1716] :
            ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1716),U_1717))
            & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_1716),U_1720)) ) )
    & ! [U_1719] :
        ( ! [U_1714] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1714),sK45(U_1719)))
            | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_1714),U_1719)) )
        | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_1719)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK45]),skolemize(U_1715,sK45(U_1719))],[f_458_3]) ).

fof(f_458_5,plain,
    ( ! [U_1720] :
        ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_1720))
        | ! [U_1717] :
            ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK46(U_1720,U_1717)),U_1717))
            & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK46(U_1720,U_1717)),U_1720)) ) )
    & ! [U_1719] :
        ( ! [U_1714] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1714),sK45(U_1719)))
            | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_1714),U_1719)) )
        | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_1719)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK46]),skolemize(U_1716,sK46(U_1720,U_1717))],[f_458_4]) ).

fof(f_458_6,plain,
    ( ! [U_1717,U_1720] :
        ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK46(U_1720,U_1717)),U_1717))
        | ~ sP91(U_1717,U_1720) )
    & ! [U_1717,U_1720] :
        ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK46(U_1720,U_1717)),U_1720))
        | ~ sP91(U_1717,U_1720) )
    & ! [U_1717,U_1720] :
        ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_1720))
        | sP91(U_1717,U_1720) )
    & ! [U_1714,U_1719] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1714),sK45(U_1719)))
        | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_1714),U_1719))
        | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_1719)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP91])],[f_458_5]) ).

cnf(f_458_7,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1714),sK45(U_1719)))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_1714),U_1719))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_1719)) ),
    inference(clausify,[status(thm)],[f_458_6]) ).

cnf(f_458_8,plain,
    ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_1720))
    | sP91(U_1717,U_1720) ),
    inference(clausify,[status(thm)],[f_458_6]) ).

cnf(f_458_9,plain,
    ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK46(U_1720,U_1717)),U_1720))
    | ~ sP91(U_1717,U_1720) ),
    inference(clausify,[status(thm)],[f_458_6]) ).

cnf(f_458_10,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK46(U_1720,U_1717)),U_1717))
    | ~ sP91(U_1717,U_1720) ),
    inference(clausify,[status(thm)],[f_458_6]) ).

fof(f_459_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_388_nat__seg__image__imp__finite]) ).

fof(f_459_2,plain,
    ! [U_1724,U_1723,U_1722,U_1721] :
      ( hBOOL(hAPP(fun(U_1724,bool),bool,finite_finite(U_1724),U_1723))
      | ti(fun(U_1724,bool),U_1723) != hAPP(fun(nat,bool),fun(U_1724,bool),hAPP(fun(nat,U_1724),fun(fun(nat,bool),fun(U_1724,bool)),image(nat,U_1724),U_1722),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_1721))) ),
    inference(variable_rename,[status(thm)],[f_459_1]) ).

fof(f_459_3,plain,
    ! [U_1724,U_1723] :
      ( ! [U_1722,U_1721] : ti(fun(U_1724,bool),U_1723) != hAPP(fun(nat,bool),fun(U_1724,bool),hAPP(fun(nat,U_1724),fun(fun(nat,bool),fun(U_1724,bool)),image(nat,U_1724),U_1722),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_1721)))
      | hBOOL(hAPP(fun(U_1724,bool),bool,finite_finite(U_1724),U_1723)) ),
    inference(miniscope,[status(thm)],[f_459_2]) ).

fof(f_459_4,plain,
    ! [U_1723,U_1722,U_1721,U_1724] :
      ( ti(fun(U_1724,bool),U_1723) != hAPP(fun(nat,bool),fun(U_1724,bool),hAPP(fun(nat,U_1724),fun(fun(nat,bool),fun(U_1724,bool)),image(nat,U_1724),U_1722),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_1721)))
      | hBOOL(hAPP(fun(U_1724,bool),bool,finite_finite(U_1724),U_1723)) ),
    inference(definitional_conversion,[status(esa)],[f_459_3]) ).

cnf(f_459_5,plain,
    ( ti(fun(U_1724,bool),U_1723) != hAPP(fun(nat,bool),fun(U_1724,bool),hAPP(fun(nat,U_1724),fun(fun(nat,bool),fun(U_1724,bool)),image(nat,U_1724),U_1722),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_1721)))
    | hBOOL(hAPP(fun(U_1724,bool),bool,finite_finite(U_1724),U_1723)) ),
    inference(clausify,[status(thm)],[f_459_4]) ).

fof(f_460_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_389_card__Collect__less__nat]) ).

fof(f_460_2,plain,
    ! [U_1725] : 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_1725))) = U_1725,
    inference(variable_rename,[status(thm)],[f_460_1]) ).

fof(f_460_3,plain,
    ! [U_1725] : 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_1725))) = U_1725,
    inference(definitional_conversion,[status(esa)],[f_460_2]) ).

cnf(f_460_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_1725))) = U_1725,
    inference(clausify,[status(thm)],[f_460_3]) ).

fof(f_461_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_390_finite__M__bounded__by__nat]) ).

fof(f_461_2,plain,
    ! [U_1727,U_1726] : 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_1727)),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_1726))))),
    inference(variable_rename,[status(thm)],[f_461_1]) ).

fof(f_461_3,plain,
    ! [U_1726,U_1727] : 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_1727)),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_1726))))),
    inference(definitional_conversion,[status(esa)],[f_461_2]) ).

cnf(f_461_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_1727)),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_1726))))),
    inference(clausify,[status(thm)],[f_461_3]) ).

fof(f_462_1,plain,
    ! [X_a] :
      ( ! [C,D,A_1,B] :
          ( 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),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)) )
      | ~ ordere223160158up_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_391_add__less__le__mono]) ).

fof(f_462_2,plain,
    ! [U_1732] :
      ( ! [U_1731,U_1730,U_1729,U_1728] :
          ( hBOOL(hAPP(U_1732,bool,hAPP(U_1732,fun(U_1732,bool),ord_less(U_1732),hAPP(U_1732,U_1732,hAPP(U_1732,fun(U_1732,U_1732),plus_plus(U_1732),U_1729),U_1731)),hAPP(U_1732,U_1732,hAPP(U_1732,fun(U_1732,U_1732),plus_plus(U_1732),U_1728),U_1730)))
          | ~ hBOOL(hAPP(U_1732,bool,hAPP(U_1732,fun(U_1732,bool),ord_less_eq(U_1732),U_1731),U_1730))
          | ~ hBOOL(hAPP(U_1732,bool,hAPP(U_1732,fun(U_1732,bool),ord_less(U_1732),U_1729),U_1728)) )
      | ~ ordere223160158up_add(U_1732) ),
    inference(variable_rename,[status(thm)],[f_462_1]) ).

fof(f_462_3,plain,
    ! [U_1728,U_1732,U_1729,U_1730,U_1731] :
      ( hBOOL(hAPP(U_1732,bool,hAPP(U_1732,fun(U_1732,bool),ord_less(U_1732),hAPP(U_1732,U_1732,hAPP(U_1732,fun(U_1732,U_1732),plus_plus(U_1732),U_1729),U_1731)),hAPP(U_1732,U_1732,hAPP(U_1732,fun(U_1732,U_1732),plus_plus(U_1732),U_1728),U_1730)))
      | ~ hBOOL(hAPP(U_1732,bool,hAPP(U_1732,fun(U_1732,bool),ord_less_eq(U_1732),U_1731),U_1730))
      | ~ hBOOL(hAPP(U_1732,bool,hAPP(U_1732,fun(U_1732,bool),ord_less(U_1732),U_1729),U_1728))
      | ~ ordere223160158up_add(U_1732) ),
    inference(definitional_conversion,[status(esa)],[f_462_2]) ).

cnf(f_462_4,plain,
    ( hBOOL(hAPP(U_1732,bool,hAPP(U_1732,fun(U_1732,bool),ord_less(U_1732),hAPP(U_1732,U_1732,hAPP(U_1732,fun(U_1732,U_1732),plus_plus(U_1732),U_1729),U_1731)),hAPP(U_1732,U_1732,hAPP(U_1732,fun(U_1732,U_1732),plus_plus(U_1732),U_1728),U_1730)))
    | ~ hBOOL(hAPP(U_1732,bool,hAPP(U_1732,fun(U_1732,bool),ord_less_eq(U_1732),U_1731),U_1730))
    | ~ hBOOL(hAPP(U_1732,bool,hAPP(U_1732,fun(U_1732,bool),ord_less(U_1732),U_1729),U_1728))
    | ~ ordere223160158up_add(U_1732) ),
    inference(clausify,[status(thm)],[f_462_3]) ).

fof(f_463_1,plain,
    ! [X_a] :
      ( ! [C,D,A_1,B] :
          ( 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),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)) )
      | ~ ordere223160158up_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_392_add__le__less__mono]) ).

fof(f_463_2,plain,
    ! [U_1737] :
      ( ! [U_1736,U_1735,U_1734,U_1733] :
          ( hBOOL(hAPP(U_1737,bool,hAPP(U_1737,fun(U_1737,bool),ord_less(U_1737),hAPP(U_1737,U_1737,hAPP(U_1737,fun(U_1737,U_1737),plus_plus(U_1737),U_1734),U_1736)),hAPP(U_1737,U_1737,hAPP(U_1737,fun(U_1737,U_1737),plus_plus(U_1737),U_1733),U_1735)))
          | ~ hBOOL(hAPP(U_1737,bool,hAPP(U_1737,fun(U_1737,bool),ord_less(U_1737),U_1736),U_1735))
          | ~ hBOOL(hAPP(U_1737,bool,hAPP(U_1737,fun(U_1737,bool),ord_less_eq(U_1737),U_1734),U_1733)) )
      | ~ ordere223160158up_add(U_1737) ),
    inference(variable_rename,[status(thm)],[f_463_1]) ).

fof(f_463_3,plain,
    ! [U_1735,U_1737,U_1734,U_1733,U_1736] :
      ( hBOOL(hAPP(U_1737,bool,hAPP(U_1737,fun(U_1737,bool),ord_less(U_1737),hAPP(U_1737,U_1737,hAPP(U_1737,fun(U_1737,U_1737),plus_plus(U_1737),U_1734),U_1736)),hAPP(U_1737,U_1737,hAPP(U_1737,fun(U_1737,U_1737),plus_plus(U_1737),U_1733),U_1735)))
      | ~ hBOOL(hAPP(U_1737,bool,hAPP(U_1737,fun(U_1737,bool),ord_less(U_1737),U_1736),U_1735))
      | ~ hBOOL(hAPP(U_1737,bool,hAPP(U_1737,fun(U_1737,bool),ord_less_eq(U_1737),U_1734),U_1733))
      | ~ ordere223160158up_add(U_1737) ),
    inference(definitional_conversion,[status(esa)],[f_463_2]) ).

cnf(f_463_4,plain,
    ( hBOOL(hAPP(U_1737,bool,hAPP(U_1737,fun(U_1737,bool),ord_less(U_1737),hAPP(U_1737,U_1737,hAPP(U_1737,fun(U_1737,U_1737),plus_plus(U_1737),U_1734),U_1736)),hAPP(U_1737,U_1737,hAPP(U_1737,fun(U_1737,U_1737),plus_plus(U_1737),U_1733),U_1735)))
    | ~ hBOOL(hAPP(U_1737,bool,hAPP(U_1737,fun(U_1737,bool),ord_less(U_1737),U_1736),U_1735))
    | ~ hBOOL(hAPP(U_1737,bool,hAPP(U_1737,fun(U_1737,bool),ord_less_eq(U_1737),U_1734),U_1733))
    | ~ ordere223160158up_add(U_1737) ),
    inference(clausify,[status(thm)],[f_463_3]) ).

fof(f_464_1,plain,
    ! [I_2,M_1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),M_1)))),
    inference(fof_nnf,[status(thm)],[fact_393_less__add__Suc1]) ).

fof(f_464_2,plain,
    ! [U_1739,U_1738] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1739),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1739),U_1738)))),
    inference(variable_rename,[status(thm)],[f_464_1]) ).

fof(f_464_3,plain,
    ! [U_1738,U_1739] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1739),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1739),U_1738)))),
    inference(definitional_conversion,[status(esa)],[f_464_2]) ).

cnf(f_464_4,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1739),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1739),U_1738)))),
    inference(clausify,[status(thm)],[f_464_3]) ).

fof(f_465_1,plain,
    ! [I_2,M_1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),I_2)))),
    inference(fof_nnf,[status(thm)],[fact_394_less__add__Suc2]) ).

fof(f_465_2,plain,
    ! [U_1741,U_1740] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1741),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1740),U_1741)))),
    inference(variable_rename,[status(thm)],[f_465_1]) ).

fof(f_465_3,plain,
    ! [U_1741,U_1740] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1741),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1740),U_1741)))),
    inference(definitional_conversion,[status(esa)],[f_465_2]) ).

cnf(f_465_4,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1741),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1740),U_1741)))),
    inference(clausify,[status(thm)],[f_465_3]) ).

fof(f_466_1,plain,
    ! [M,Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))
        | ! [K_2] : Na != hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_2)) )
      & ( ? [K_2] : Na = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_2))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_395_less__iff__Suc__add]) ).

fof(f_466_2,plain,
    ! [U_1745,U_1744] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1745),U_1744))
        | ! [U_1743] : U_1744 != hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1745),U_1743)) )
      & ( ? [U_1742] : U_1744 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1745),U_1742))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1745),U_1744)) ) ),
    inference(variable_rename,[status(thm)],[f_466_1]) ).

fof(f_466_3,plain,
    ( ! [U_1749,U_1747] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1749),U_1747))
        | ! [U_1743] : U_1747 != hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1749),U_1743)) )
    & ! [U_1748,U_1746] :
        ( ? [U_1742] : U_1746 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1748),U_1742))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1748),U_1746)) ) ),
    inference(miniscope,[status(thm)],[f_466_2]) ).

fof(f_466_4,plain,
    ( ! [U_1749,U_1747] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1749),U_1747))
        | ! [U_1743] : U_1747 != hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1749),U_1743)) )
    & ! [U_1748,U_1746] :
        ( U_1746 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1748),sK47(U_1748,U_1746)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1748),U_1746)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK47]),skolemize(U_1742,sK47(U_1748,U_1746))],[f_466_3]) ).

fof(f_466_5,plain,
    ( ! [U_1747,U_1743,U_1749] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1749),U_1747))
        | U_1747 != hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1749),U_1743)) )
    & ! [U_1746,U_1748] :
        ( U_1746 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1748),sK47(U_1748,U_1746)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1748),U_1746)) ) ),
    inference(definitional_conversion,[status(esa)],[f_466_4]) ).

cnf(f_466_6,plain,
    ( U_1746 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1748),sK47(U_1748,U_1746)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1748),U_1746)) ),
    inference(clausify,[status(thm)],[f_466_5]) ).

cnf(f_466_7,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1749),U_1747))
    | U_1747 != hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1749),U_1743)) ),
    inference(clausify,[status(thm)],[f_466_5]) ).

fof(f_467_1,plain,
    ! [Na,M] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Na)),M)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Na)),M))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M)) ) ),
    inference(fof_nnf,[status(thm)],[fact_396_less__eq__Suc__le]) ).

fof(f_467_2,plain,
    ! [U_1751,U_1750] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1751),U_1750))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1751)),U_1750)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1751)),U_1750))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1751),U_1750)) ) ),
    inference(variable_rename,[status(thm)],[f_467_1]) ).

fof(f_467_3,plain,
    ( ! [U_1755,U_1753] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1755),U_1753))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1755)),U_1753)) )
    & ! [U_1754,U_1752] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1754)),U_1752))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1754),U_1752)) ) ),
    inference(miniscope,[status(thm)],[f_467_2]) ).

fof(f_467_4,plain,
    ( ! [U_1753,U_1755] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1755),U_1753))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1755)),U_1753)) )
    & ! [U_1752,U_1754] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1754)),U_1752))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1754),U_1752)) ) ),
    inference(definitional_conversion,[status(esa)],[f_467_3]) ).

cnf(f_467_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1754)),U_1752))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1754),U_1752)) ),
    inference(clausify,[status(thm)],[f_467_4]) ).

cnf(f_467_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1755),U_1753))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1755)),U_1753)) ),
    inference(clausify,[status(thm)],[f_467_4]) ).

fof(f_468_1,plain,
    ! [M,Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,Na)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_397_less__Suc__eq__le]) ).

fof(f_468_2,plain,
    ! [U_1757,U_1756] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1757),hAPP(nat,nat,suc,U_1756)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1757),U_1756)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1757),U_1756))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1757),hAPP(nat,nat,suc,U_1756))) ) ),
    inference(variable_rename,[status(thm)],[f_468_1]) ).

fof(f_468_3,plain,
    ( ! [U_1761,U_1759] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1761),hAPP(nat,nat,suc,U_1759)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1761),U_1759)) )
    & ! [U_1760,U_1758] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1760),U_1758))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1760),hAPP(nat,nat,suc,U_1758))) ) ),
    inference(miniscope,[status(thm)],[f_468_2]) ).

fof(f_468_4,plain,
    ( ! [U_1761,U_1759] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1761),hAPP(nat,nat,suc,U_1759)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1761),U_1759)) )
    & ! [U_1758,U_1760] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1760),U_1758))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1760),hAPP(nat,nat,suc,U_1758))) ) ),
    inference(definitional_conversion,[status(esa)],[f_468_3]) ).

cnf(f_468_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1760),U_1758))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1760),hAPP(nat,nat,suc,U_1758))) ),
    inference(clausify,[status(thm)],[f_468_4]) ).

cnf(f_468_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1761),hAPP(nat,nat,suc,U_1759)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1761),U_1759)) ),
    inference(clausify,[status(thm)],[f_468_4]) ).

fof(f_469_1,plain,
    ! [M,Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M)),Na))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M)),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_398_Suc__le__eq]) ).

fof(f_469_2,plain,
    ! [U_1763,U_1762] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1763)),U_1762))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1763),U_1762)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1763),U_1762))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1763)),U_1762)) ) ),
    inference(variable_rename,[status(thm)],[f_469_1]) ).

fof(f_469_3,plain,
    ( ! [U_1767,U_1765] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1767)),U_1765))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1767),U_1765)) )
    & ! [U_1766,U_1764] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1766),U_1764))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1766)),U_1764)) ) ),
    inference(miniscope,[status(thm)],[f_469_2]) ).

fof(f_469_4,plain,
    ( ! [U_1765,U_1767] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1767)),U_1765))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1767),U_1765)) )
    & ! [U_1766,U_1764] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1766),U_1764))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1766)),U_1764)) ) ),
    inference(definitional_conversion,[status(esa)],[f_469_3]) ).

cnf(f_469_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1766),U_1764))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1766)),U_1764)) ),
    inference(clausify,[status(thm)],[f_469_4]) ).

cnf(f_469_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1767)),U_1765))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1767),U_1765)) ),
    inference(clausify,[status(thm)],[f_469_4]) ).

fof(f_470_1,plain,
    ! [M_1,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)) ),
    inference(fof_nnf,[status(thm)],[fact_399_le__imp__less__Suc]) ).

fof(f_470_2,plain,
    ! [U_1769,U_1768] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1769),hAPP(nat,nat,suc,U_1768)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1769),U_1768)) ),
    inference(variable_rename,[status(thm)],[f_470_1]) ).

fof(f_470_3,plain,
    ! [U_1768,U_1769] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1769),hAPP(nat,nat,suc,U_1768)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1769),U_1768)) ),
    inference(definitional_conversion,[status(esa)],[f_470_2]) ).

cnf(f_470_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1769),hAPP(nat,nat,suc,U_1768)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1769),U_1768)) ),
    inference(clausify,[status(thm)],[f_470_3]) ).

fof(f_471_1,plain,
    ! [M_1,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M_1)),N))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)) ),
    inference(fof_nnf,[status(thm)],[fact_400_Suc__leI]) ).

fof(f_471_2,plain,
    ! [U_1771,U_1770] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1771)),U_1770))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1771),U_1770)) ),
    inference(variable_rename,[status(thm)],[f_471_1]) ).

fof(f_471_3,plain,
    ! [U_1770,U_1771] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1771)),U_1770))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1771),U_1770)) ),
    inference(definitional_conversion,[status(esa)],[f_471_2]) ).

cnf(f_471_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1771)),U_1770))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1771),U_1770)) ),
    inference(clausify,[status(thm)],[f_471_3]) ).

fof(f_472_1,plain,
    ! [M,Na] :
      ( ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,M)))
          | Na != M )
        & ( Na = M
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,M))) ) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)) ),
    inference(fof_nnf,[status(thm)],[fact_401_le__less__Suc__eq]) ).

fof(f_472_2,plain,
    ! [U_1773,U_1772] :
      ( ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1772),hAPP(nat,nat,suc,U_1773)))
          | U_1772 != U_1773 )
        & ( U_1772 = U_1773
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1772),hAPP(nat,nat,suc,U_1773))) ) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1773),U_1772)) ),
    inference(variable_rename,[status(thm)],[f_472_1]) ).

fof(f_472_3,plain,
    ( ! [U_1773,U_1772] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1772),hAPP(nat,nat,suc,U_1773)))
        | U_1772 != U_1773
        | ~ sP92(U_1773,U_1772) )
    & ! [U_1773,U_1772] :
        ( U_1772 = U_1773
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1772),hAPP(nat,nat,suc,U_1773)))
        | ~ sP92(U_1773,U_1772) )
    & ! [U_1773,U_1772] :
        ( sP92(U_1773,U_1772)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1773),U_1772)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP92])],[f_472_2]) ).

cnf(f_472_4,plain,
    ( sP92(U_1773,U_1772)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1773),U_1772)) ),
    inference(clausify,[status(thm)],[f_472_3]) ).

cnf(f_472_5,plain,
    ( U_1772 = U_1773
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1772),hAPP(nat,nat,suc,U_1773)))
    | ~ sP92(U_1773,U_1772) ),
    inference(clausify,[status(thm)],[f_472_3]) ).

cnf(f_472_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1772),hAPP(nat,nat,suc,U_1773)))
    | U_1772 != U_1773
    | ~ sP92(U_1773,U_1772) ),
    inference(clausify,[status(thm)],[f_472_3]) ).

fof(f_473_1,plain,
    ! [M_1,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M_1)),N)) ),
    inference(fof_nnf,[status(thm)],[fact_402_Suc__le__lessD]) ).

fof(f_473_2,plain,
    ! [U_1775,U_1774] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1775),U_1774))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1775)),U_1774)) ),
    inference(variable_rename,[status(thm)],[f_473_1]) ).

fof(f_473_3,plain,
    ! [U_1775,U_1774] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1775),U_1774))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1775)),U_1774)) ),
    inference(definitional_conversion,[status(esa)],[f_473_2]) ).

cnf(f_473_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1775),U_1774))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1775)),U_1774)) ),
    inference(clausify,[status(thm)],[f_473_3]) ).

fof(f_474_1,plain,
    ! [M_1,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_1),N)),hAPP(nat,nat,suc,M_1))),
    inference(fof_nnf,[status(thm)],[fact_403_diff__less__Suc]) ).

fof(f_474_2,plain,
    ! [U_1777,U_1776] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1777),U_1776)),hAPP(nat,nat,suc,U_1777))),
    inference(variable_rename,[status(thm)],[f_474_1]) ).

fof(f_474_3,plain,
    ! [U_1776,U_1777] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1777),U_1776)),hAPP(nat,nat,suc,U_1777))),
    inference(definitional_conversion,[status(esa)],[f_474_2]) ).

cnf(f_474_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_1777),U_1776)),hAPP(nat,nat,suc,U_1777))),
    inference(clausify,[status(thm)],[f_474_3]) ).

fof(f_475_1,plain,
    ! [I_1,J_1,K] :
      ( ( 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)))
        | ~ 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)),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)),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))) ) ),
    inference(fof_nnf,[status(thm)],[fact_404_less__diff__conv]) ).

fof(f_475_2,plain,
    ! [U_1780,U_1779,U_1778] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1780),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1779),U_1778)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1780),U_1778)),U_1779)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1780),U_1778)),U_1779))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1780),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1779),U_1778))) ) ),
    inference(variable_rename,[status(thm)],[f_475_1]) ).

fof(f_475_3,plain,
    ( ! [U_1786,U_1784,U_1782] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1786),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1784),U_1782)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1786),U_1782)),U_1784)) )
    & ! [U_1785,U_1783,U_1781] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1785),U_1781)),U_1783))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1785),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1783),U_1781))) ) ),
    inference(miniscope,[status(thm)],[f_475_2]) ).

fof(f_475_4,plain,
    ( ! [U_1784,U_1782,U_1786] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1786),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1784),U_1782)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1786),U_1782)),U_1784)) )
    & ! [U_1783,U_1781,U_1785] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1785),U_1781)),U_1783))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1785),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1783),U_1781))) ) ),
    inference(definitional_conversion,[status(esa)],[f_475_3]) ).

cnf(f_475_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_1785),U_1781)),U_1783))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1785),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1783),U_1781))) ),
    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_1786),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1784),U_1782)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1786),U_1782)),U_1784)) ),
    inference(clausify,[status(thm)],[f_475_4]) ).

fof(f_476_1,plain,
    ! [M_1,N] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N)) = M_1
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)) ),
    inference(fof_nnf,[status(thm)],[fact_405_add__diff__inverse]) ).

fof(f_476_2,plain,
    ! [U_1788,U_1787] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1787),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1788),U_1787)) = U_1788
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1788),U_1787)) ),
    inference(variable_rename,[status(thm)],[f_476_1]) ).

fof(f_476_3,plain,
    ! [U_1788,U_1787] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1787),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1788),U_1787)) = U_1788
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1788),U_1787)) ),
    inference(definitional_conversion,[status(esa)],[f_476_2]) ).

cnf(f_476_4,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1787),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1788),U_1787)) = U_1788
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1788),U_1787)) ),
    inference(clausify,[status(thm)],[f_476_3]) ).

fof(f_477_1,plain,
    ! [C,A_1,B] :
      ( 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),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)) ),
    inference(fof_nnf,[status(thm)],[fact_406_diff__less__mono]) ).

fof(f_477_2,plain,
    ! [U_1791,U_1790,U_1789] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1790),U_1791)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1789),U_1791)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1791),U_1790))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1790),U_1789)) ),
    inference(variable_rename,[status(thm)],[f_477_1]) ).

fof(f_477_3,plain,
    ! [U_1790,U_1789,U_1791] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1790),U_1791)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1789),U_1791)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1791),U_1790))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1790),U_1789)) ),
    inference(definitional_conversion,[status(esa)],[f_477_2]) ).

cnf(f_477_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_1790),U_1791)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1789),U_1791)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1791),U_1790))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1790),U_1789)) ),
    inference(clausify,[status(thm)],[f_477_3]) ).

fof(f_478_1,plain,
    ! [Na,K,M] :
      ( ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Na),K)))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)) )
        & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),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),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Na),K))) ) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),Na))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),M)) ),
    inference(fof_nnf,[status(thm)],[fact_407_less__diff__iff]) ).

fof(f_478_2,plain,
    ! [U_1794,U_1793,U_1792] :
      ( ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1792),U_1793)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1794),U_1793)))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1792),U_1794)) )
        & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1792),U_1794))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1792),U_1793)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1794),U_1793))) ) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1793),U_1794))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1793),U_1792)) ),
    inference(variable_rename,[status(thm)],[f_478_1]) ).

fof(f_478_3,plain,
    ( ! [U_1792,U_1793,U_1794] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1792),U_1793)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1794),U_1793)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1792),U_1794))
        | ~ sP93(U_1792,U_1793,U_1794) )
    & ! [U_1792,U_1793,U_1794] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1792),U_1794))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1792),U_1793)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1794),U_1793)))
        | ~ sP93(U_1792,U_1793,U_1794) )
    & ! [U_1792,U_1793,U_1794] :
        ( sP93(U_1792,U_1793,U_1794)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1793),U_1794))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1793),U_1792)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP93])],[f_478_2]) ).

cnf(f_478_4,plain,
    ( sP93(U_1792,U_1793,U_1794)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1793),U_1794))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1793),U_1792)) ),
    inference(clausify,[status(thm)],[f_478_3]) ).

cnf(f_478_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1792),U_1794))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1792),U_1793)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1794),U_1793)))
    | ~ sP93(U_1792,U_1793,U_1794) ),
    inference(clausify,[status(thm)],[f_478_3]) ).

cnf(f_478_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_1792),U_1793)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1794),U_1793)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1792),U_1794))
    | ~ sP93(U_1792,U_1793,U_1794) ),
    inference(clausify,[status(thm)],[f_478_3]) ).

fof(f_479_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_408_less__eq__Suc__le__raw]) ).

fof(f_479_2,plain,
    ! [U_1795] : hAPP(nat,fun(nat,bool),ord_less(nat),U_1795) = hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1795)),
    inference(variable_rename,[status(thm)],[f_479_1]) ).

fof(f_479_3,plain,
    ! [U_1795] : hAPP(nat,fun(nat,bool),ord_less(nat),U_1795) = hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1795)),
    inference(definitional_conversion,[status(esa)],[f_479_2]) ).

cnf(f_479_4,plain,
    hAPP(nat,fun(nat,bool),ord_less(nat),U_1795) = hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1795)),
    inference(clausify,[status(thm)],[f_479_3]) ).

fof(f_480_1,plain,
    ! [M,K,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)),K)),hAPP(nat,nat,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K))))
      | ? [M_2,N_1] :
          ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,F,M_2)),hAPP(nat,nat,F,N_1)))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_409_mono__nat__linear__lb]) ).

fof(f_480_2,plain,
    ! [U_1800,U_1799,U_1798] :
      ( 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_1798,U_1800)),U_1799)),hAPP(nat,nat,U_1798,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1800),U_1799))))
      | ? [U_1797,U_1796] :
          ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,U_1798,U_1797)),hAPP(nat,nat,U_1798,U_1796)))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1797),U_1796)) ) ),
    inference(variable_rename,[status(thm)],[f_480_1]) ).

fof(f_480_3,plain,
    ! [U_1800,U_1799,U_1798] :
      ( 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_1798,U_1800)),U_1799)),hAPP(nat,nat,U_1798,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1800),U_1799))))
      | ? [U_1796] :
          ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,U_1798,sK48(U_1800,U_1799,U_1798))),hAPP(nat,nat,U_1798,U_1796)))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK48(U_1800,U_1799,U_1798)),U_1796)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK48]),skolemize(U_1797,sK48(U_1800,U_1799,U_1798))],[f_480_2]) ).

fof(f_480_4,plain,
    ! [U_1800,U_1799,U_1798] :
      ( 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_1798,U_1800)),U_1799)),hAPP(nat,nat,U_1798,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1800),U_1799))))
      | ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,U_1798,sK48(U_1800,U_1799,U_1798))),hAPP(nat,nat,U_1798,sK49(U_1800,U_1799,U_1798))))
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK48(U_1800,U_1799,U_1798)),sK49(U_1800,U_1799,U_1798))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK49]),skolemize(U_1796,sK49(U_1800,U_1799,U_1798))],[f_480_3]) ).

fof(f_480_5,plain,
    ( ! [U_1798,U_1799,U_1800] :
        ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,U_1798,sK48(U_1800,U_1799,U_1798))),hAPP(nat,nat,U_1798,sK49(U_1800,U_1799,U_1798))))
        | ~ sP94(U_1798,U_1799,U_1800) )
    & ! [U_1798,U_1799,U_1800] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK48(U_1800,U_1799,U_1798)),sK49(U_1800,U_1799,U_1798)))
        | ~ sP94(U_1798,U_1799,U_1800) )
    & ! [U_1798,U_1799,U_1800] :
        ( 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_1798,U_1800)),U_1799)),hAPP(nat,nat,U_1798,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1800),U_1799))))
        | sP94(U_1798,U_1799,U_1800) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP94])],[f_480_4]) ).

cnf(f_480_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_1798,U_1800)),U_1799)),hAPP(nat,nat,U_1798,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1800),U_1799))))
    | sP94(U_1798,U_1799,U_1800) ),
    inference(clausify,[status(thm)],[f_480_5]) ).

cnf(f_480_7,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK48(U_1800,U_1799,U_1798)),sK49(U_1800,U_1799,U_1798)))
    | ~ sP94(U_1798,U_1799,U_1800) ),
    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_1798,sK48(U_1800,U_1799,U_1798))),hAPP(nat,nat,U_1798,sK49(U_1800,U_1799,U_1798))))
    | ~ sP94(U_1798,U_1799,U_1800) ),
    inference(clausify,[status(thm)],[f_480_5]) ).

fof(f_481_1,plain,
    ! [Pa,I_1,J_1] :
      ( hBOOL(hAPP(nat,bool,Pa,I_1))
      | ? [I] :
          ( ~ hBOOL(hAPP(nat,bool,Pa,I))
          & hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,I)))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),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_410_inc__induct]) ).

fof(f_481_2,plain,
    ! [U_1804,U_1803,U_1802] :
      ( hBOOL(hAPP(nat,bool,U_1804,U_1803))
      | ? [U_1801] :
          ( ~ hBOOL(hAPP(nat,bool,U_1804,U_1801))
          & hBOOL(hAPP(nat,bool,U_1804,hAPP(nat,nat,suc,U_1801)))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1801),U_1802)) )
      | ~ hBOOL(hAPP(nat,bool,U_1804,U_1802))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1803),U_1802)) ),
    inference(variable_rename,[status(thm)],[f_481_1]) ).

fof(f_481_3,plain,
    ! [U_1804,U_1803,U_1802] :
      ( hBOOL(hAPP(nat,bool,U_1804,U_1803))
      | ( ~ hBOOL(hAPP(nat,bool,U_1804,sK50(U_1804,U_1803,U_1802)))
        & hBOOL(hAPP(nat,bool,U_1804,hAPP(nat,nat,suc,sK50(U_1804,U_1803,U_1802))))
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK50(U_1804,U_1803,U_1802)),U_1802)) )
      | ~ hBOOL(hAPP(nat,bool,U_1804,U_1802))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1803),U_1802)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK50]),skolemize(U_1801,sK50(U_1804,U_1803,U_1802))],[f_481_2]) ).

fof(f_481_4,plain,
    ( ! [U_1803,U_1804,U_1802] :
        ( ~ hBOOL(hAPP(nat,bool,U_1804,sK50(U_1804,U_1803,U_1802)))
        | ~ sP95(U_1803,U_1804,U_1802) )
    & ! [U_1803,U_1804,U_1802] :
        ( hBOOL(hAPP(nat,bool,U_1804,hAPP(nat,nat,suc,sK50(U_1804,U_1803,U_1802))))
        | ~ sP95(U_1803,U_1804,U_1802) )
    & ! [U_1803,U_1804,U_1802] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK50(U_1804,U_1803,U_1802)),U_1802))
        | ~ sP95(U_1803,U_1804,U_1802) )
    & ! [U_1803,U_1804,U_1802] :
        ( hBOOL(hAPP(nat,bool,U_1804,U_1803))
        | sP95(U_1803,U_1804,U_1802)
        | ~ hBOOL(hAPP(nat,bool,U_1804,U_1802))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1803),U_1802)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP95])],[f_481_3]) ).

cnf(f_481_5,plain,
    ( hBOOL(hAPP(nat,bool,U_1804,U_1803))
    | sP95(U_1803,U_1804,U_1802)
    | ~ hBOOL(hAPP(nat,bool,U_1804,U_1802))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1803),U_1802)) ),
    inference(clausify,[status(thm)],[f_481_4]) ).

cnf(f_481_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK50(U_1804,U_1803,U_1802)),U_1802))
    | ~ sP95(U_1803,U_1804,U_1802) ),
    inference(clausify,[status(thm)],[f_481_4]) ).

cnf(f_481_7,plain,
    ( hBOOL(hAPP(nat,bool,U_1804,hAPP(nat,nat,suc,sK50(U_1804,U_1803,U_1802))))
    | ~ sP95(U_1803,U_1804,U_1802) ),
    inference(clausify,[status(thm)],[f_481_4]) ).

cnf(f_481_8,plain,
    ( ~ hBOOL(hAPP(nat,bool,U_1804,sK50(U_1804,U_1803,U_1802)))
    | ~ sP95(U_1803,U_1804,U_1802) ),
    inference(clausify,[status(thm)],[f_481_4]) ).

fof(f_482_1,plain,
    ! [M_1,N] :
      ( ? [K_2] : N = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_2))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)) ),
    inference(fof_nnf,[status(thm)],[fact_411_less__imp__Suc__add]) ).

fof(f_482_2,plain,
    ! [U_1807,U_1806] :
      ( ? [U_1805] : U_1806 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1807),U_1805))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1807),U_1806)) ),
    inference(variable_rename,[status(thm)],[f_482_1]) ).

fof(f_482_3,plain,
    ! [U_1807,U_1806] :
      ( U_1806 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1807),sK51(U_1807,U_1806)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1807),U_1806)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK51]),skolemize(U_1805,sK51(U_1807,U_1806))],[f_482_2]) ).

fof(f_482_4,plain,
    ! [U_1807,U_1806] :
      ( U_1806 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1807),sK51(U_1807,U_1806)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1807),U_1806)) ),
    inference(definitional_conversion,[status(esa)],[f_482_3]) ).

cnf(f_482_5,plain,
    ( U_1806 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1807),sK51(U_1807,U_1806)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1807),U_1806)) ),
    inference(clausify,[status(thm)],[f_482_4]) ).

fof(f_483_1,plain,
    ! [X_b] :
      ( ! [Na,M,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)))
              | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M)) )
            & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M))
              | ~ 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))) ) )
          | ? [N_1] : ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(nat,X_b,F,N_1)),hAPP(nat,X_b,F,hAPP(nat,nat,suc,N_1)))) )
      | ~ order(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_412_lift__Suc__mono__less__iff]) ).

fof(f_483_2,plain,
    ! [U_1812] :
      ( ! [U_1811,U_1810,U_1809] :
          ( ( ( hBOOL(hAPP(U_1812,bool,hAPP(U_1812,fun(U_1812,bool),ord_less(U_1812),hAPP(nat,U_1812,U_1809,U_1811)),hAPP(nat,U_1812,U_1809,U_1810)))
              | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1811),U_1810)) )
            & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1811),U_1810))
              | ~ hBOOL(hAPP(U_1812,bool,hAPP(U_1812,fun(U_1812,bool),ord_less(U_1812),hAPP(nat,U_1812,U_1809,U_1811)),hAPP(nat,U_1812,U_1809,U_1810))) ) )
          | ? [U_1808] : ~ hBOOL(hAPP(U_1812,bool,hAPP(U_1812,fun(U_1812,bool),ord_less(U_1812),hAPP(nat,U_1812,U_1809,U_1808)),hAPP(nat,U_1812,U_1809,hAPP(nat,nat,suc,U_1808)))) )
      | ~ order(U_1812) ),
    inference(variable_rename,[status(thm)],[f_483_1]) ).

fof(f_483_3,plain,
    ! [U_1812] :
      ( ! [U_1811,U_1810,U_1809] :
          ( ( ( hBOOL(hAPP(U_1812,bool,hAPP(U_1812,fun(U_1812,bool),ord_less(U_1812),hAPP(nat,U_1812,U_1809,U_1811)),hAPP(nat,U_1812,U_1809,U_1810)))
              | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1811),U_1810)) )
            & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1811),U_1810))
              | ~ hBOOL(hAPP(U_1812,bool,hAPP(U_1812,fun(U_1812,bool),ord_less(U_1812),hAPP(nat,U_1812,U_1809,U_1811)),hAPP(nat,U_1812,U_1809,U_1810))) ) )
          | ~ hBOOL(hAPP(U_1812,bool,hAPP(U_1812,fun(U_1812,bool),ord_less(U_1812),hAPP(nat,U_1812,U_1809,sK52(U_1812,U_1811,U_1810,U_1809))),hAPP(nat,U_1812,U_1809,hAPP(nat,nat,suc,sK52(U_1812,U_1811,U_1810,U_1809))))) )
      | ~ order(U_1812) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK52]),skolemize(U_1808,sK52(U_1812,U_1811,U_1810,U_1809))],[f_483_2]) ).

fof(f_483_4,plain,
    ( ! [U_1809,U_1812,U_1810,U_1811] :
        ( hBOOL(hAPP(U_1812,bool,hAPP(U_1812,fun(U_1812,bool),ord_less(U_1812),hAPP(nat,U_1812,U_1809,U_1811)),hAPP(nat,U_1812,U_1809,U_1810)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1811),U_1810))
        | ~ sP96(U_1809,U_1812,U_1810,U_1811) )
    & ! [U_1809,U_1812,U_1810,U_1811] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1811),U_1810))
        | ~ hBOOL(hAPP(U_1812,bool,hAPP(U_1812,fun(U_1812,bool),ord_less(U_1812),hAPP(nat,U_1812,U_1809,U_1811)),hAPP(nat,U_1812,U_1809,U_1810)))
        | ~ sP96(U_1809,U_1812,U_1810,U_1811) )
    & ! [U_1809,U_1812,U_1810,U_1811] :
        ( sP96(U_1809,U_1812,U_1810,U_1811)
        | ~ hBOOL(hAPP(U_1812,bool,hAPP(U_1812,fun(U_1812,bool),ord_less(U_1812),hAPP(nat,U_1812,U_1809,sK52(U_1812,U_1811,U_1810,U_1809))),hAPP(nat,U_1812,U_1809,hAPP(nat,nat,suc,sK52(U_1812,U_1811,U_1810,U_1809)))))
        | ~ order(U_1812) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP96])],[f_483_3]) ).

cnf(f_483_5,plain,
    ( sP96(U_1809,U_1812,U_1810,U_1811)
    | ~ hBOOL(hAPP(U_1812,bool,hAPP(U_1812,fun(U_1812,bool),ord_less(U_1812),hAPP(nat,U_1812,U_1809,sK52(U_1812,U_1811,U_1810,U_1809))),hAPP(nat,U_1812,U_1809,hAPP(nat,nat,suc,sK52(U_1812,U_1811,U_1810,U_1809)))))
    | ~ order(U_1812) ),
    inference(clausify,[status(thm)],[f_483_4]) ).

cnf(f_483_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1811),U_1810))
    | ~ hBOOL(hAPP(U_1812,bool,hAPP(U_1812,fun(U_1812,bool),ord_less(U_1812),hAPP(nat,U_1812,U_1809,U_1811)),hAPP(nat,U_1812,U_1809,U_1810)))
    | ~ sP96(U_1809,U_1812,U_1810,U_1811) ),
    inference(clausify,[status(thm)],[f_483_4]) ).

cnf(f_483_7,plain,
    ( hBOOL(hAPP(U_1812,bool,hAPP(U_1812,fun(U_1812,bool),ord_less(U_1812),hAPP(nat,U_1812,U_1809,U_1811)),hAPP(nat,U_1812,U_1809,U_1810)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1811),U_1810))
    | ~ sP96(U_1809,U_1812,U_1810,U_1811) ),
    inference(clausify,[status(thm)],[f_483_4]) ).

fof(f_484_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_1] : ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(nat,X_b,F,N_1)),hAPP(nat,X_b,F,hAPP(nat,nat,suc,N_1)))) )
      | ~ order(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_413_lift__Suc__mono__less]) ).

fof(f_484_2,plain,
    ! [U_1817] :
      ( ! [U_1816,U_1815,U_1814] :
          ( hBOOL(hAPP(U_1817,bool,hAPP(U_1817,fun(U_1817,bool),ord_less(U_1817),hAPP(nat,U_1817,U_1814,U_1816)),hAPP(nat,U_1817,U_1814,U_1815)))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1816),U_1815))
          | ? [U_1813] : ~ hBOOL(hAPP(U_1817,bool,hAPP(U_1817,fun(U_1817,bool),ord_less(U_1817),hAPP(nat,U_1817,U_1814,U_1813)),hAPP(nat,U_1817,U_1814,hAPP(nat,nat,suc,U_1813)))) )
      | ~ order(U_1817) ),
    inference(variable_rename,[status(thm)],[f_484_1]) ).

fof(f_484_3,plain,
    ! [U_1817] :
      ( ! [U_1816,U_1815,U_1814] :
          ( hBOOL(hAPP(U_1817,bool,hAPP(U_1817,fun(U_1817,bool),ord_less(U_1817),hAPP(nat,U_1817,U_1814,U_1816)),hAPP(nat,U_1817,U_1814,U_1815)))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1816),U_1815))
          | ~ hBOOL(hAPP(U_1817,bool,hAPP(U_1817,fun(U_1817,bool),ord_less(U_1817),hAPP(nat,U_1817,U_1814,sK53(U_1817,U_1816,U_1815,U_1814))),hAPP(nat,U_1817,U_1814,hAPP(nat,nat,suc,sK53(U_1817,U_1816,U_1815,U_1814))))) )
      | ~ order(U_1817) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK53]),skolemize(U_1813,sK53(U_1817,U_1816,U_1815,U_1814))],[f_484_2]) ).

fof(f_484_4,plain,
    ! [U_1816,U_1815,U_1814,U_1817] :
      ( hBOOL(hAPP(U_1817,bool,hAPP(U_1817,fun(U_1817,bool),ord_less(U_1817),hAPP(nat,U_1817,U_1814,U_1816)),hAPP(nat,U_1817,U_1814,U_1815)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1816),U_1815))
      | ~ hBOOL(hAPP(U_1817,bool,hAPP(U_1817,fun(U_1817,bool),ord_less(U_1817),hAPP(nat,U_1817,U_1814,sK53(U_1817,U_1816,U_1815,U_1814))),hAPP(nat,U_1817,U_1814,hAPP(nat,nat,suc,sK53(U_1817,U_1816,U_1815,U_1814)))))
      | ~ order(U_1817) ),
    inference(definitional_conversion,[status(esa)],[f_484_3]) ).

cnf(f_484_5,plain,
    ( hBOOL(hAPP(U_1817,bool,hAPP(U_1817,fun(U_1817,bool),ord_less(U_1817),hAPP(nat,U_1817,U_1814,U_1816)),hAPP(nat,U_1817,U_1814,U_1815)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1816),U_1815))
    | ~ hBOOL(hAPP(U_1817,bool,hAPP(U_1817,fun(U_1817,bool),ord_less(U_1817),hAPP(nat,U_1817,U_1814,sK53(U_1817,U_1816,U_1815,U_1814))),hAPP(nat,U_1817,U_1814,hAPP(nat,nat,suc,sK53(U_1817,U_1816,U_1815,U_1814)))))
    | ~ order(U_1817) ),
    inference(clausify,[status(thm)],[f_484_4]) ).

fof(f_485_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_414_less__add__one]) ).

fof(f_485_2,plain,
    ! [U_1819] :
      ( ! [U_1818] : hBOOL(hAPP(U_1819,bool,hAPP(U_1819,fun(U_1819,bool),ord_less(U_1819),U_1818),hAPP(U_1819,U_1819,hAPP(U_1819,fun(U_1819,U_1819),plus_plus(U_1819),U_1818),one_one(U_1819))))
      | ~ linordered_semidom(U_1819) ),
    inference(variable_rename,[status(thm)],[f_485_1]) ).

fof(f_485_3,plain,
    ! [U_1819,U_1818] :
      ( hBOOL(hAPP(U_1819,bool,hAPP(U_1819,fun(U_1819,bool),ord_less(U_1819),U_1818),hAPP(U_1819,U_1819,hAPP(U_1819,fun(U_1819,U_1819),plus_plus(U_1819),U_1818),one_one(U_1819))))
      | ~ linordered_semidom(U_1819) ),
    inference(definitional_conversion,[status(esa)],[f_485_2]) ).

cnf(f_485_4,plain,
    ( hBOOL(hAPP(U_1819,bool,hAPP(U_1819,fun(U_1819,bool),ord_less(U_1819),U_1818),hAPP(U_1819,U_1819,hAPP(U_1819,fun(U_1819,U_1819),plus_plus(U_1819),U_1818),one_one(U_1819))))
    | ~ linordered_semidom(U_1819) ),
    inference(clausify,[status(thm)],[f_485_3]) ).

fof(f_486_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_415_less__fun__def]) ).

fof(f_486_2,plain,
    ! [U_1823,U_1822] :
      ( ! [U_1821,U_1820] :
          ( ( hBOOL(hAPP(fun(U_1823,U_1822),bool,hAPP(fun(U_1823,U_1822),fun(fun(U_1823,U_1822),bool),ord_less(fun(U_1823,U_1822)),U_1821),U_1820))
            | hBOOL(hAPP(fun(U_1823,U_1822),bool,hAPP(fun(U_1823,U_1822),fun(fun(U_1823,U_1822),bool),ord_less_eq(fun(U_1823,U_1822)),U_1820),U_1821))
            | ~ hBOOL(hAPP(fun(U_1823,U_1822),bool,hAPP(fun(U_1823,U_1822),fun(fun(U_1823,U_1822),bool),ord_less_eq(fun(U_1823,U_1822)),U_1821),U_1820)) )
          & ( ( ~ hBOOL(hAPP(fun(U_1823,U_1822),bool,hAPP(fun(U_1823,U_1822),fun(fun(U_1823,U_1822),bool),ord_less_eq(fun(U_1823,U_1822)),U_1820),U_1821))
              & hBOOL(hAPP(fun(U_1823,U_1822),bool,hAPP(fun(U_1823,U_1822),fun(fun(U_1823,U_1822),bool),ord_less_eq(fun(U_1823,U_1822)),U_1821),U_1820)) )
            | ~ hBOOL(hAPP(fun(U_1823,U_1822),bool,hAPP(fun(U_1823,U_1822),fun(fun(U_1823,U_1822),bool),ord_less(fun(U_1823,U_1822)),U_1821),U_1820)) ) )
      | ~ ord(U_1822) ),
    inference(variable_rename,[status(thm)],[f_486_1]) ).

fof(f_486_3,plain,
    ! [U_1823,U_1822] :
      ( ( ! [U_1827,U_1825] :
            ( hBOOL(hAPP(fun(U_1823,U_1822),bool,hAPP(fun(U_1823,U_1822),fun(fun(U_1823,U_1822),bool),ord_less(fun(U_1823,U_1822)),U_1827),U_1825))
            | hBOOL(hAPP(fun(U_1823,U_1822),bool,hAPP(fun(U_1823,U_1822),fun(fun(U_1823,U_1822),bool),ord_less_eq(fun(U_1823,U_1822)),U_1825),U_1827))
            | ~ hBOOL(hAPP(fun(U_1823,U_1822),bool,hAPP(fun(U_1823,U_1822),fun(fun(U_1823,U_1822),bool),ord_less_eq(fun(U_1823,U_1822)),U_1827),U_1825)) )
        & ! [U_1826,U_1824] :
            ( ( ~ hBOOL(hAPP(fun(U_1823,U_1822),bool,hAPP(fun(U_1823,U_1822),fun(fun(U_1823,U_1822),bool),ord_less_eq(fun(U_1823,U_1822)),U_1824),U_1826))
              & hBOOL(hAPP(fun(U_1823,U_1822),bool,hAPP(fun(U_1823,U_1822),fun(fun(U_1823,U_1822),bool),ord_less_eq(fun(U_1823,U_1822)),U_1826),U_1824)) )
            | ~ hBOOL(hAPP(fun(U_1823,U_1822),bool,hAPP(fun(U_1823,U_1822),fun(fun(U_1823,U_1822),bool),ord_less(fun(U_1823,U_1822)),U_1826),U_1824)) ) )
      | ~ ord(U_1822) ),
    inference(miniscope,[status(thm)],[f_486_2]) ).

fof(f_486_4,plain,
    ( ! [U_1822,U_1823,U_1824,U_1826] :
        ( ~ hBOOL(hAPP(fun(U_1823,U_1822),bool,hAPP(fun(U_1823,U_1822),fun(fun(U_1823,U_1822),bool),ord_less_eq(fun(U_1823,U_1822)),U_1824),U_1826))
        | ~ sP97(U_1822,U_1823,U_1824,U_1826) )
    & ! [U_1822,U_1823,U_1824,U_1826] :
        ( hBOOL(hAPP(fun(U_1823,U_1822),bool,hAPP(fun(U_1823,U_1822),fun(fun(U_1823,U_1822),bool),ord_less_eq(fun(U_1823,U_1822)),U_1826),U_1824))
        | ~ sP97(U_1822,U_1823,U_1824,U_1826) )
    & ! [U_1827,U_1822,U_1823,U_1825,U_1824,U_1826] :
        ( hBOOL(hAPP(fun(U_1823,U_1822),bool,hAPP(fun(U_1823,U_1822),fun(fun(U_1823,U_1822),bool),ord_less(fun(U_1823,U_1822)),U_1827),U_1825))
        | hBOOL(hAPP(fun(U_1823,U_1822),bool,hAPP(fun(U_1823,U_1822),fun(fun(U_1823,U_1822),bool),ord_less_eq(fun(U_1823,U_1822)),U_1825),U_1827))
        | ~ hBOOL(hAPP(fun(U_1823,U_1822),bool,hAPP(fun(U_1823,U_1822),fun(fun(U_1823,U_1822),bool),ord_less_eq(fun(U_1823,U_1822)),U_1827),U_1825))
        | ~ sP98(U_1827,U_1822,U_1823,U_1825,U_1824,U_1826) )
    & ! [U_1827,U_1822,U_1823,U_1825,U_1824,U_1826] :
        ( sP97(U_1822,U_1823,U_1824,U_1826)
        | ~ hBOOL(hAPP(fun(U_1823,U_1822),bool,hAPP(fun(U_1823,U_1822),fun(fun(U_1823,U_1822),bool),ord_less(fun(U_1823,U_1822)),U_1826),U_1824))
        | ~ sP98(U_1827,U_1822,U_1823,U_1825,U_1824,U_1826) )
    & ! [U_1827,U_1822,U_1823,U_1825,U_1824,U_1826] :
        ( sP98(U_1827,U_1822,U_1823,U_1825,U_1824,U_1826)
        | ~ ord(U_1822) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP97,sP98])],[f_486_3]) ).

cnf(f_486_5,plain,
    ( sP98(U_1827,U_1822,U_1823,U_1825,U_1824,U_1826)
    | ~ ord(U_1822) ),
    inference(clausify,[status(thm)],[f_486_4]) ).

cnf(f_486_6,plain,
    ( sP97(U_1822,U_1823,U_1824,U_1826)
    | ~ hBOOL(hAPP(fun(U_1823,U_1822),bool,hAPP(fun(U_1823,U_1822),fun(fun(U_1823,U_1822),bool),ord_less(fun(U_1823,U_1822)),U_1826),U_1824))
    | ~ sP98(U_1827,U_1822,U_1823,U_1825,U_1824,U_1826) ),
    inference(clausify,[status(thm)],[f_486_4]) ).

cnf(f_486_7,plain,
    ( hBOOL(hAPP(fun(U_1823,U_1822),bool,hAPP(fun(U_1823,U_1822),fun(fun(U_1823,U_1822),bool),ord_less(fun(U_1823,U_1822)),U_1827),U_1825))
    | hBOOL(hAPP(fun(U_1823,U_1822),bool,hAPP(fun(U_1823,U_1822),fun(fun(U_1823,U_1822),bool),ord_less_eq(fun(U_1823,U_1822)),U_1825),U_1827))
    | ~ hBOOL(hAPP(fun(U_1823,U_1822),bool,hAPP(fun(U_1823,U_1822),fun(fun(U_1823,U_1822),bool),ord_less_eq(fun(U_1823,U_1822)),U_1827),U_1825))
    | ~ sP98(U_1827,U_1822,U_1823,U_1825,U_1824,U_1826) ),
    inference(clausify,[status(thm)],[f_486_4]) ).

cnf(f_486_8,plain,
    ( hBOOL(hAPP(fun(U_1823,U_1822),bool,hAPP(fun(U_1823,U_1822),fun(fun(U_1823,U_1822),bool),ord_less_eq(fun(U_1823,U_1822)),U_1826),U_1824))
    | ~ sP97(U_1822,U_1823,U_1824,U_1826) ),
    inference(clausify,[status(thm)],[f_486_4]) ).

cnf(f_486_9,plain,
    ( ~ hBOOL(hAPP(fun(U_1823,U_1822),bool,hAPP(fun(U_1823,U_1822),fun(fun(U_1823,U_1822),bool),ord_less_eq(fun(U_1823,U_1822)),U_1824),U_1826))
    | ~ sP97(U_1822,U_1823,U_1824,U_1826) ),
    inference(clausify,[status(thm)],[f_486_4]) ).

fof(f_487_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_416_not__psubset__empty]) ).

fof(f_487_2,plain,
    ! [U_1829,U_1828] : ~ hBOOL(hAPP(fun(U_1829,bool),bool,hAPP(fun(U_1829,bool),fun(fun(U_1829,bool),bool),ord_less(fun(U_1829,bool)),U_1828),bot_bot(fun(U_1829,bool)))),
    inference(variable_rename,[status(thm)],[f_487_1]) ).

fof(f_487_3,plain,
    ! [U_1828,U_1829] : ~ hBOOL(hAPP(fun(U_1829,bool),bool,hAPP(fun(U_1829,bool),fun(fun(U_1829,bool),bool),ord_less(fun(U_1829,bool)),U_1828),bot_bot(fun(U_1829,bool)))),
    inference(definitional_conversion,[status(esa)],[f_487_2]) ).

cnf(f_487_4,plain,
    ~ hBOOL(hAPP(fun(U_1829,bool),bool,hAPP(fun(U_1829,bool),fun(fun(U_1829,bool),bool),ord_less(fun(U_1829,bool)),U_1828),bot_bot(fun(U_1829,bool)))),
    inference(clausify,[status(thm)],[f_487_3]) ).

fof(f_488_1,plain,
    ! [X_b,C_2,A_3,B_1] :
      ( 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_1),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_1)) ),
    inference(fof_nnf,[status(thm)],[fact_417_subset__psubset__trans]) ).

fof(f_488_2,plain,
    ! [U_1833,U_1832,U_1831,U_1830] :
      ( hBOOL(hAPP(fun(U_1833,bool),bool,hAPP(fun(U_1833,bool),fun(fun(U_1833,bool),bool),ord_less(fun(U_1833,bool)),U_1831),U_1832))
      | ~ hBOOL(hAPP(fun(U_1833,bool),bool,hAPP(fun(U_1833,bool),fun(fun(U_1833,bool),bool),ord_less(fun(U_1833,bool)),U_1830),U_1832))
      | ~ hBOOL(hAPP(fun(U_1833,bool),bool,hAPP(fun(U_1833,bool),fun(fun(U_1833,bool),bool),ord_less_eq(fun(U_1833,bool)),U_1831),U_1830)) ),
    inference(variable_rename,[status(thm)],[f_488_1]) ).

fof(f_488_3,plain,
    ! [U_1833,U_1830,U_1831,U_1832] :
      ( hBOOL(hAPP(fun(U_1833,bool),bool,hAPP(fun(U_1833,bool),fun(fun(U_1833,bool),bool),ord_less(fun(U_1833,bool)),U_1831),U_1832))
      | ~ hBOOL(hAPP(fun(U_1833,bool),bool,hAPP(fun(U_1833,bool),fun(fun(U_1833,bool),bool),ord_less(fun(U_1833,bool)),U_1830),U_1832))
      | ~ hBOOL(hAPP(fun(U_1833,bool),bool,hAPP(fun(U_1833,bool),fun(fun(U_1833,bool),bool),ord_less_eq(fun(U_1833,bool)),U_1831),U_1830)) ),
    inference(definitional_conversion,[status(esa)],[f_488_2]) ).

cnf(f_488_4,plain,
    ( hBOOL(hAPP(fun(U_1833,bool),bool,hAPP(fun(U_1833,bool),fun(fun(U_1833,bool),bool),ord_less(fun(U_1833,bool)),U_1831),U_1832))
    | ~ hBOOL(hAPP(fun(U_1833,bool),bool,hAPP(fun(U_1833,bool),fun(fun(U_1833,bool),bool),ord_less(fun(U_1833,bool)),U_1830),U_1832))
    | ~ hBOOL(hAPP(fun(U_1833,bool),bool,hAPP(fun(U_1833,bool),fun(fun(U_1833,bool),bool),ord_less_eq(fun(U_1833,bool)),U_1831),U_1830)) ),
    inference(clausify,[status(thm)],[f_488_3]) ).

fof(f_489_1,plain,
    ! [X_b,C_2,A_3,B_1] :
      ( 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_1),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_1)) ),
    inference(fof_nnf,[status(thm)],[fact_418_psubset__subset__trans]) ).

fof(f_489_2,plain,
    ! [U_1837,U_1836,U_1835,U_1834] :
      ( 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_1836))
      | ~ hBOOL(hAPP(fun(U_1837,bool),bool,hAPP(fun(U_1837,bool),fun(fun(U_1837,bool),bool),ord_less_eq(fun(U_1837,bool)),U_1834),U_1836))
      | ~ 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_489_1]) ).

fof(f_489_3,plain,
    ! [U_1834,U_1837,U_1835,U_1836] :
      ( 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_1836))
      | ~ hBOOL(hAPP(fun(U_1837,bool),bool,hAPP(fun(U_1837,bool),fun(fun(U_1837,bool),bool),ord_less_eq(fun(U_1837,bool)),U_1834),U_1836))
      | ~ 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_489_2]) ).

cnf(f_489_4,plain,
    ( 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_1836))
    | ~ hBOOL(hAPP(fun(U_1837,bool),bool,hAPP(fun(U_1837,bool),fun(fun(U_1837,bool),bool),ord_less_eq(fun(U_1837,bool)),U_1834),U_1836))
    | ~ 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_489_3]) ).

fof(f_490_1,plain,
    ! [X_b,A_3,B_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),B_1))
      | ~ 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_1)) ),
    inference(fof_nnf,[status(thm)],[fact_419_psubset__imp__subset]) ).

fof(f_490_2,plain,
    ! [U_1840,U_1839,U_1838] :
      ( hBOOL(hAPP(fun(U_1840,bool),bool,hAPP(fun(U_1840,bool),fun(fun(U_1840,bool),bool),ord_less_eq(fun(U_1840,bool)),U_1839),U_1838))
      | ~ hBOOL(hAPP(fun(U_1840,bool),bool,hAPP(fun(U_1840,bool),fun(fun(U_1840,bool),bool),ord_less(fun(U_1840,bool)),U_1839),U_1838)) ),
    inference(variable_rename,[status(thm)],[f_490_1]) ).

fof(f_490_3,plain,
    ! [U_1838,U_1840,U_1839] :
      ( hBOOL(hAPP(fun(U_1840,bool),bool,hAPP(fun(U_1840,bool),fun(fun(U_1840,bool),bool),ord_less_eq(fun(U_1840,bool)),U_1839),U_1838))
      | ~ hBOOL(hAPP(fun(U_1840,bool),bool,hAPP(fun(U_1840,bool),fun(fun(U_1840,bool),bool),ord_less(fun(U_1840,bool)),U_1839),U_1838)) ),
    inference(definitional_conversion,[status(esa)],[f_490_2]) ).

cnf(f_490_4,plain,
    ( hBOOL(hAPP(fun(U_1840,bool),bool,hAPP(fun(U_1840,bool),fun(fun(U_1840,bool),bool),ord_less_eq(fun(U_1840,bool)),U_1839),U_1838))
    | ~ hBOOL(hAPP(fun(U_1840,bool),bool,hAPP(fun(U_1840,bool),fun(fun(U_1840,bool),bool),ord_less(fun(U_1840,bool)),U_1839),U_1838)) ),
    inference(clausify,[status(thm)],[f_490_3]) ).

fof(f_491_1,plain,
    ! [X_b,A_3,B_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),B_1))
        | ( ti(fun(X_b,bool),A_3) != ti(fun(X_b,bool),B_1)
          & ~ 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_1)) ) )
      & ( ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_1)
        | 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_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),B_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_420_subset__iff__psubset__eq]) ).

fof(f_491_2,plain,
    ! [U_1843,U_1842,U_1841] :
      ( ( hBOOL(hAPP(fun(U_1843,bool),bool,hAPP(fun(U_1843,bool),fun(fun(U_1843,bool),bool),ord_less_eq(fun(U_1843,bool)),U_1842),U_1841))
        | ( ti(fun(U_1843,bool),U_1842) != ti(fun(U_1843,bool),U_1841)
          & ~ hBOOL(hAPP(fun(U_1843,bool),bool,hAPP(fun(U_1843,bool),fun(fun(U_1843,bool),bool),ord_less(fun(U_1843,bool)),U_1842),U_1841)) ) )
      & ( ti(fun(U_1843,bool),U_1842) = ti(fun(U_1843,bool),U_1841)
        | hBOOL(hAPP(fun(U_1843,bool),bool,hAPP(fun(U_1843,bool),fun(fun(U_1843,bool),bool),ord_less(fun(U_1843,bool)),U_1842),U_1841))
        | ~ hBOOL(hAPP(fun(U_1843,bool),bool,hAPP(fun(U_1843,bool),fun(fun(U_1843,bool),bool),ord_less_eq(fun(U_1843,bool)),U_1842),U_1841)) ) ),
    inference(variable_rename,[status(thm)],[f_491_1]) ).

fof(f_491_3,plain,
    ( ! [U_1849,U_1847,U_1845] :
        ( hBOOL(hAPP(fun(U_1849,bool),bool,hAPP(fun(U_1849,bool),fun(fun(U_1849,bool),bool),ord_less_eq(fun(U_1849,bool)),U_1847),U_1845))
        | ( ti(fun(U_1849,bool),U_1847) != ti(fun(U_1849,bool),U_1845)
          & ~ hBOOL(hAPP(fun(U_1849,bool),bool,hAPP(fun(U_1849,bool),fun(fun(U_1849,bool),bool),ord_less(fun(U_1849,bool)),U_1847),U_1845)) ) )
    & ! [U_1848,U_1846,U_1844] :
        ( ti(fun(U_1848,bool),U_1846) = ti(fun(U_1848,bool),U_1844)
        | hBOOL(hAPP(fun(U_1848,bool),bool,hAPP(fun(U_1848,bool),fun(fun(U_1848,bool),bool),ord_less(fun(U_1848,bool)),U_1846),U_1844))
        | ~ hBOOL(hAPP(fun(U_1848,bool),bool,hAPP(fun(U_1848,bool),fun(fun(U_1848,bool),bool),ord_less_eq(fun(U_1848,bool)),U_1846),U_1844)) ) ),
    inference(miniscope,[status(thm)],[f_491_2]) ).

fof(f_491_4,plain,
    ( ! [U_1845,U_1847,U_1849] :
        ( ti(fun(U_1849,bool),U_1847) != ti(fun(U_1849,bool),U_1845)
        | ~ sP99(U_1845,U_1847,U_1849) )
    & ! [U_1845,U_1847,U_1849] :
        ( ~ hBOOL(hAPP(fun(U_1849,bool),bool,hAPP(fun(U_1849,bool),fun(fun(U_1849,bool),bool),ord_less(fun(U_1849,bool)),U_1847),U_1845))
        | ~ sP99(U_1845,U_1847,U_1849) )
    & ! [U_1845,U_1847,U_1849] :
        ( hBOOL(hAPP(fun(U_1849,bool),bool,hAPP(fun(U_1849,bool),fun(fun(U_1849,bool),bool),ord_less_eq(fun(U_1849,bool)),U_1847),U_1845))
        | sP99(U_1845,U_1847,U_1849) )
    & ! [U_1844,U_1846,U_1848] :
        ( ti(fun(U_1848,bool),U_1846) = ti(fun(U_1848,bool),U_1844)
        | hBOOL(hAPP(fun(U_1848,bool),bool,hAPP(fun(U_1848,bool),fun(fun(U_1848,bool),bool),ord_less(fun(U_1848,bool)),U_1846),U_1844))
        | ~ hBOOL(hAPP(fun(U_1848,bool),bool,hAPP(fun(U_1848,bool),fun(fun(U_1848,bool),bool),ord_less_eq(fun(U_1848,bool)),U_1846),U_1844)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP99])],[f_491_3]) ).

cnf(f_491_5,plain,
    ( ti(fun(U_1848,bool),U_1846) = ti(fun(U_1848,bool),U_1844)
    | hBOOL(hAPP(fun(U_1848,bool),bool,hAPP(fun(U_1848,bool),fun(fun(U_1848,bool),bool),ord_less(fun(U_1848,bool)),U_1846),U_1844))
    | ~ hBOOL(hAPP(fun(U_1848,bool),bool,hAPP(fun(U_1848,bool),fun(fun(U_1848,bool),bool),ord_less_eq(fun(U_1848,bool)),U_1846),U_1844)) ),
    inference(clausify,[status(thm)],[f_491_4]) ).

cnf(f_491_6,plain,
    ( hBOOL(hAPP(fun(U_1849,bool),bool,hAPP(fun(U_1849,bool),fun(fun(U_1849,bool),bool),ord_less_eq(fun(U_1849,bool)),U_1847),U_1845))
    | sP99(U_1845,U_1847,U_1849) ),
    inference(clausify,[status(thm)],[f_491_4]) ).

cnf(f_491_7,plain,
    ( ~ hBOOL(hAPP(fun(U_1849,bool),bool,hAPP(fun(U_1849,bool),fun(fun(U_1849,bool),bool),ord_less(fun(U_1849,bool)),U_1847),U_1845))
    | ~ sP99(U_1845,U_1847,U_1849) ),
    inference(clausify,[status(thm)],[f_491_4]) ).

cnf(f_491_8,plain,
    ( ti(fun(U_1849,bool),U_1847) != ti(fun(U_1849,bool),U_1845)
    | ~ sP99(U_1845,U_1847,U_1849) ),
    inference(clausify,[status(thm)],[f_491_4]) ).

fof(f_492_1,plain,
    ! [X_b,A_3,B_1] :
      ( ( 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_1))
        | ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_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),B_1)) )
      & ( ( ti(fun(X_b,bool),A_3) != ti(fun(X_b,bool),B_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),B_1)) )
        | ~ 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_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_421_psubset__eq]) ).

fof(f_492_2,plain,
    ! [U_1852,U_1851,U_1850] :
      ( ( hBOOL(hAPP(fun(U_1852,bool),bool,hAPP(fun(U_1852,bool),fun(fun(U_1852,bool),bool),ord_less(fun(U_1852,bool)),U_1851),U_1850))
        | ti(fun(U_1852,bool),U_1851) = ti(fun(U_1852,bool),U_1850)
        | ~ hBOOL(hAPP(fun(U_1852,bool),bool,hAPP(fun(U_1852,bool),fun(fun(U_1852,bool),bool),ord_less_eq(fun(U_1852,bool)),U_1851),U_1850)) )
      & ( ( ti(fun(U_1852,bool),U_1851) != ti(fun(U_1852,bool),U_1850)
          & hBOOL(hAPP(fun(U_1852,bool),bool,hAPP(fun(U_1852,bool),fun(fun(U_1852,bool),bool),ord_less_eq(fun(U_1852,bool)),U_1851),U_1850)) )
        | ~ hBOOL(hAPP(fun(U_1852,bool),bool,hAPP(fun(U_1852,bool),fun(fun(U_1852,bool),bool),ord_less(fun(U_1852,bool)),U_1851),U_1850)) ) ),
    inference(variable_rename,[status(thm)],[f_492_1]) ).

fof(f_492_3,plain,
    ( ! [U_1858,U_1856,U_1854] :
        ( 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_1856),U_1854))
        | ti(fun(U_1858,bool),U_1856) = ti(fun(U_1858,bool),U_1854)
        | ~ hBOOL(hAPP(fun(U_1858,bool),bool,hAPP(fun(U_1858,bool),fun(fun(U_1858,bool),bool),ord_less_eq(fun(U_1858,bool)),U_1856),U_1854)) )
    & ! [U_1857,U_1855,U_1853] :
        ( ( ti(fun(U_1857,bool),U_1855) != ti(fun(U_1857,bool),U_1853)
          & hBOOL(hAPP(fun(U_1857,bool),bool,hAPP(fun(U_1857,bool),fun(fun(U_1857,bool),bool),ord_less_eq(fun(U_1857,bool)),U_1855),U_1853)) )
        | ~ hBOOL(hAPP(fun(U_1857,bool),bool,hAPP(fun(U_1857,bool),fun(fun(U_1857,bool),bool),ord_less(fun(U_1857,bool)),U_1855),U_1853)) ) ),
    inference(miniscope,[status(thm)],[f_492_2]) ).

fof(f_492_4,plain,
    ( ! [U_1853,U_1855,U_1857] :
        ( ti(fun(U_1857,bool),U_1855) != ti(fun(U_1857,bool),U_1853)
        | ~ sP100(U_1853,U_1855,U_1857) )
    & ! [U_1853,U_1855,U_1857] :
        ( hBOOL(hAPP(fun(U_1857,bool),bool,hAPP(fun(U_1857,bool),fun(fun(U_1857,bool),bool),ord_less_eq(fun(U_1857,bool)),U_1855),U_1853))
        | ~ sP100(U_1853,U_1855,U_1857) )
    & ! [U_1856,U_1854,U_1858] :
        ( 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_1856),U_1854))
        | ti(fun(U_1858,bool),U_1856) = ti(fun(U_1858,bool),U_1854)
        | ~ hBOOL(hAPP(fun(U_1858,bool),bool,hAPP(fun(U_1858,bool),fun(fun(U_1858,bool),bool),ord_less_eq(fun(U_1858,bool)),U_1856),U_1854)) )
    & ! [U_1853,U_1855,U_1857] :
        ( sP100(U_1853,U_1855,U_1857)
        | ~ hBOOL(hAPP(fun(U_1857,bool),bool,hAPP(fun(U_1857,bool),fun(fun(U_1857,bool),bool),ord_less(fun(U_1857,bool)),U_1855),U_1853)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP100])],[f_492_3]) ).

cnf(f_492_5,plain,
    ( sP100(U_1853,U_1855,U_1857)
    | ~ hBOOL(hAPP(fun(U_1857,bool),bool,hAPP(fun(U_1857,bool),fun(fun(U_1857,bool),bool),ord_less(fun(U_1857,bool)),U_1855),U_1853)) ),
    inference(clausify,[status(thm)],[f_492_4]) ).

cnf(f_492_6,plain,
    ( 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_1856),U_1854))
    | ti(fun(U_1858,bool),U_1856) = ti(fun(U_1858,bool),U_1854)
    | ~ hBOOL(hAPP(fun(U_1858,bool),bool,hAPP(fun(U_1858,bool),fun(fun(U_1858,bool),bool),ord_less_eq(fun(U_1858,bool)),U_1856),U_1854)) ),
    inference(clausify,[status(thm)],[f_492_4]) ).

cnf(f_492_7,plain,
    ( hBOOL(hAPP(fun(U_1857,bool),bool,hAPP(fun(U_1857,bool),fun(fun(U_1857,bool),bool),ord_less_eq(fun(U_1857,bool)),U_1855),U_1853))
    | ~ sP100(U_1853,U_1855,U_1857) ),
    inference(clausify,[status(thm)],[f_492_4]) ).

cnf(f_492_8,plain,
    ( ti(fun(U_1857,bool),U_1855) != ti(fun(U_1857,bool),U_1853)
    | ~ sP100(U_1853,U_1855,U_1857) ),
    inference(clausify,[status(thm)],[f_492_4]) ).

fof(f_493_1,plain,
    ! [X_b,A_3,B_1] :
      ( 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_1)))
      | ~ 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_1))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_1)) ),
    inference(fof_nnf,[status(thm)],[fact_422_psubset__card__mono]) ).

fof(f_493_2,plain,
    ! [U_1861,U_1860,U_1859] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(U_1861,bool),nat,finite_card(U_1861),U_1860)),hAPP(fun(U_1861,bool),nat,finite_card(U_1861),U_1859)))
      | ~ hBOOL(hAPP(fun(U_1861,bool),bool,hAPP(fun(U_1861,bool),fun(fun(U_1861,bool),bool),ord_less(fun(U_1861,bool)),U_1860),U_1859))
      | ~ hBOOL(hAPP(fun(U_1861,bool),bool,finite_finite(U_1861),U_1859)) ),
    inference(variable_rename,[status(thm)],[f_493_1]) ).

fof(f_493_3,plain,
    ! [U_1860,U_1859,U_1861] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(U_1861,bool),nat,finite_card(U_1861),U_1860)),hAPP(fun(U_1861,bool),nat,finite_card(U_1861),U_1859)))
      | ~ hBOOL(hAPP(fun(U_1861,bool),bool,hAPP(fun(U_1861,bool),fun(fun(U_1861,bool),bool),ord_less(fun(U_1861,bool)),U_1860),U_1859))
      | ~ hBOOL(hAPP(fun(U_1861,bool),bool,finite_finite(U_1861),U_1859)) ),
    inference(definitional_conversion,[status(esa)],[f_493_2]) ).

cnf(f_493_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(U_1861,bool),nat,finite_card(U_1861),U_1860)),hAPP(fun(U_1861,bool),nat,finite_card(U_1861),U_1859)))
    | ~ hBOOL(hAPP(fun(U_1861,bool),bool,hAPP(fun(U_1861,bool),fun(fun(U_1861,bool),bool),ord_less(fun(U_1861,bool)),U_1860),U_1859))
    | ~ hBOOL(hAPP(fun(U_1861,bool),bool,finite_finite(U_1861),U_1859)) ),
    inference(clausify,[status(thm)],[f_493_3]) ).

fof(f_494_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_423_linorder__neqE__linordered__idom]) ).

fof(f_494_2,plain,
    ! [U_1864] :
      ( ! [U_1863,U_1862] :
          ( hBOOL(hAPP(U_1864,bool,hAPP(U_1864,fun(U_1864,bool),ord_less(U_1864),U_1862),U_1863))
          | hBOOL(hAPP(U_1864,bool,hAPP(U_1864,fun(U_1864,bool),ord_less(U_1864),U_1863),U_1862))
          | ti(U_1864,U_1863) = ti(U_1864,U_1862) )
      | ~ linordered_idom(U_1864) ),
    inference(variable_rename,[status(thm)],[f_494_1]) ).

fof(f_494_3,plain,
    ! [U_1862,U_1863,U_1864] :
      ( hBOOL(hAPP(U_1864,bool,hAPP(U_1864,fun(U_1864,bool),ord_less(U_1864),U_1862),U_1863))
      | hBOOL(hAPP(U_1864,bool,hAPP(U_1864,fun(U_1864,bool),ord_less(U_1864),U_1863),U_1862))
      | ti(U_1864,U_1863) = ti(U_1864,U_1862)
      | ~ linordered_idom(U_1864) ),
    inference(definitional_conversion,[status(esa)],[f_494_2]) ).

cnf(f_494_4,plain,
    ( hBOOL(hAPP(U_1864,bool,hAPP(U_1864,fun(U_1864,bool),ord_less(U_1864),U_1862),U_1863))
    | hBOOL(hAPP(U_1864,bool,hAPP(U_1864,fun(U_1864,bool),ord_less(U_1864),U_1863),U_1862))
    | ti(U_1864,U_1863) = ti(U_1864,U_1862)
    | ~ linordered_idom(U_1864) ),
    inference(clausify,[status(thm)],[f_494_3]) ).

fof(f_495_1,plain,
    ! [X_b,A_3,X_1,B_1] :
      ( ( 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_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),B_1))
              & ~ 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_1))
              & 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_1)) )
        | ( ~ 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_1))
          & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_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),B_1))
                | 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_1))
                | ~ 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_1)) )
          & ( 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_1))
            | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_1)) ) )
        | ~ 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_1))) ) ),
    inference(fof_nnf,[status(thm)],[fact_424_psubset__insert__iff]) ).

fof(f_495_2,plain,
    ! [U_1868,U_1867,U_1866,U_1865] :
      ( ( hBOOL(hAPP(fun(U_1868,bool),bool,hAPP(fun(U_1868,bool),fun(fun(U_1868,bool),bool),ord_less(fun(U_1868,bool)),U_1867),hAPP(fun(U_1868,bool),fun(U_1868,bool),hAPP(U_1868,fun(fun(U_1868,bool),fun(U_1868,bool)),insert(U_1868),U_1866),U_1865)))
        | ( ( ( ~ hBOOL(hAPP(fun(U_1868,bool),bool,hAPP(fun(U_1868,bool),fun(fun(U_1868,bool),bool),ord_less_eq(fun(U_1868,bool)),U_1867),U_1865))
              & ~ hBOOL(hAPP(fun(U_1868,bool),bool,hAPP(U_1868,fun(fun(U_1868,bool),bool),member(U_1868),U_1866),U_1867)) )
            | ( ~ hBOOL(hAPP(fun(U_1868,bool),bool,hAPP(fun(U_1868,bool),fun(fun(U_1868,bool),bool),ord_less(fun(U_1868,bool)),hAPP(fun(U_1868,bool),fun(U_1868,bool),hAPP(fun(U_1868,bool),fun(fun(U_1868,bool),fun(U_1868,bool)),minus_minus(fun(U_1868,bool)),U_1867),hAPP(fun(U_1868,bool),fun(U_1868,bool),hAPP(U_1868,fun(fun(U_1868,bool),fun(U_1868,bool)),insert(U_1868),U_1866),bot_bot(fun(U_1868,bool))))),U_1865))
              & hBOOL(hAPP(fun(U_1868,bool),bool,hAPP(U_1868,fun(fun(U_1868,bool),bool),member(U_1868),U_1866),U_1867)) ) )
          & ~ hBOOL(hAPP(fun(U_1868,bool),bool,hAPP(U_1868,fun(fun(U_1868,bool),bool),member(U_1868),U_1866),U_1865)) )
        | ( ~ hBOOL(hAPP(fun(U_1868,bool),bool,hAPP(fun(U_1868,bool),fun(fun(U_1868,bool),bool),ord_less(fun(U_1868,bool)),U_1867),U_1865))
          & hBOOL(hAPP(fun(U_1868,bool),bool,hAPP(U_1868,fun(fun(U_1868,bool),bool),member(U_1868),U_1866),U_1865)) ) )
      & ( ( ( ( ( hBOOL(hAPP(fun(U_1868,bool),bool,hAPP(fun(U_1868,bool),fun(fun(U_1868,bool),bool),ord_less_eq(fun(U_1868,bool)),U_1867),U_1865))
                | hBOOL(hAPP(fun(U_1868,bool),bool,hAPP(U_1868,fun(fun(U_1868,bool),bool),member(U_1868),U_1866),U_1867)) )
              & ( hBOOL(hAPP(fun(U_1868,bool),bool,hAPP(fun(U_1868,bool),fun(fun(U_1868,bool),bool),ord_less(fun(U_1868,bool)),hAPP(fun(U_1868,bool),fun(U_1868,bool),hAPP(fun(U_1868,bool),fun(fun(U_1868,bool),fun(U_1868,bool)),minus_minus(fun(U_1868,bool)),U_1867),hAPP(fun(U_1868,bool),fun(U_1868,bool),hAPP(U_1868,fun(fun(U_1868,bool),fun(U_1868,bool)),insert(U_1868),U_1866),bot_bot(fun(U_1868,bool))))),U_1865))
                | ~ hBOOL(hAPP(fun(U_1868,bool),bool,hAPP(U_1868,fun(fun(U_1868,bool),bool),member(U_1868),U_1866),U_1867)) ) )
            | hBOOL(hAPP(fun(U_1868,bool),bool,hAPP(U_1868,fun(fun(U_1868,bool),bool),member(U_1868),U_1866),U_1865)) )
          & ( hBOOL(hAPP(fun(U_1868,bool),bool,hAPP(fun(U_1868,bool),fun(fun(U_1868,bool),bool),ord_less(fun(U_1868,bool)),U_1867),U_1865))
            | ~ hBOOL(hAPP(fun(U_1868,bool),bool,hAPP(U_1868,fun(fun(U_1868,bool),bool),member(U_1868),U_1866),U_1865)) ) )
        | ~ hBOOL(hAPP(fun(U_1868,bool),bool,hAPP(fun(U_1868,bool),fun(fun(U_1868,bool),bool),ord_less(fun(U_1868,bool)),U_1867),hAPP(fun(U_1868,bool),fun(U_1868,bool),hAPP(U_1868,fun(fun(U_1868,bool),fun(U_1868,bool)),insert(U_1868),U_1866),U_1865))) ) ),
    inference(variable_rename,[status(thm)],[f_495_1]) ).

fof(f_495_3,plain,
    ( ! [U_1876,U_1874,U_1872,U_1870] :
        ( hBOOL(hAPP(fun(U_1876,bool),bool,hAPP(fun(U_1876,bool),fun(fun(U_1876,bool),bool),ord_less(fun(U_1876,bool)),U_1874),hAPP(fun(U_1876,bool),fun(U_1876,bool),hAPP(U_1876,fun(fun(U_1876,bool),fun(U_1876,bool)),insert(U_1876),U_1872),U_1870)))
        | ( ( ( ~ hBOOL(hAPP(fun(U_1876,bool),bool,hAPP(fun(U_1876,bool),fun(fun(U_1876,bool),bool),ord_less_eq(fun(U_1876,bool)),U_1874),U_1870))
              & ~ hBOOL(hAPP(fun(U_1876,bool),bool,hAPP(U_1876,fun(fun(U_1876,bool),bool),member(U_1876),U_1872),U_1874)) )
            | ( ~ hBOOL(hAPP(fun(U_1876,bool),bool,hAPP(fun(U_1876,bool),fun(fun(U_1876,bool),bool),ord_less(fun(U_1876,bool)),hAPP(fun(U_1876,bool),fun(U_1876,bool),hAPP(fun(U_1876,bool),fun(fun(U_1876,bool),fun(U_1876,bool)),minus_minus(fun(U_1876,bool)),U_1874),hAPP(fun(U_1876,bool),fun(U_1876,bool),hAPP(U_1876,fun(fun(U_1876,bool),fun(U_1876,bool)),insert(U_1876),U_1872),bot_bot(fun(U_1876,bool))))),U_1870))
              & hBOOL(hAPP(fun(U_1876,bool),bool,hAPP(U_1876,fun(fun(U_1876,bool),bool),member(U_1876),U_1872),U_1874)) ) )
          & ~ hBOOL(hAPP(fun(U_1876,bool),bool,hAPP(U_1876,fun(fun(U_1876,bool),bool),member(U_1876),U_1872),U_1870)) )
        | ( ~ hBOOL(hAPP(fun(U_1876,bool),bool,hAPP(fun(U_1876,bool),fun(fun(U_1876,bool),bool),ord_less(fun(U_1876,bool)),U_1874),U_1870))
          & hBOOL(hAPP(fun(U_1876,bool),bool,hAPP(U_1876,fun(fun(U_1876,bool),bool),member(U_1876),U_1872),U_1870)) ) )
    & ! [U_1875,U_1873,U_1871,U_1869] :
        ( ( ( ( ( hBOOL(hAPP(fun(U_1875,bool),bool,hAPP(fun(U_1875,bool),fun(fun(U_1875,bool),bool),ord_less_eq(fun(U_1875,bool)),U_1873),U_1869))
                | hBOOL(hAPP(fun(U_1875,bool),bool,hAPP(U_1875,fun(fun(U_1875,bool),bool),member(U_1875),U_1871),U_1873)) )
              & ( hBOOL(hAPP(fun(U_1875,bool),bool,hAPP(fun(U_1875,bool),fun(fun(U_1875,bool),bool),ord_less(fun(U_1875,bool)),hAPP(fun(U_1875,bool),fun(U_1875,bool),hAPP(fun(U_1875,bool),fun(fun(U_1875,bool),fun(U_1875,bool)),minus_minus(fun(U_1875,bool)),U_1873),hAPP(fun(U_1875,bool),fun(U_1875,bool),hAPP(U_1875,fun(fun(U_1875,bool),fun(U_1875,bool)),insert(U_1875),U_1871),bot_bot(fun(U_1875,bool))))),U_1869))
                | ~ hBOOL(hAPP(fun(U_1875,bool),bool,hAPP(U_1875,fun(fun(U_1875,bool),bool),member(U_1875),U_1871),U_1873)) ) )
            | hBOOL(hAPP(fun(U_1875,bool),bool,hAPP(U_1875,fun(fun(U_1875,bool),bool),member(U_1875),U_1871),U_1869)) )
          & ( hBOOL(hAPP(fun(U_1875,bool),bool,hAPP(fun(U_1875,bool),fun(fun(U_1875,bool),bool),ord_less(fun(U_1875,bool)),U_1873),U_1869))
            | ~ hBOOL(hAPP(fun(U_1875,bool),bool,hAPP(U_1875,fun(fun(U_1875,bool),bool),member(U_1875),U_1871),U_1869)) ) )
        | ~ hBOOL(hAPP(fun(U_1875,bool),bool,hAPP(fun(U_1875,bool),fun(fun(U_1875,bool),bool),ord_less(fun(U_1875,bool)),U_1873),hAPP(fun(U_1875,bool),fun(U_1875,bool),hAPP(U_1875,fun(fun(U_1875,bool),fun(U_1875,bool)),insert(U_1875),U_1871),U_1869))) ) ),
    inference(miniscope,[status(thm)],[f_495_2]) ).

fof(f_495_4,plain,
    ( ! [U_1872,U_1870,U_1876,U_1874] :
        ( ~ hBOOL(hAPP(fun(U_1876,bool),bool,hAPP(fun(U_1876,bool),fun(fun(U_1876,bool),bool),ord_less_eq(fun(U_1876,bool)),U_1874),U_1870))
        | ~ sP105(U_1872,U_1870,U_1876,U_1874) )
    & ! [U_1872,U_1870,U_1876,U_1874] :
        ( ~ hBOOL(hAPP(fun(U_1876,bool),bool,hAPP(U_1876,fun(fun(U_1876,bool),bool),member(U_1876),U_1872),U_1874))
        | ~ sP105(U_1872,U_1870,U_1876,U_1874) )
    & ! [U_1872,U_1870,U_1876,U_1874] :
        ( ~ hBOOL(hAPP(fun(U_1876,bool),bool,hAPP(fun(U_1876,bool),fun(fun(U_1876,bool),bool),ord_less(fun(U_1876,bool)),hAPP(fun(U_1876,bool),fun(U_1876,bool),hAPP(fun(U_1876,bool),fun(fun(U_1876,bool),fun(U_1876,bool)),minus_minus(fun(U_1876,bool)),U_1874),hAPP(fun(U_1876,bool),fun(U_1876,bool),hAPP(U_1876,fun(fun(U_1876,bool),fun(U_1876,bool)),insert(U_1876),U_1872),bot_bot(fun(U_1876,bool))))),U_1870))
        | ~ sP104(U_1872,U_1870,U_1876,U_1874) )
    & ! [U_1872,U_1870,U_1876,U_1874] :
        ( hBOOL(hAPP(fun(U_1876,bool),bool,hAPP(U_1876,fun(fun(U_1876,bool),bool),member(U_1876),U_1872),U_1874))
        | ~ sP104(U_1872,U_1870,U_1876,U_1874) )
    & ! [U_1872,U_1870,U_1876,U_1874] :
        ( sP105(U_1872,U_1870,U_1876,U_1874)
        | sP104(U_1872,U_1870,U_1876,U_1874)
        | ~ sP106(U_1872,U_1870,U_1876,U_1874) )
    & ! [U_1872,U_1870,U_1876,U_1874] :
        ( ~ hBOOL(hAPP(fun(U_1876,bool),bool,hAPP(U_1876,fun(fun(U_1876,bool),bool),member(U_1876),U_1872),U_1870))
        | ~ sP106(U_1872,U_1870,U_1876,U_1874) )
    & ! [U_1872,U_1870,U_1876,U_1874] :
        ( ~ hBOOL(hAPP(fun(U_1876,bool),bool,hAPP(fun(U_1876,bool),fun(fun(U_1876,bool),bool),ord_less(fun(U_1876,bool)),U_1874),U_1870))
        | ~ sP103(U_1872,U_1870,U_1876,U_1874) )
    & ! [U_1872,U_1870,U_1876,U_1874] :
        ( hBOOL(hAPP(fun(U_1876,bool),bool,hAPP(U_1876,fun(fun(U_1876,bool),bool),member(U_1876),U_1872),U_1870))
        | ~ sP103(U_1872,U_1870,U_1876,U_1874) )
    & ! [U_1873,U_1875,U_1869,U_1871] :
        ( hBOOL(hAPP(fun(U_1875,bool),bool,hAPP(fun(U_1875,bool),fun(fun(U_1875,bool),bool),ord_less_eq(fun(U_1875,bool)),U_1873),U_1869))
        | hBOOL(hAPP(fun(U_1875,bool),bool,hAPP(U_1875,fun(fun(U_1875,bool),bool),member(U_1875),U_1871),U_1873))
        | ~ sP101(U_1873,U_1875,U_1869,U_1871) )
    & ! [U_1873,U_1875,U_1869,U_1871] :
        ( hBOOL(hAPP(fun(U_1875,bool),bool,hAPP(fun(U_1875,bool),fun(fun(U_1875,bool),bool),ord_less(fun(U_1875,bool)),hAPP(fun(U_1875,bool),fun(U_1875,bool),hAPP(fun(U_1875,bool),fun(fun(U_1875,bool),fun(U_1875,bool)),minus_minus(fun(U_1875,bool)),U_1873),hAPP(fun(U_1875,bool),fun(U_1875,bool),hAPP(U_1875,fun(fun(U_1875,bool),fun(U_1875,bool)),insert(U_1875),U_1871),bot_bot(fun(U_1875,bool))))),U_1869))
        | ~ hBOOL(hAPP(fun(U_1875,bool),bool,hAPP(U_1875,fun(fun(U_1875,bool),bool),member(U_1875),U_1871),U_1873))
        | ~ sP101(U_1873,U_1875,U_1869,U_1871) )
    & ! [U_1873,U_1875,U_1869,U_1871] :
        ( sP101(U_1873,U_1875,U_1869,U_1871)
        | hBOOL(hAPP(fun(U_1875,bool),bool,hAPP(U_1875,fun(fun(U_1875,bool),bool),member(U_1875),U_1871),U_1869))
        | ~ sP102(U_1873,U_1875,U_1869,U_1871) )
    & ! [U_1873,U_1875,U_1869,U_1871] :
        ( hBOOL(hAPP(fun(U_1875,bool),bool,hAPP(fun(U_1875,bool),fun(fun(U_1875,bool),bool),ord_less(fun(U_1875,bool)),U_1873),U_1869))
        | ~ hBOOL(hAPP(fun(U_1875,bool),bool,hAPP(U_1875,fun(fun(U_1875,bool),bool),member(U_1875),U_1871),U_1869))
        | ~ sP102(U_1873,U_1875,U_1869,U_1871) )
    & ! [U_1872,U_1870,U_1876,U_1874] :
        ( hBOOL(hAPP(fun(U_1876,bool),bool,hAPP(fun(U_1876,bool),fun(fun(U_1876,bool),bool),ord_less(fun(U_1876,bool)),U_1874),hAPP(fun(U_1876,bool),fun(U_1876,bool),hAPP(U_1876,fun(fun(U_1876,bool),fun(U_1876,bool)),insert(U_1876),U_1872),U_1870)))
        | sP106(U_1872,U_1870,U_1876,U_1874)
        | sP103(U_1872,U_1870,U_1876,U_1874) )
    & ! [U_1873,U_1875,U_1869,U_1871] :
        ( sP102(U_1873,U_1875,U_1869,U_1871)
        | ~ hBOOL(hAPP(fun(U_1875,bool),bool,hAPP(fun(U_1875,bool),fun(fun(U_1875,bool),bool),ord_less(fun(U_1875,bool)),U_1873),hAPP(fun(U_1875,bool),fun(U_1875,bool),hAPP(U_1875,fun(fun(U_1875,bool),fun(U_1875,bool)),insert(U_1875),U_1871),U_1869))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP101,sP102,sP103,sP104,sP105,sP106])],[f_495_3]) ).

cnf(f_495_5,plain,
    ( sP102(U_1873,U_1875,U_1869,U_1871)
    | ~ hBOOL(hAPP(fun(U_1875,bool),bool,hAPP(fun(U_1875,bool),fun(fun(U_1875,bool),bool),ord_less(fun(U_1875,bool)),U_1873),hAPP(fun(U_1875,bool),fun(U_1875,bool),hAPP(U_1875,fun(fun(U_1875,bool),fun(U_1875,bool)),insert(U_1875),U_1871),U_1869))) ),
    inference(clausify,[status(thm)],[f_495_4]) ).

cnf(f_495_6,plain,
    ( hBOOL(hAPP(fun(U_1876,bool),bool,hAPP(fun(U_1876,bool),fun(fun(U_1876,bool),bool),ord_less(fun(U_1876,bool)),U_1874),hAPP(fun(U_1876,bool),fun(U_1876,bool),hAPP(U_1876,fun(fun(U_1876,bool),fun(U_1876,bool)),insert(U_1876),U_1872),U_1870)))
    | sP106(U_1872,U_1870,U_1876,U_1874)
    | sP103(U_1872,U_1870,U_1876,U_1874) ),
    inference(clausify,[status(thm)],[f_495_4]) ).

cnf(f_495_7,plain,
    ( hBOOL(hAPP(fun(U_1875,bool),bool,hAPP(fun(U_1875,bool),fun(fun(U_1875,bool),bool),ord_less(fun(U_1875,bool)),U_1873),U_1869))
    | ~ hBOOL(hAPP(fun(U_1875,bool),bool,hAPP(U_1875,fun(fun(U_1875,bool),bool),member(U_1875),U_1871),U_1869))
    | ~ sP102(U_1873,U_1875,U_1869,U_1871) ),
    inference(clausify,[status(thm)],[f_495_4]) ).

cnf(f_495_8,plain,
    ( sP101(U_1873,U_1875,U_1869,U_1871)
    | hBOOL(hAPP(fun(U_1875,bool),bool,hAPP(U_1875,fun(fun(U_1875,bool),bool),member(U_1875),U_1871),U_1869))
    | ~ sP102(U_1873,U_1875,U_1869,U_1871) ),
    inference(clausify,[status(thm)],[f_495_4]) ).

cnf(f_495_9,plain,
    ( hBOOL(hAPP(fun(U_1875,bool),bool,hAPP(fun(U_1875,bool),fun(fun(U_1875,bool),bool),ord_less(fun(U_1875,bool)),hAPP(fun(U_1875,bool),fun(U_1875,bool),hAPP(fun(U_1875,bool),fun(fun(U_1875,bool),fun(U_1875,bool)),minus_minus(fun(U_1875,bool)),U_1873),hAPP(fun(U_1875,bool),fun(U_1875,bool),hAPP(U_1875,fun(fun(U_1875,bool),fun(U_1875,bool)),insert(U_1875),U_1871),bot_bot(fun(U_1875,bool))))),U_1869))
    | ~ hBOOL(hAPP(fun(U_1875,bool),bool,hAPP(U_1875,fun(fun(U_1875,bool),bool),member(U_1875),U_1871),U_1873))
    | ~ sP101(U_1873,U_1875,U_1869,U_1871) ),
    inference(clausify,[status(thm)],[f_495_4]) ).

cnf(f_495_10,plain,
    ( hBOOL(hAPP(fun(U_1875,bool),bool,hAPP(fun(U_1875,bool),fun(fun(U_1875,bool),bool),ord_less_eq(fun(U_1875,bool)),U_1873),U_1869))
    | hBOOL(hAPP(fun(U_1875,bool),bool,hAPP(U_1875,fun(fun(U_1875,bool),bool),member(U_1875),U_1871),U_1873))
    | ~ sP101(U_1873,U_1875,U_1869,U_1871) ),
    inference(clausify,[status(thm)],[f_495_4]) ).

cnf(f_495_11,plain,
    ( hBOOL(hAPP(fun(U_1876,bool),bool,hAPP(U_1876,fun(fun(U_1876,bool),bool),member(U_1876),U_1872),U_1870))
    | ~ sP103(U_1872,U_1870,U_1876,U_1874) ),
    inference(clausify,[status(thm)],[f_495_4]) ).

cnf(f_495_12,plain,
    ( ~ hBOOL(hAPP(fun(U_1876,bool),bool,hAPP(fun(U_1876,bool),fun(fun(U_1876,bool),bool),ord_less(fun(U_1876,bool)),U_1874),U_1870))
    | ~ sP103(U_1872,U_1870,U_1876,U_1874) ),
    inference(clausify,[status(thm)],[f_495_4]) ).

cnf(f_495_13,plain,
    ( ~ hBOOL(hAPP(fun(U_1876,bool),bool,hAPP(U_1876,fun(fun(U_1876,bool),bool),member(U_1876),U_1872),U_1870))
    | ~ sP106(U_1872,U_1870,U_1876,U_1874) ),
    inference(clausify,[status(thm)],[f_495_4]) ).

cnf(f_495_14,plain,
    ( sP105(U_1872,U_1870,U_1876,U_1874)
    | sP104(U_1872,U_1870,U_1876,U_1874)
    | ~ sP106(U_1872,U_1870,U_1876,U_1874) ),
    inference(clausify,[status(thm)],[f_495_4]) ).

cnf(f_495_15,plain,
    ( hBOOL(hAPP(fun(U_1876,bool),bool,hAPP(U_1876,fun(fun(U_1876,bool),bool),member(U_1876),U_1872),U_1874))
    | ~ sP104(U_1872,U_1870,U_1876,U_1874) ),
    inference(clausify,[status(thm)],[f_495_4]) ).

cnf(f_495_16,plain,
    ( ~ hBOOL(hAPP(fun(U_1876,bool),bool,hAPP(fun(U_1876,bool),fun(fun(U_1876,bool),bool),ord_less(fun(U_1876,bool)),hAPP(fun(U_1876,bool),fun(U_1876,bool),hAPP(fun(U_1876,bool),fun(fun(U_1876,bool),fun(U_1876,bool)),minus_minus(fun(U_1876,bool)),U_1874),hAPP(fun(U_1876,bool),fun(U_1876,bool),hAPP(U_1876,fun(fun(U_1876,bool),fun(U_1876,bool)),insert(U_1876),U_1872),bot_bot(fun(U_1876,bool))))),U_1870))
    | ~ sP104(U_1872,U_1870,U_1876,U_1874) ),
    inference(clausify,[status(thm)],[f_495_4]) ).

cnf(f_495_17,plain,
    ( ~ hBOOL(hAPP(fun(U_1876,bool),bool,hAPP(U_1876,fun(fun(U_1876,bool),bool),member(U_1876),U_1872),U_1874))
    | ~ sP105(U_1872,U_1870,U_1876,U_1874) ),
    inference(clausify,[status(thm)],[f_495_4]) ).

cnf(f_495_18,plain,
    ( ~ hBOOL(hAPP(fun(U_1876,bool),bool,hAPP(fun(U_1876,bool),fun(fun(U_1876,bool),bool),ord_less_eq(fun(U_1876,bool)),U_1874),U_1870))
    | ~ sP105(U_1872,U_1870,U_1876,U_1874) ),
    inference(clausify,[status(thm)],[f_495_4]) ).

fof(f_496_1,plain,
    ! [X_b,A_3,B_1] :
      ( 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_1))
      | ~ 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_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),B_1))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_1)) ),
    inference(fof_nnf,[status(thm)],[fact_425_card__psubset]) ).

fof(f_496_2,plain,
    ! [U_1879,U_1878,U_1877] :
      ( hBOOL(hAPP(fun(U_1879,bool),bool,hAPP(fun(U_1879,bool),fun(fun(U_1879,bool),bool),ord_less(fun(U_1879,bool)),U_1878),U_1877))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(U_1879,bool),nat,finite_card(U_1879),U_1878)),hAPP(fun(U_1879,bool),nat,finite_card(U_1879),U_1877)))
      | ~ hBOOL(hAPP(fun(U_1879,bool),bool,hAPP(fun(U_1879,bool),fun(fun(U_1879,bool),bool),ord_less_eq(fun(U_1879,bool)),U_1878),U_1877))
      | ~ hBOOL(hAPP(fun(U_1879,bool),bool,finite_finite(U_1879),U_1877)) ),
    inference(variable_rename,[status(thm)],[f_496_1]) ).

fof(f_496_3,plain,
    ! [U_1877,U_1879,U_1878] :
      ( hBOOL(hAPP(fun(U_1879,bool),bool,hAPP(fun(U_1879,bool),fun(fun(U_1879,bool),bool),ord_less(fun(U_1879,bool)),U_1878),U_1877))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(U_1879,bool),nat,finite_card(U_1879),U_1878)),hAPP(fun(U_1879,bool),nat,finite_card(U_1879),U_1877)))
      | ~ hBOOL(hAPP(fun(U_1879,bool),bool,hAPP(fun(U_1879,bool),fun(fun(U_1879,bool),bool),ord_less_eq(fun(U_1879,bool)),U_1878),U_1877))
      | ~ hBOOL(hAPP(fun(U_1879,bool),bool,finite_finite(U_1879),U_1877)) ),
    inference(definitional_conversion,[status(esa)],[f_496_2]) ).

cnf(f_496_4,plain,
    ( hBOOL(hAPP(fun(U_1879,bool),bool,hAPP(fun(U_1879,bool),fun(fun(U_1879,bool),bool),ord_less(fun(U_1879,bool)),U_1878),U_1877))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(U_1879,bool),nat,finite_card(U_1879),U_1878)),hAPP(fun(U_1879,bool),nat,finite_card(U_1879),U_1877)))
    | ~ hBOOL(hAPP(fun(U_1879,bool),bool,hAPP(fun(U_1879,bool),fun(fun(U_1879,bool),bool),ord_less_eq(fun(U_1879,bool)),U_1878),U_1877))
    | ~ hBOOL(hAPP(fun(U_1879,bool),bool,finite_finite(U_1879),U_1877)) ),
    inference(clausify,[status(thm)],[f_496_3]) ).

fof(f_497_1,plain,
    ! [X_b,A_3] :
      ( ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))
        | ! [N_1,F_2] : 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_2),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_1))) )
      & ( ? [N_1,F_2] : 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_2),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_1)))
        | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) ) ),
    inference(fof_nnf,[status(thm)],[fact_426_finite__conv__nat__seg__image]) ).

fof(f_497_2,plain,
    ! [U_1885,U_1884] :
      ( ( hBOOL(hAPP(fun(U_1885,bool),bool,finite_finite(U_1885),U_1884))
        | ! [U_1883,U_1882] : ti(fun(U_1885,bool),U_1884) != hAPP(fun(nat,bool),fun(U_1885,bool),hAPP(fun(nat,U_1885),fun(fun(nat,bool),fun(U_1885,bool)),image(nat,U_1885),U_1882),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_1883))) )
      & ( ? [U_1881,U_1880] : ti(fun(U_1885,bool),U_1884) = hAPP(fun(nat,bool),fun(U_1885,bool),hAPP(fun(nat,U_1885),fun(fun(nat,bool),fun(U_1885,bool)),image(nat,U_1885),U_1880),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_1881)))
        | ~ hBOOL(hAPP(fun(U_1885,bool),bool,finite_finite(U_1885),U_1884)) ) ),
    inference(variable_rename,[status(thm)],[f_497_1]) ).

fof(f_497_3,plain,
    ( ! [U_1889,U_1887] :
        ( hBOOL(hAPP(fun(U_1889,bool),bool,finite_finite(U_1889),U_1887))
        | ! [U_1883,U_1882] : ti(fun(U_1889,bool),U_1887) != hAPP(fun(nat,bool),fun(U_1889,bool),hAPP(fun(nat,U_1889),fun(fun(nat,bool),fun(U_1889,bool)),image(nat,U_1889),U_1882),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_1883))) )
    & ! [U_1888,U_1886] :
        ( ? [U_1881,U_1880] : ti(fun(U_1888,bool),U_1886) = hAPP(fun(nat,bool),fun(U_1888,bool),hAPP(fun(nat,U_1888),fun(fun(nat,bool),fun(U_1888,bool)),image(nat,U_1888),U_1880),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_1881)))
        | ~ hBOOL(hAPP(fun(U_1888,bool),bool,finite_finite(U_1888),U_1886)) ) ),
    inference(miniscope,[status(thm)],[f_497_2]) ).

fof(f_497_4,plain,
    ( ! [U_1889,U_1887] :
        ( hBOOL(hAPP(fun(U_1889,bool),bool,finite_finite(U_1889),U_1887))
        | ! [U_1883,U_1882] : ti(fun(U_1889,bool),U_1887) != hAPP(fun(nat,bool),fun(U_1889,bool),hAPP(fun(nat,U_1889),fun(fun(nat,bool),fun(U_1889,bool)),image(nat,U_1889),U_1882),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_1883))) )
    & ! [U_1888,U_1886] :
        ( ? [U_1880] : ti(fun(U_1888,bool),U_1886) = hAPP(fun(nat,bool),fun(U_1888,bool),hAPP(fun(nat,U_1888),fun(fun(nat,bool),fun(U_1888,bool)),image(nat,U_1888),U_1880),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)),sK54(U_1888,U_1886))))
        | ~ hBOOL(hAPP(fun(U_1888,bool),bool,finite_finite(U_1888),U_1886)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK54]),skolemize(U_1881,sK54(U_1888,U_1886))],[f_497_3]) ).

fof(f_497_5,plain,
    ( ! [U_1889,U_1887] :
        ( hBOOL(hAPP(fun(U_1889,bool),bool,finite_finite(U_1889),U_1887))
        | ! [U_1883,U_1882] : ti(fun(U_1889,bool),U_1887) != hAPP(fun(nat,bool),fun(U_1889,bool),hAPP(fun(nat,U_1889),fun(fun(nat,bool),fun(U_1889,bool)),image(nat,U_1889),U_1882),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_1883))) )
    & ! [U_1888,U_1886] :
        ( ti(fun(U_1888,bool),U_1886) = hAPP(fun(nat,bool),fun(U_1888,bool),hAPP(fun(nat,U_1888),fun(fun(nat,bool),fun(U_1888,bool)),image(nat,U_1888),sK55(U_1888,U_1886)),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)),sK54(U_1888,U_1886))))
        | ~ hBOOL(hAPP(fun(U_1888,bool),bool,finite_finite(U_1888),U_1886)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK55]),skolemize(U_1880,sK55(U_1888,U_1886))],[f_497_4]) ).

fof(f_497_6,plain,
    ( ! [U_1883,U_1882,U_1889,U_1887] :
        ( hBOOL(hAPP(fun(U_1889,bool),bool,finite_finite(U_1889),U_1887))
        | ti(fun(U_1889,bool),U_1887) != hAPP(fun(nat,bool),fun(U_1889,bool),hAPP(fun(nat,U_1889),fun(fun(nat,bool),fun(U_1889,bool)),image(nat,U_1889),U_1882),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_1883))) )
    & ! [U_1888,U_1886] :
        ( ti(fun(U_1888,bool),U_1886) = hAPP(fun(nat,bool),fun(U_1888,bool),hAPP(fun(nat,U_1888),fun(fun(nat,bool),fun(U_1888,bool)),image(nat,U_1888),sK55(U_1888,U_1886)),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)),sK54(U_1888,U_1886))))
        | ~ hBOOL(hAPP(fun(U_1888,bool),bool,finite_finite(U_1888),U_1886)) ) ),
    inference(definitional_conversion,[status(esa)],[f_497_5]) ).

cnf(f_497_7,plain,
    ( ti(fun(U_1888,bool),U_1886) = hAPP(fun(nat,bool),fun(U_1888,bool),hAPP(fun(nat,U_1888),fun(fun(nat,bool),fun(U_1888,bool)),image(nat,U_1888),sK55(U_1888,U_1886)),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)),sK54(U_1888,U_1886))))
    | ~ hBOOL(hAPP(fun(U_1888,bool),bool,finite_finite(U_1888),U_1886)) ),
    inference(clausify,[status(thm)],[f_497_6]) ).

cnf(f_497_8,plain,
    ( hBOOL(hAPP(fun(U_1889,bool),bool,finite_finite(U_1889),U_1887))
    | ti(fun(U_1889,bool),U_1887) != hAPP(fun(nat,bool),fun(U_1889,bool),hAPP(fun(nat,U_1889),fun(fun(nat,bool),fun(U_1889,bool)),image(nat,U_1889),U_1882),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_1883))) ),
    inference(clausify,[status(thm)],[f_497_6]) ).

fof(f_498_1,plain,
    ! [Na,N_2] :
      ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),N_2))
      | ? [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_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_427_bounded__nat__set__is__finite]) ).

fof(f_498_2,plain,
    ! [U_1892,U_1891] :
      ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_1891))
      | ? [U_1890] :
          ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1890),U_1892))
          & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_1890),U_1891)) ) ),
    inference(variable_rename,[status(thm)],[f_498_1]) ).

fof(f_498_3,plain,
    ! [U_1892,U_1891] :
      ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_1891))
      | ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK56(U_1892,U_1891)),U_1892))
        & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK56(U_1892,U_1891)),U_1891)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK56]),skolemize(U_1890,sK56(U_1892,U_1891))],[f_498_2]) ).

fof(f_498_4,plain,
    ( ! [U_1891,U_1892] :
        ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK56(U_1892,U_1891)),U_1892))
        | ~ sP107(U_1891,U_1892) )
    & ! [U_1891,U_1892] :
        ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK56(U_1892,U_1891)),U_1891))
        | ~ sP107(U_1891,U_1892) )
    & ! [U_1891,U_1892] :
        ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_1891))
        | sP107(U_1891,U_1892) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP107])],[f_498_3]) ).

cnf(f_498_5,plain,
    ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_1891))
    | sP107(U_1891,U_1892) ),
    inference(clausify,[status(thm)],[f_498_4]) ).

cnf(f_498_6,plain,
    ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK56(U_1892,U_1891)),U_1891))
    | ~ sP107(U_1891,U_1892) ),
    inference(clausify,[status(thm)],[f_498_4]) ).

cnf(f_498_7,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK56(U_1892,U_1891)),U_1892))
    | ~ sP107(U_1891,U_1892) ),
    inference(clausify,[status(thm)],[f_498_4]) ).

fof(f_499_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,J_2] :
          ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,F,I)),hAPP(nat,nat,F,J_2)))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_428_less__mono__imp__le__mono]) ).

fof(f_499_2,plain,
    ! [U_1897,U_1896,U_1895] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,U_1895,U_1897)),hAPP(nat,nat,U_1895,U_1896)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1897),U_1896))
      | ? [U_1894,U_1893] :
          ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,U_1895,U_1894)),hAPP(nat,nat,U_1895,U_1893)))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1894),U_1893)) ) ),
    inference(variable_rename,[status(thm)],[f_499_1]) ).

fof(f_499_3,plain,
    ! [U_1897,U_1896,U_1895] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,U_1895,U_1897)),hAPP(nat,nat,U_1895,U_1896)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1897),U_1896))
      | ? [U_1893] :
          ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,U_1895,sK57(U_1897,U_1896,U_1895))),hAPP(nat,nat,U_1895,U_1893)))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK57(U_1897,U_1896,U_1895)),U_1893)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK57]),skolemize(U_1894,sK57(U_1897,U_1896,U_1895))],[f_499_2]) ).

fof(f_499_4,plain,
    ! [U_1897,U_1896,U_1895] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,U_1895,U_1897)),hAPP(nat,nat,U_1895,U_1896)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1897),U_1896))
      | ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,U_1895,sK57(U_1897,U_1896,U_1895))),hAPP(nat,nat,U_1895,sK58(U_1897,U_1896,U_1895))))
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK57(U_1897,U_1896,U_1895)),sK58(U_1897,U_1896,U_1895))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK58]),skolemize(U_1893,sK58(U_1897,U_1896,U_1895))],[f_499_3]) ).

fof(f_499_5,plain,
    ( ! [U_1895,U_1896,U_1897] :
        ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,U_1895,sK57(U_1897,U_1896,U_1895))),hAPP(nat,nat,U_1895,sK58(U_1897,U_1896,U_1895))))
        | ~ sP108(U_1895,U_1896,U_1897) )
    & ! [U_1895,U_1896,U_1897] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK57(U_1897,U_1896,U_1895)),sK58(U_1897,U_1896,U_1895)))
        | ~ sP108(U_1895,U_1896,U_1897) )
    & ! [U_1895,U_1896,U_1897] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,U_1895,U_1897)),hAPP(nat,nat,U_1895,U_1896)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1897),U_1896))
        | sP108(U_1895,U_1896,U_1897) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP108])],[f_499_4]) ).

cnf(f_499_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,U_1895,U_1897)),hAPP(nat,nat,U_1895,U_1896)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1897),U_1896))
    | sP108(U_1895,U_1896,U_1897) ),
    inference(clausify,[status(thm)],[f_499_5]) ).

cnf(f_499_7,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK57(U_1897,U_1896,U_1895)),sK58(U_1897,U_1896,U_1895)))
    | ~ sP108(U_1895,U_1896,U_1897) ),
    inference(clausify,[status(thm)],[f_499_5]) ).

cnf(f_499_8,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,U_1895,sK57(U_1897,U_1896,U_1895))),hAPP(nat,nat,U_1895,sK58(U_1897,U_1896,U_1895))))
    | ~ sP108(U_1895,U_1896,U_1897) ),
    inference(clausify,[status(thm)],[f_499_5]) ).

fof(f_500_1,plain,
    ! [I_2,K_1] :
      ( ? [J_2] :
          ( K_1 = hAPP(nat,nat,suc,J_2)
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_2)) )
      | K_1 = hAPP(nat,nat,suc,I_2)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),K_1)) ),
    inference(fof_nnf,[status(thm)],[fact_429_lessE]) ).

fof(f_500_2,plain,
    ! [U_1900,U_1899] :
      ( ? [U_1898] :
          ( U_1899 = hAPP(nat,nat,suc,U_1898)
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1900),U_1898)) )
      | U_1899 = hAPP(nat,nat,suc,U_1900)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1900),U_1899)) ),
    inference(variable_rename,[status(thm)],[f_500_1]) ).

fof(f_500_3,plain,
    ! [U_1900,U_1899] :
      ( ( U_1899 = hAPP(nat,nat,suc,sK59(U_1900,U_1899))
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1900),sK59(U_1900,U_1899))) )
      | U_1899 = hAPP(nat,nat,suc,U_1900)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1900),U_1899)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK59]),skolemize(U_1898,sK59(U_1900,U_1899))],[f_500_2]) ).

fof(f_500_4,plain,
    ( ! [U_1900,U_1899] :
        ( U_1899 = hAPP(nat,nat,suc,sK59(U_1900,U_1899))
        | ~ sP109(U_1900,U_1899) )
    & ! [U_1900,U_1899] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1900),sK59(U_1900,U_1899)))
        | ~ sP109(U_1900,U_1899) )
    & ! [U_1900,U_1899] :
        ( sP109(U_1900,U_1899)
        | U_1899 = hAPP(nat,nat,suc,U_1900)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1900),U_1899)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP109])],[f_500_3]) ).

cnf(f_500_5,plain,
    ( sP109(U_1900,U_1899)
    | U_1899 = hAPP(nat,nat,suc,U_1900)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1900),U_1899)) ),
    inference(clausify,[status(thm)],[f_500_4]) ).

cnf(f_500_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1900),sK59(U_1900,U_1899)))
    | ~ sP109(U_1900,U_1899) ),
    inference(clausify,[status(thm)],[f_500_4]) ).

cnf(f_500_7,plain,
    ( U_1899 = hAPP(nat,nat,suc,sK59(U_1900,U_1899))
    | ~ sP109(U_1900,U_1899) ),
    inference(clausify,[status(thm)],[f_500_4]) ).

fof(f_501_1,plain,
    ! [I_2,K_1] :
      ( ? [J_2] :
          ( K_1 = hAPP(nat,nat,suc,J_2)
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_2)) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,I_2)),K_1)) ),
    inference(fof_nnf,[status(thm)],[fact_430_Suc__lessE]) ).

fof(f_501_2,plain,
    ! [U_1903,U_1902] :
      ( ? [U_1901] :
          ( U_1902 = hAPP(nat,nat,suc,U_1901)
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1903),U_1901)) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1903)),U_1902)) ),
    inference(variable_rename,[status(thm)],[f_501_1]) ).

fof(f_501_3,plain,
    ! [U_1903,U_1902] :
      ( ( U_1902 = hAPP(nat,nat,suc,sK60(U_1903,U_1902))
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1903),sK60(U_1903,U_1902))) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1903)),U_1902)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK60]),skolemize(U_1901,sK60(U_1903,U_1902))],[f_501_2]) ).

fof(f_501_4,plain,
    ( ! [U_1903,U_1902] :
        ( U_1902 = hAPP(nat,nat,suc,sK60(U_1903,U_1902))
        | ~ sP110(U_1903,U_1902) )
    & ! [U_1903,U_1902] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1903),sK60(U_1903,U_1902)))
        | ~ sP110(U_1903,U_1902) )
    & ! [U_1903,U_1902] :
        ( sP110(U_1903,U_1902)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1903)),U_1902)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP110])],[f_501_3]) ).

cnf(f_501_5,plain,
    ( sP110(U_1903,U_1902)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1903)),U_1902)) ),
    inference(clausify,[status(thm)],[f_501_4]) ).

cnf(f_501_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1903),sK60(U_1903,U_1902)))
    | ~ sP110(U_1903,U_1902) ),
    inference(clausify,[status(thm)],[f_501_4]) ).

cnf(f_501_7,plain,
    ( U_1902 = hAPP(nat,nat,suc,sK60(U_1903,U_1902))
    | ~ sP110(U_1903,U_1902) ),
    inference(clausify,[status(thm)],[f_501_4]) ).

fof(f_502_1,plain,
    ! [X_b,C_1,A_3,B_1] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_1))
      | ~ 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_1)) ),
    inference(fof_nnf,[status(thm)],[fact_431_psubsetD]) ).

fof(f_502_2,plain,
    ! [U_1907,U_1906,U_1905,U_1904] :
      ( hBOOL(hAPP(fun(U_1907,bool),bool,hAPP(U_1907,fun(fun(U_1907,bool),bool),member(U_1907),U_1906),U_1904))
      | ~ hBOOL(hAPP(fun(U_1907,bool),bool,hAPP(U_1907,fun(fun(U_1907,bool),bool),member(U_1907),U_1906),U_1905))
      | ~ hBOOL(hAPP(fun(U_1907,bool),bool,hAPP(fun(U_1907,bool),fun(fun(U_1907,bool),bool),ord_less(fun(U_1907,bool)),U_1905),U_1904)) ),
    inference(variable_rename,[status(thm)],[f_502_1]) ).

fof(f_502_3,plain,
    ! [U_1905,U_1904,U_1907,U_1906] :
      ( hBOOL(hAPP(fun(U_1907,bool),bool,hAPP(U_1907,fun(fun(U_1907,bool),bool),member(U_1907),U_1906),U_1904))
      | ~ hBOOL(hAPP(fun(U_1907,bool),bool,hAPP(U_1907,fun(fun(U_1907,bool),bool),member(U_1907),U_1906),U_1905))
      | ~ hBOOL(hAPP(fun(U_1907,bool),bool,hAPP(fun(U_1907,bool),fun(fun(U_1907,bool),bool),ord_less(fun(U_1907,bool)),U_1905),U_1904)) ),
    inference(definitional_conversion,[status(esa)],[f_502_2]) ).

cnf(f_502_4,plain,
    ( hBOOL(hAPP(fun(U_1907,bool),bool,hAPP(U_1907,fun(fun(U_1907,bool),bool),member(U_1907),U_1906),U_1904))
    | ~ hBOOL(hAPP(fun(U_1907,bool),bool,hAPP(U_1907,fun(fun(U_1907,bool),bool),member(U_1907),U_1906),U_1905))
    | ~ hBOOL(hAPP(fun(U_1907,bool),bool,hAPP(fun(U_1907,bool),fun(fun(U_1907,bool),bool),ord_less(fun(U_1907,bool)),U_1905),U_1904)) ),
    inference(clausify,[status(thm)],[f_502_3]) ).

fof(f_503_1,plain,
    ! [X_b,C_2,A_3,B_1] :
      ( 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_1),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_1)) ),
    inference(fof_nnf,[status(thm)],[fact_432_psubset__trans]) ).

fof(f_503_2,plain,
    ! [U_1911,U_1910,U_1909,U_1908] :
      ( hBOOL(hAPP(fun(U_1911,bool),bool,hAPP(fun(U_1911,bool),fun(fun(U_1911,bool),bool),ord_less(fun(U_1911,bool)),U_1909),U_1910))
      | ~ hBOOL(hAPP(fun(U_1911,bool),bool,hAPP(fun(U_1911,bool),fun(fun(U_1911,bool),bool),ord_less(fun(U_1911,bool)),U_1908),U_1910))
      | ~ hBOOL(hAPP(fun(U_1911,bool),bool,hAPP(fun(U_1911,bool),fun(fun(U_1911,bool),bool),ord_less(fun(U_1911,bool)),U_1909),U_1908)) ),
    inference(variable_rename,[status(thm)],[f_503_1]) ).

fof(f_503_3,plain,
    ! [U_1909,U_1908,U_1911,U_1910] :
      ( hBOOL(hAPP(fun(U_1911,bool),bool,hAPP(fun(U_1911,bool),fun(fun(U_1911,bool),bool),ord_less(fun(U_1911,bool)),U_1909),U_1910))
      | ~ hBOOL(hAPP(fun(U_1911,bool),bool,hAPP(fun(U_1911,bool),fun(fun(U_1911,bool),bool),ord_less(fun(U_1911,bool)),U_1908),U_1910))
      | ~ hBOOL(hAPP(fun(U_1911,bool),bool,hAPP(fun(U_1911,bool),fun(fun(U_1911,bool),bool),ord_less(fun(U_1911,bool)),U_1909),U_1908)) ),
    inference(definitional_conversion,[status(esa)],[f_503_2]) ).

cnf(f_503_4,plain,
    ( hBOOL(hAPP(fun(U_1911,bool),bool,hAPP(fun(U_1911,bool),fun(fun(U_1911,bool),bool),ord_less(fun(U_1911,bool)),U_1909),U_1910))
    | ~ hBOOL(hAPP(fun(U_1911,bool),bool,hAPP(fun(U_1911,bool),fun(fun(U_1911,bool),bool),ord_less(fun(U_1911,bool)),U_1908),U_1910))
    | ~ hBOOL(hAPP(fun(U_1911,bool),bool,hAPP(fun(U_1911,bool),fun(fun(U_1911,bool),bool),ord_less(fun(U_1911,bool)),U_1909),U_1908)) ),
    inference(clausify,[status(thm)],[f_503_3]) ).

fof(f_504_1,plain,
    ! [X_b,A_3,B_1] :
      ( ? [B_5] : hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_5),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_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_1)) ),
    inference(fof_nnf,[status(thm)],[fact_433_psubset__imp__ex__mem]) ).

fof(f_504_2,plain,
    ! [U_1915,U_1914,U_1913] :
      ( ? [U_1912] : hBOOL(hAPP(fun(U_1915,bool),bool,hAPP(U_1915,fun(fun(U_1915,bool),bool),member(U_1915),U_1912),hAPP(fun(U_1915,bool),fun(U_1915,bool),hAPP(fun(U_1915,bool),fun(fun(U_1915,bool),fun(U_1915,bool)),minus_minus(fun(U_1915,bool)),U_1913),U_1914)))
      | ~ hBOOL(hAPP(fun(U_1915,bool),bool,hAPP(fun(U_1915,bool),fun(fun(U_1915,bool),bool),ord_less(fun(U_1915,bool)),U_1914),U_1913)) ),
    inference(variable_rename,[status(thm)],[f_504_1]) ).

fof(f_504_3,plain,
    ! [U_1915,U_1914,U_1913] :
      ( hBOOL(hAPP(fun(U_1915,bool),bool,hAPP(U_1915,fun(fun(U_1915,bool),bool),member(U_1915),sK61(U_1915,U_1914,U_1913)),hAPP(fun(U_1915,bool),fun(U_1915,bool),hAPP(fun(U_1915,bool),fun(fun(U_1915,bool),fun(U_1915,bool)),minus_minus(fun(U_1915,bool)),U_1913),U_1914)))
      | ~ hBOOL(hAPP(fun(U_1915,bool),bool,hAPP(fun(U_1915,bool),fun(fun(U_1915,bool),bool),ord_less(fun(U_1915,bool)),U_1914),U_1913)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK61]),skolemize(U_1912,sK61(U_1915,U_1914,U_1913))],[f_504_2]) ).

fof(f_504_4,plain,
    ! [U_1915,U_1913,U_1914] :
      ( hBOOL(hAPP(fun(U_1915,bool),bool,hAPP(U_1915,fun(fun(U_1915,bool),bool),member(U_1915),sK61(U_1915,U_1914,U_1913)),hAPP(fun(U_1915,bool),fun(U_1915,bool),hAPP(fun(U_1915,bool),fun(fun(U_1915,bool),fun(U_1915,bool)),minus_minus(fun(U_1915,bool)),U_1913),U_1914)))
      | ~ hBOOL(hAPP(fun(U_1915,bool),bool,hAPP(fun(U_1915,bool),fun(fun(U_1915,bool),bool),ord_less(fun(U_1915,bool)),U_1914),U_1913)) ),
    inference(definitional_conversion,[status(esa)],[f_504_3]) ).

cnf(f_504_5,plain,
    ( hBOOL(hAPP(fun(U_1915,bool),bool,hAPP(U_1915,fun(fun(U_1915,bool),bool),member(U_1915),sK61(U_1915,U_1914,U_1913)),hAPP(fun(U_1915,bool),fun(U_1915,bool),hAPP(fun(U_1915,bool),fun(fun(U_1915,bool),fun(U_1915,bool)),minus_minus(fun(U_1915,bool)),U_1913),U_1914)))
    | ~ hBOOL(hAPP(fun(U_1915,bool),bool,hAPP(fun(U_1915,bool),fun(fun(U_1915,bool),bool),ord_less(fun(U_1915,bool)),U_1914),U_1913)) ),
    inference(clausify,[status(thm)],[f_504_4]) ).

fof(f_505_1,plain,
    ! [X_c,X_b] :
      ( ! [C_1,F,B_3,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_1] :
              ( ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_c,X_b,F,Y_1)),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_1),X_2)) )
          | ~ hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),C_1),B_3))
          | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_c,X_b,F,B_3)),A_2)) )
      | ~ ord(X_c)
      | ~ order(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_434_xt6]) ).

fof(f_505_2,plain,
    ! [U_1923,U_1922] :
      ( ! [U_1921,U_1920,U_1919,U_1918] :
          ( hBOOL(hAPP(U_1922,bool,hAPP(U_1922,fun(U_1922,bool),ord_less(U_1922),hAPP(U_1923,U_1922,U_1920,U_1921)),U_1918))
          | ? [U_1917,U_1916] :
              ( ~ hBOOL(hAPP(U_1922,bool,hAPP(U_1922,fun(U_1922,bool),ord_less(U_1922),hAPP(U_1923,U_1922,U_1920,U_1916)),hAPP(U_1923,U_1922,U_1920,U_1917)))
              & hBOOL(hAPP(U_1923,bool,hAPP(U_1923,fun(U_1923,bool),ord_less(U_1923),U_1916),U_1917)) )
          | ~ hBOOL(hAPP(U_1923,bool,hAPP(U_1923,fun(U_1923,bool),ord_less(U_1923),U_1921),U_1919))
          | ~ hBOOL(hAPP(U_1922,bool,hAPP(U_1922,fun(U_1922,bool),ord_less_eq(U_1922),hAPP(U_1923,U_1922,U_1920,U_1919)),U_1918)) )
      | ~ ord(U_1923)
      | ~ order(U_1922) ),
    inference(variable_rename,[status(thm)],[f_505_1]) ).

fof(f_505_3,plain,
    ! [U_1923,U_1922] :
      ( ! [U_1921,U_1920,U_1919,U_1918] :
          ( hBOOL(hAPP(U_1922,bool,hAPP(U_1922,fun(U_1922,bool),ord_less(U_1922),hAPP(U_1923,U_1922,U_1920,U_1921)),U_1918))
          | ? [U_1916] :
              ( ~ hBOOL(hAPP(U_1922,bool,hAPP(U_1922,fun(U_1922,bool),ord_less(U_1922),hAPP(U_1923,U_1922,U_1920,U_1916)),hAPP(U_1923,U_1922,U_1920,sK62(U_1923,U_1922,U_1921,U_1920,U_1919,U_1918))))
              & hBOOL(hAPP(U_1923,bool,hAPP(U_1923,fun(U_1923,bool),ord_less(U_1923),U_1916),sK62(U_1923,U_1922,U_1921,U_1920,U_1919,U_1918))) )
          | ~ hBOOL(hAPP(U_1923,bool,hAPP(U_1923,fun(U_1923,bool),ord_less(U_1923),U_1921),U_1919))
          | ~ hBOOL(hAPP(U_1922,bool,hAPP(U_1922,fun(U_1922,bool),ord_less_eq(U_1922),hAPP(U_1923,U_1922,U_1920,U_1919)),U_1918)) )
      | ~ ord(U_1923)
      | ~ order(U_1922) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK62]),skolemize(U_1917,sK62(U_1923,U_1922,U_1921,U_1920,U_1919,U_1918))],[f_505_2]) ).

fof(f_505_4,plain,
    ! [U_1923,U_1922] :
      ( ! [U_1921,U_1920,U_1919,U_1918] :
          ( hBOOL(hAPP(U_1922,bool,hAPP(U_1922,fun(U_1922,bool),ord_less(U_1922),hAPP(U_1923,U_1922,U_1920,U_1921)),U_1918))
          | ( ~ hBOOL(hAPP(U_1922,bool,hAPP(U_1922,fun(U_1922,bool),ord_less(U_1922),hAPP(U_1923,U_1922,U_1920,sK63(U_1923,U_1922,U_1921,U_1920,U_1919,U_1918))),hAPP(U_1923,U_1922,U_1920,sK62(U_1923,U_1922,U_1921,U_1920,U_1919,U_1918))))
            & hBOOL(hAPP(U_1923,bool,hAPP(U_1923,fun(U_1923,bool),ord_less(U_1923),sK63(U_1923,U_1922,U_1921,U_1920,U_1919,U_1918)),sK62(U_1923,U_1922,U_1921,U_1920,U_1919,U_1918))) )
          | ~ hBOOL(hAPP(U_1923,bool,hAPP(U_1923,fun(U_1923,bool),ord_less(U_1923),U_1921),U_1919))
          | ~ hBOOL(hAPP(U_1922,bool,hAPP(U_1922,fun(U_1922,bool),ord_less_eq(U_1922),hAPP(U_1923,U_1922,U_1920,U_1919)),U_1918)) )
      | ~ ord(U_1923)
      | ~ order(U_1922) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK63]),skolemize(U_1916,sK63(U_1923,U_1922,U_1921,U_1920,U_1919,U_1918))],[f_505_3]) ).

fof(f_505_5,plain,
    ( ! [U_1922,U_1918,U_1920,U_1919,U_1921,U_1923] :
        ( ~ hBOOL(hAPP(U_1922,bool,hAPP(U_1922,fun(U_1922,bool),ord_less(U_1922),hAPP(U_1923,U_1922,U_1920,sK63(U_1923,U_1922,U_1921,U_1920,U_1919,U_1918))),hAPP(U_1923,U_1922,U_1920,sK62(U_1923,U_1922,U_1921,U_1920,U_1919,U_1918))))
        | ~ sP111(U_1922,U_1918,U_1920,U_1919,U_1921,U_1923) )
    & ! [U_1922,U_1918,U_1920,U_1919,U_1921,U_1923] :
        ( hBOOL(hAPP(U_1923,bool,hAPP(U_1923,fun(U_1923,bool),ord_less(U_1923),sK63(U_1923,U_1922,U_1921,U_1920,U_1919,U_1918)),sK62(U_1923,U_1922,U_1921,U_1920,U_1919,U_1918)))
        | ~ sP111(U_1922,U_1918,U_1920,U_1919,U_1921,U_1923) )
    & ! [U_1922,U_1918,U_1920,U_1919,U_1921,U_1923] :
        ( hBOOL(hAPP(U_1922,bool,hAPP(U_1922,fun(U_1922,bool),ord_less(U_1922),hAPP(U_1923,U_1922,U_1920,U_1921)),U_1918))
        | sP111(U_1922,U_1918,U_1920,U_1919,U_1921,U_1923)
        | ~ hBOOL(hAPP(U_1923,bool,hAPP(U_1923,fun(U_1923,bool),ord_less(U_1923),U_1921),U_1919))
        | ~ hBOOL(hAPP(U_1922,bool,hAPP(U_1922,fun(U_1922,bool),ord_less_eq(U_1922),hAPP(U_1923,U_1922,U_1920,U_1919)),U_1918))
        | ~ ord(U_1923)
        | ~ order(U_1922) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP111])],[f_505_4]) ).

cnf(f_505_6,plain,
    ( hBOOL(hAPP(U_1922,bool,hAPP(U_1922,fun(U_1922,bool),ord_less(U_1922),hAPP(U_1923,U_1922,U_1920,U_1921)),U_1918))
    | sP111(U_1922,U_1918,U_1920,U_1919,U_1921,U_1923)
    | ~ hBOOL(hAPP(U_1923,bool,hAPP(U_1923,fun(U_1923,bool),ord_less(U_1923),U_1921),U_1919))
    | ~ hBOOL(hAPP(U_1922,bool,hAPP(U_1922,fun(U_1922,bool),ord_less_eq(U_1922),hAPP(U_1923,U_1922,U_1920,U_1919)),U_1918))
    | ~ ord(U_1923)
    | ~ order(U_1922) ),
    inference(clausify,[status(thm)],[f_505_5]) ).

cnf(f_505_7,plain,
    ( hBOOL(hAPP(U_1923,bool,hAPP(U_1923,fun(U_1923,bool),ord_less(U_1923),sK63(U_1923,U_1922,U_1921,U_1920,U_1919,U_1918)),sK62(U_1923,U_1922,U_1921,U_1920,U_1919,U_1918)))
    | ~ sP111(U_1922,U_1918,U_1920,U_1919,U_1921,U_1923) ),
    inference(clausify,[status(thm)],[f_505_5]) ).

cnf(f_505_8,plain,
    ( ~ hBOOL(hAPP(U_1922,bool,hAPP(U_1922,fun(U_1922,bool),ord_less(U_1922),hAPP(U_1923,U_1922,U_1920,sK63(U_1923,U_1922,U_1921,U_1920,U_1919,U_1918))),hAPP(U_1923,U_1922,U_1920,sK62(U_1923,U_1922,U_1921,U_1920,U_1919,U_1918))))
    | ~ sP111(U_1922,U_1918,U_1920,U_1919,U_1921,U_1923) ),
    inference(clausify,[status(thm)],[f_505_5]) ).

fof(f_506_1,plain,
    ! [X_c,X_b] :
      ( ! [C_1,F,B_3,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_1] :
              ( ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_c,X_b,F,Y_1)),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_1),X_2)) )
          | ~ hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),C_1),B_3))
          | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_c,X_b,F,B_3)),A_2)) )
      | ~ order(X_c)
      | ~ order(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_435_xt4]) ).

fof(f_506_2,plain,
    ! [U_1931,U_1930] :
      ( ! [U_1929,U_1928,U_1927,U_1926] :
          ( hBOOL(hAPP(U_1930,bool,hAPP(U_1930,fun(U_1930,bool),ord_less(U_1930),hAPP(U_1931,U_1930,U_1928,U_1929)),U_1926))
          | ? [U_1925,U_1924] :
              ( ~ hBOOL(hAPP(U_1930,bool,hAPP(U_1930,fun(U_1930,bool),ord_less_eq(U_1930),hAPP(U_1931,U_1930,U_1928,U_1924)),hAPP(U_1931,U_1930,U_1928,U_1925)))
              & hBOOL(hAPP(U_1931,bool,hAPP(U_1931,fun(U_1931,bool),ord_less_eq(U_1931),U_1924),U_1925)) )
          | ~ hBOOL(hAPP(U_1931,bool,hAPP(U_1931,fun(U_1931,bool),ord_less_eq(U_1931),U_1929),U_1927))
          | ~ hBOOL(hAPP(U_1930,bool,hAPP(U_1930,fun(U_1930,bool),ord_less(U_1930),hAPP(U_1931,U_1930,U_1928,U_1927)),U_1926)) )
      | ~ order(U_1931)
      | ~ order(U_1930) ),
    inference(variable_rename,[status(thm)],[f_506_1]) ).

fof(f_506_3,plain,
    ! [U_1931,U_1930] :
      ( ! [U_1929,U_1928,U_1927,U_1926] :
          ( hBOOL(hAPP(U_1930,bool,hAPP(U_1930,fun(U_1930,bool),ord_less(U_1930),hAPP(U_1931,U_1930,U_1928,U_1929)),U_1926))
          | ? [U_1924] :
              ( ~ hBOOL(hAPP(U_1930,bool,hAPP(U_1930,fun(U_1930,bool),ord_less_eq(U_1930),hAPP(U_1931,U_1930,U_1928,U_1924)),hAPP(U_1931,U_1930,U_1928,sK64(U_1931,U_1930,U_1929,U_1928,U_1927,U_1926))))
              & hBOOL(hAPP(U_1931,bool,hAPP(U_1931,fun(U_1931,bool),ord_less_eq(U_1931),U_1924),sK64(U_1931,U_1930,U_1929,U_1928,U_1927,U_1926))) )
          | ~ hBOOL(hAPP(U_1931,bool,hAPP(U_1931,fun(U_1931,bool),ord_less_eq(U_1931),U_1929),U_1927))
          | ~ hBOOL(hAPP(U_1930,bool,hAPP(U_1930,fun(U_1930,bool),ord_less(U_1930),hAPP(U_1931,U_1930,U_1928,U_1927)),U_1926)) )
      | ~ order(U_1931)
      | ~ order(U_1930) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK64]),skolemize(U_1925,sK64(U_1931,U_1930,U_1929,U_1928,U_1927,U_1926))],[f_506_2]) ).

fof(f_506_4,plain,
    ! [U_1931,U_1930] :
      ( ! [U_1929,U_1928,U_1927,U_1926] :
          ( hBOOL(hAPP(U_1930,bool,hAPP(U_1930,fun(U_1930,bool),ord_less(U_1930),hAPP(U_1931,U_1930,U_1928,U_1929)),U_1926))
          | ( ~ hBOOL(hAPP(U_1930,bool,hAPP(U_1930,fun(U_1930,bool),ord_less_eq(U_1930),hAPP(U_1931,U_1930,U_1928,sK65(U_1931,U_1930,U_1929,U_1928,U_1927,U_1926))),hAPP(U_1931,U_1930,U_1928,sK64(U_1931,U_1930,U_1929,U_1928,U_1927,U_1926))))
            & hBOOL(hAPP(U_1931,bool,hAPP(U_1931,fun(U_1931,bool),ord_less_eq(U_1931),sK65(U_1931,U_1930,U_1929,U_1928,U_1927,U_1926)),sK64(U_1931,U_1930,U_1929,U_1928,U_1927,U_1926))) )
          | ~ hBOOL(hAPP(U_1931,bool,hAPP(U_1931,fun(U_1931,bool),ord_less_eq(U_1931),U_1929),U_1927))
          | ~ hBOOL(hAPP(U_1930,bool,hAPP(U_1930,fun(U_1930,bool),ord_less(U_1930),hAPP(U_1931,U_1930,U_1928,U_1927)),U_1926)) )
      | ~ order(U_1931)
      | ~ order(U_1930) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK65]),skolemize(U_1924,sK65(U_1931,U_1930,U_1929,U_1928,U_1927,U_1926))],[f_506_3]) ).

fof(f_506_5,plain,
    ( ! [U_1928,U_1927,U_1926,U_1930,U_1929,U_1931] :
        ( ~ hBOOL(hAPP(U_1930,bool,hAPP(U_1930,fun(U_1930,bool),ord_less_eq(U_1930),hAPP(U_1931,U_1930,U_1928,sK65(U_1931,U_1930,U_1929,U_1928,U_1927,U_1926))),hAPP(U_1931,U_1930,U_1928,sK64(U_1931,U_1930,U_1929,U_1928,U_1927,U_1926))))
        | ~ sP112(U_1928,U_1927,U_1926,U_1930,U_1929,U_1931) )
    & ! [U_1928,U_1927,U_1926,U_1930,U_1929,U_1931] :
        ( hBOOL(hAPP(U_1931,bool,hAPP(U_1931,fun(U_1931,bool),ord_less_eq(U_1931),sK65(U_1931,U_1930,U_1929,U_1928,U_1927,U_1926)),sK64(U_1931,U_1930,U_1929,U_1928,U_1927,U_1926)))
        | ~ sP112(U_1928,U_1927,U_1926,U_1930,U_1929,U_1931) )
    & ! [U_1928,U_1927,U_1926,U_1930,U_1929,U_1931] :
        ( hBOOL(hAPP(U_1930,bool,hAPP(U_1930,fun(U_1930,bool),ord_less(U_1930),hAPP(U_1931,U_1930,U_1928,U_1929)),U_1926))
        | sP112(U_1928,U_1927,U_1926,U_1930,U_1929,U_1931)
        | ~ hBOOL(hAPP(U_1931,bool,hAPP(U_1931,fun(U_1931,bool),ord_less_eq(U_1931),U_1929),U_1927))
        | ~ hBOOL(hAPP(U_1930,bool,hAPP(U_1930,fun(U_1930,bool),ord_less(U_1930),hAPP(U_1931,U_1930,U_1928,U_1927)),U_1926))
        | ~ order(U_1931)
        | ~ order(U_1930) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP112])],[f_506_4]) ).

cnf(f_506_6,plain,
    ( hBOOL(hAPP(U_1930,bool,hAPP(U_1930,fun(U_1930,bool),ord_less(U_1930),hAPP(U_1931,U_1930,U_1928,U_1929)),U_1926))
    | sP112(U_1928,U_1927,U_1926,U_1930,U_1929,U_1931)
    | ~ hBOOL(hAPP(U_1931,bool,hAPP(U_1931,fun(U_1931,bool),ord_less_eq(U_1931),U_1929),U_1927))
    | ~ hBOOL(hAPP(U_1930,bool,hAPP(U_1930,fun(U_1930,bool),ord_less(U_1930),hAPP(U_1931,U_1930,U_1928,U_1927)),U_1926))
    | ~ order(U_1931)
    | ~ order(U_1930) ),
    inference(clausify,[status(thm)],[f_506_5]) ).

cnf(f_506_7,plain,
    ( hBOOL(hAPP(U_1931,bool,hAPP(U_1931,fun(U_1931,bool),ord_less_eq(U_1931),sK65(U_1931,U_1930,U_1929,U_1928,U_1927,U_1926)),sK64(U_1931,U_1930,U_1929,U_1928,U_1927,U_1926)))
    | ~ sP112(U_1928,U_1927,U_1926,U_1930,U_1929,U_1931) ),
    inference(clausify,[status(thm)],[f_506_5]) ).

cnf(f_506_8,plain,
    ( ~ hBOOL(hAPP(U_1930,bool,hAPP(U_1930,fun(U_1930,bool),ord_less_eq(U_1930),hAPP(U_1931,U_1930,U_1928,sK65(U_1931,U_1930,U_1929,U_1928,U_1927,U_1926))),hAPP(U_1931,U_1930,U_1928,sK64(U_1931,U_1930,U_1929,U_1928,U_1927,U_1926))))
    | ~ sP112(U_1928,U_1927,U_1926,U_1930,U_1929,U_1931) ),
    inference(clausify,[status(thm)],[f_506_5]) ).

fof(f_507_1,plain,
    ! [X_b,X_c] :
      ( ! [C_1,A_2,F,B_3] :
          ( 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_1] :
              ( ~ 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_1)))
              & hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),X_2),Y_1)) )
          | ~ hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),B_3),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_3))) )
      | ~ order(X_b)
      | ~ order(X_c) ),
    inference(fof_nnf,[status(thm)],[fact_436_order__le__less__subst1]) ).

fof(f_507_2,plain,
    ! [U_1939,U_1938] :
      ( ! [U_1937,U_1936,U_1935,U_1934] :
          ( hBOOL(hAPP(U_1939,bool,hAPP(U_1939,fun(U_1939,bool),ord_less(U_1939),U_1936),hAPP(U_1938,U_1939,U_1935,U_1937)))
          | ? [U_1933,U_1932] :
              ( ~ hBOOL(hAPP(U_1939,bool,hAPP(U_1939,fun(U_1939,bool),ord_less(U_1939),hAPP(U_1938,U_1939,U_1935,U_1933)),hAPP(U_1938,U_1939,U_1935,U_1932)))
              & hBOOL(hAPP(U_1938,bool,hAPP(U_1938,fun(U_1938,bool),ord_less(U_1938),U_1933),U_1932)) )
          | ~ hBOOL(hAPP(U_1938,bool,hAPP(U_1938,fun(U_1938,bool),ord_less(U_1938),U_1934),U_1937))
          | ~ hBOOL(hAPP(U_1939,bool,hAPP(U_1939,fun(U_1939,bool),ord_less_eq(U_1939),U_1936),hAPP(U_1938,U_1939,U_1935,U_1934))) )
      | ~ order(U_1939)
      | ~ order(U_1938) ),
    inference(variable_rename,[status(thm)],[f_507_1]) ).

fof(f_507_3,plain,
    ! [U_1939,U_1938] :
      ( ! [U_1937,U_1936,U_1935,U_1934] :
          ( hBOOL(hAPP(U_1939,bool,hAPP(U_1939,fun(U_1939,bool),ord_less(U_1939),U_1936),hAPP(U_1938,U_1939,U_1935,U_1937)))
          | ? [U_1932] :
              ( ~ hBOOL(hAPP(U_1939,bool,hAPP(U_1939,fun(U_1939,bool),ord_less(U_1939),hAPP(U_1938,U_1939,U_1935,sK66(U_1939,U_1938,U_1937,U_1936,U_1935,U_1934))),hAPP(U_1938,U_1939,U_1935,U_1932)))
              & hBOOL(hAPP(U_1938,bool,hAPP(U_1938,fun(U_1938,bool),ord_less(U_1938),sK66(U_1939,U_1938,U_1937,U_1936,U_1935,U_1934)),U_1932)) )
          | ~ hBOOL(hAPP(U_1938,bool,hAPP(U_1938,fun(U_1938,bool),ord_less(U_1938),U_1934),U_1937))
          | ~ hBOOL(hAPP(U_1939,bool,hAPP(U_1939,fun(U_1939,bool),ord_less_eq(U_1939),U_1936),hAPP(U_1938,U_1939,U_1935,U_1934))) )
      | ~ order(U_1939)
      | ~ order(U_1938) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK66]),skolemize(U_1933,sK66(U_1939,U_1938,U_1937,U_1936,U_1935,U_1934))],[f_507_2]) ).

fof(f_507_4,plain,
    ! [U_1939,U_1938] :
      ( ! [U_1937,U_1936,U_1935,U_1934] :
          ( hBOOL(hAPP(U_1939,bool,hAPP(U_1939,fun(U_1939,bool),ord_less(U_1939),U_1936),hAPP(U_1938,U_1939,U_1935,U_1937)))
          | ( ~ hBOOL(hAPP(U_1939,bool,hAPP(U_1939,fun(U_1939,bool),ord_less(U_1939),hAPP(U_1938,U_1939,U_1935,sK66(U_1939,U_1938,U_1937,U_1936,U_1935,U_1934))),hAPP(U_1938,U_1939,U_1935,sK67(U_1939,U_1938,U_1937,U_1936,U_1935,U_1934))))
            & hBOOL(hAPP(U_1938,bool,hAPP(U_1938,fun(U_1938,bool),ord_less(U_1938),sK66(U_1939,U_1938,U_1937,U_1936,U_1935,U_1934)),sK67(U_1939,U_1938,U_1937,U_1936,U_1935,U_1934))) )
          | ~ hBOOL(hAPP(U_1938,bool,hAPP(U_1938,fun(U_1938,bool),ord_less(U_1938),U_1934),U_1937))
          | ~ hBOOL(hAPP(U_1939,bool,hAPP(U_1939,fun(U_1939,bool),ord_less_eq(U_1939),U_1936),hAPP(U_1938,U_1939,U_1935,U_1934))) )
      | ~ order(U_1939)
      | ~ order(U_1938) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK67]),skolemize(U_1932,sK67(U_1939,U_1938,U_1937,U_1936,U_1935,U_1934))],[f_507_3]) ).

fof(f_507_5,plain,
    ( ! [U_1934,U_1937,U_1935,U_1938,U_1936,U_1939] :
        ( ~ hBOOL(hAPP(U_1939,bool,hAPP(U_1939,fun(U_1939,bool),ord_less(U_1939),hAPP(U_1938,U_1939,U_1935,sK66(U_1939,U_1938,U_1937,U_1936,U_1935,U_1934))),hAPP(U_1938,U_1939,U_1935,sK67(U_1939,U_1938,U_1937,U_1936,U_1935,U_1934))))
        | ~ sP113(U_1934,U_1937,U_1935,U_1938,U_1936,U_1939) )
    & ! [U_1934,U_1937,U_1935,U_1938,U_1936,U_1939] :
        ( hBOOL(hAPP(U_1938,bool,hAPP(U_1938,fun(U_1938,bool),ord_less(U_1938),sK66(U_1939,U_1938,U_1937,U_1936,U_1935,U_1934)),sK67(U_1939,U_1938,U_1937,U_1936,U_1935,U_1934)))
        | ~ sP113(U_1934,U_1937,U_1935,U_1938,U_1936,U_1939) )
    & ! [U_1934,U_1937,U_1935,U_1938,U_1936,U_1939] :
        ( hBOOL(hAPP(U_1939,bool,hAPP(U_1939,fun(U_1939,bool),ord_less(U_1939),U_1936),hAPP(U_1938,U_1939,U_1935,U_1937)))
        | sP113(U_1934,U_1937,U_1935,U_1938,U_1936,U_1939)
        | ~ hBOOL(hAPP(U_1938,bool,hAPP(U_1938,fun(U_1938,bool),ord_less(U_1938),U_1934),U_1937))
        | ~ hBOOL(hAPP(U_1939,bool,hAPP(U_1939,fun(U_1939,bool),ord_less_eq(U_1939),U_1936),hAPP(U_1938,U_1939,U_1935,U_1934)))
        | ~ order(U_1939)
        | ~ order(U_1938) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP113])],[f_507_4]) ).

cnf(f_507_6,plain,
    ( hBOOL(hAPP(U_1939,bool,hAPP(U_1939,fun(U_1939,bool),ord_less(U_1939),U_1936),hAPP(U_1938,U_1939,U_1935,U_1937)))
    | sP113(U_1934,U_1937,U_1935,U_1938,U_1936,U_1939)
    | ~ hBOOL(hAPP(U_1938,bool,hAPP(U_1938,fun(U_1938,bool),ord_less(U_1938),U_1934),U_1937))
    | ~ hBOOL(hAPP(U_1939,bool,hAPP(U_1939,fun(U_1939,bool),ord_less_eq(U_1939),U_1936),hAPP(U_1938,U_1939,U_1935,U_1934)))
    | ~ order(U_1939)
    | ~ order(U_1938) ),
    inference(clausify,[status(thm)],[f_507_5]) ).

cnf(f_507_7,plain,
    ( hBOOL(hAPP(U_1938,bool,hAPP(U_1938,fun(U_1938,bool),ord_less(U_1938),sK66(U_1939,U_1938,U_1937,U_1936,U_1935,U_1934)),sK67(U_1939,U_1938,U_1937,U_1936,U_1935,U_1934)))
    | ~ sP113(U_1934,U_1937,U_1935,U_1938,U_1936,U_1939) ),
    inference(clausify,[status(thm)],[f_507_5]) ).

cnf(f_507_8,plain,
    ( ~ hBOOL(hAPP(U_1939,bool,hAPP(U_1939,fun(U_1939,bool),ord_less(U_1939),hAPP(U_1938,U_1939,U_1935,sK66(U_1939,U_1938,U_1937,U_1936,U_1935,U_1934))),hAPP(U_1938,U_1939,U_1935,sK67(U_1939,U_1938,U_1937,U_1936,U_1935,U_1934))))
    | ~ sP113(U_1934,U_1937,U_1935,U_1938,U_1936,U_1939) ),
    inference(clausify,[status(thm)],[f_507_5]) ).

fof(f_508_1,plain,
    ! [X_b,X_c] :
      ( ! [C_1,A_2,F,B_3] :
          ( 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_1] :
              ( ~ 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_1)))
              & hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),X_2),Y_1)) )
          | ~ hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),B_3),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_3))) )
      | ~ order(X_b)
      | ~ order(X_c) ),
    inference(fof_nnf,[status(thm)],[fact_437_order__less__le__subst1]) ).

fof(f_508_2,plain,
    ! [U_1947,U_1946] :
      ( ! [U_1945,U_1944,U_1943,U_1942] :
          ( hBOOL(hAPP(U_1947,bool,hAPP(U_1947,fun(U_1947,bool),ord_less(U_1947),U_1944),hAPP(U_1946,U_1947,U_1943,U_1945)))
          | ? [U_1941,U_1940] :
              ( ~ hBOOL(hAPP(U_1947,bool,hAPP(U_1947,fun(U_1947,bool),ord_less_eq(U_1947),hAPP(U_1946,U_1947,U_1943,U_1941)),hAPP(U_1946,U_1947,U_1943,U_1940)))
              & hBOOL(hAPP(U_1946,bool,hAPP(U_1946,fun(U_1946,bool),ord_less_eq(U_1946),U_1941),U_1940)) )
          | ~ hBOOL(hAPP(U_1946,bool,hAPP(U_1946,fun(U_1946,bool),ord_less_eq(U_1946),U_1942),U_1945))
          | ~ hBOOL(hAPP(U_1947,bool,hAPP(U_1947,fun(U_1947,bool),ord_less(U_1947),U_1944),hAPP(U_1946,U_1947,U_1943,U_1942))) )
      | ~ order(U_1947)
      | ~ order(U_1946) ),
    inference(variable_rename,[status(thm)],[f_508_1]) ).

fof(f_508_3,plain,
    ! [U_1947,U_1946] :
      ( ! [U_1945,U_1944,U_1943,U_1942] :
          ( hBOOL(hAPP(U_1947,bool,hAPP(U_1947,fun(U_1947,bool),ord_less(U_1947),U_1944),hAPP(U_1946,U_1947,U_1943,U_1945)))
          | ? [U_1940] :
              ( ~ hBOOL(hAPP(U_1947,bool,hAPP(U_1947,fun(U_1947,bool),ord_less_eq(U_1947),hAPP(U_1946,U_1947,U_1943,sK68(U_1947,U_1946,U_1945,U_1944,U_1943,U_1942))),hAPP(U_1946,U_1947,U_1943,U_1940)))
              & hBOOL(hAPP(U_1946,bool,hAPP(U_1946,fun(U_1946,bool),ord_less_eq(U_1946),sK68(U_1947,U_1946,U_1945,U_1944,U_1943,U_1942)),U_1940)) )
          | ~ hBOOL(hAPP(U_1946,bool,hAPP(U_1946,fun(U_1946,bool),ord_less_eq(U_1946),U_1942),U_1945))
          | ~ hBOOL(hAPP(U_1947,bool,hAPP(U_1947,fun(U_1947,bool),ord_less(U_1947),U_1944),hAPP(U_1946,U_1947,U_1943,U_1942))) )
      | ~ order(U_1947)
      | ~ order(U_1946) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK68]),skolemize(U_1941,sK68(U_1947,U_1946,U_1945,U_1944,U_1943,U_1942))],[f_508_2]) ).

fof(f_508_4,plain,
    ! [U_1947,U_1946] :
      ( ! [U_1945,U_1944,U_1943,U_1942] :
          ( hBOOL(hAPP(U_1947,bool,hAPP(U_1947,fun(U_1947,bool),ord_less(U_1947),U_1944),hAPP(U_1946,U_1947,U_1943,U_1945)))
          | ( ~ hBOOL(hAPP(U_1947,bool,hAPP(U_1947,fun(U_1947,bool),ord_less_eq(U_1947),hAPP(U_1946,U_1947,U_1943,sK68(U_1947,U_1946,U_1945,U_1944,U_1943,U_1942))),hAPP(U_1946,U_1947,U_1943,sK69(U_1947,U_1946,U_1945,U_1944,U_1943,U_1942))))
            & hBOOL(hAPP(U_1946,bool,hAPP(U_1946,fun(U_1946,bool),ord_less_eq(U_1946),sK68(U_1947,U_1946,U_1945,U_1944,U_1943,U_1942)),sK69(U_1947,U_1946,U_1945,U_1944,U_1943,U_1942))) )
          | ~ hBOOL(hAPP(U_1946,bool,hAPP(U_1946,fun(U_1946,bool),ord_less_eq(U_1946),U_1942),U_1945))
          | ~ hBOOL(hAPP(U_1947,bool,hAPP(U_1947,fun(U_1947,bool),ord_less(U_1947),U_1944),hAPP(U_1946,U_1947,U_1943,U_1942))) )
      | ~ order(U_1947)
      | ~ order(U_1946) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK69]),skolemize(U_1940,sK69(U_1947,U_1946,U_1945,U_1944,U_1943,U_1942))],[f_508_3]) ).

fof(f_508_5,plain,
    ( ! [U_1943,U_1944,U_1945,U_1942,U_1946,U_1947] :
        ( ~ hBOOL(hAPP(U_1947,bool,hAPP(U_1947,fun(U_1947,bool),ord_less_eq(U_1947),hAPP(U_1946,U_1947,U_1943,sK68(U_1947,U_1946,U_1945,U_1944,U_1943,U_1942))),hAPP(U_1946,U_1947,U_1943,sK69(U_1947,U_1946,U_1945,U_1944,U_1943,U_1942))))
        | ~ sP114(U_1943,U_1944,U_1945,U_1942,U_1946,U_1947) )
    & ! [U_1943,U_1944,U_1945,U_1942,U_1946,U_1947] :
        ( hBOOL(hAPP(U_1946,bool,hAPP(U_1946,fun(U_1946,bool),ord_less_eq(U_1946),sK68(U_1947,U_1946,U_1945,U_1944,U_1943,U_1942)),sK69(U_1947,U_1946,U_1945,U_1944,U_1943,U_1942)))
        | ~ sP114(U_1943,U_1944,U_1945,U_1942,U_1946,U_1947) )
    & ! [U_1943,U_1944,U_1945,U_1942,U_1946,U_1947] :
        ( hBOOL(hAPP(U_1947,bool,hAPP(U_1947,fun(U_1947,bool),ord_less(U_1947),U_1944),hAPP(U_1946,U_1947,U_1943,U_1945)))
        | sP114(U_1943,U_1944,U_1945,U_1942,U_1946,U_1947)
        | ~ hBOOL(hAPP(U_1946,bool,hAPP(U_1946,fun(U_1946,bool),ord_less_eq(U_1946),U_1942),U_1945))
        | ~ hBOOL(hAPP(U_1947,bool,hAPP(U_1947,fun(U_1947,bool),ord_less(U_1947),U_1944),hAPP(U_1946,U_1947,U_1943,U_1942)))
        | ~ order(U_1947)
        | ~ order(U_1946) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP114])],[f_508_4]) ).

cnf(f_508_6,plain,
    ( hBOOL(hAPP(U_1947,bool,hAPP(U_1947,fun(U_1947,bool),ord_less(U_1947),U_1944),hAPP(U_1946,U_1947,U_1943,U_1945)))
    | sP114(U_1943,U_1944,U_1945,U_1942,U_1946,U_1947)
    | ~ hBOOL(hAPP(U_1946,bool,hAPP(U_1946,fun(U_1946,bool),ord_less_eq(U_1946),U_1942),U_1945))
    | ~ hBOOL(hAPP(U_1947,bool,hAPP(U_1947,fun(U_1947,bool),ord_less(U_1947),U_1944),hAPP(U_1946,U_1947,U_1943,U_1942)))
    | ~ order(U_1947)
    | ~ order(U_1946) ),
    inference(clausify,[status(thm)],[f_508_5]) ).

cnf(f_508_7,plain,
    ( hBOOL(hAPP(U_1946,bool,hAPP(U_1946,fun(U_1946,bool),ord_less_eq(U_1946),sK68(U_1947,U_1946,U_1945,U_1944,U_1943,U_1942)),sK69(U_1947,U_1946,U_1945,U_1944,U_1943,U_1942)))
    | ~ sP114(U_1943,U_1944,U_1945,U_1942,U_1946,U_1947) ),
    inference(clausify,[status(thm)],[f_508_5]) ).

cnf(f_508_8,plain,
    ( ~ hBOOL(hAPP(U_1947,bool,hAPP(U_1947,fun(U_1947,bool),ord_less_eq(U_1947),hAPP(U_1946,U_1947,U_1943,sK68(U_1947,U_1946,U_1945,U_1944,U_1943,U_1942))),hAPP(U_1946,U_1947,U_1943,sK69(U_1947,U_1946,U_1945,U_1944,U_1943,U_1942))))
    | ~ sP114(U_1943,U_1944,U_1945,U_1942,U_1946,U_1947) ),
    inference(clausify,[status(thm)],[f_508_5]) ).

fof(f_509_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_438_dense__le]) ).

fof(f_509_2,plain,
    ! [U_1951] :
      ( ! [U_1950,U_1949] :
          ( hBOOL(hAPP(U_1951,bool,hAPP(U_1951,fun(U_1951,bool),ord_less_eq(U_1951),U_1949),U_1950))
          | ? [U_1948] :
              ( ~ hBOOL(hAPP(U_1951,bool,hAPP(U_1951,fun(U_1951,bool),ord_less_eq(U_1951),U_1948),U_1950))
              & hBOOL(hAPP(U_1951,bool,hAPP(U_1951,fun(U_1951,bool),ord_less(U_1951),U_1948),U_1949)) ) )
      | ~ dense_linorder(U_1951) ),
    inference(variable_rename,[status(thm)],[f_509_1]) ).

fof(f_509_3,plain,
    ! [U_1951] :
      ( ! [U_1950,U_1949] :
          ( hBOOL(hAPP(U_1951,bool,hAPP(U_1951,fun(U_1951,bool),ord_less_eq(U_1951),U_1949),U_1950))
          | ( ~ hBOOL(hAPP(U_1951,bool,hAPP(U_1951,fun(U_1951,bool),ord_less_eq(U_1951),sK70(U_1951,U_1950,U_1949)),U_1950))
            & hBOOL(hAPP(U_1951,bool,hAPP(U_1951,fun(U_1951,bool),ord_less(U_1951),sK70(U_1951,U_1950,U_1949)),U_1949)) ) )
      | ~ dense_linorder(U_1951) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK70]),skolemize(U_1948,sK70(U_1951,U_1950,U_1949))],[f_509_2]) ).

fof(f_509_4,plain,
    ( ! [U_1949,U_1950,U_1951] :
        ( ~ hBOOL(hAPP(U_1951,bool,hAPP(U_1951,fun(U_1951,bool),ord_less_eq(U_1951),sK70(U_1951,U_1950,U_1949)),U_1950))
        | ~ sP115(U_1949,U_1950,U_1951) )
    & ! [U_1949,U_1950,U_1951] :
        ( hBOOL(hAPP(U_1951,bool,hAPP(U_1951,fun(U_1951,bool),ord_less(U_1951),sK70(U_1951,U_1950,U_1949)),U_1949))
        | ~ sP115(U_1949,U_1950,U_1951) )
    & ! [U_1949,U_1950,U_1951] :
        ( hBOOL(hAPP(U_1951,bool,hAPP(U_1951,fun(U_1951,bool),ord_less_eq(U_1951),U_1949),U_1950))
        | sP115(U_1949,U_1950,U_1951)
        | ~ dense_linorder(U_1951) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP115])],[f_509_3]) ).

cnf(f_509_5,plain,
    ( hBOOL(hAPP(U_1951,bool,hAPP(U_1951,fun(U_1951,bool),ord_less_eq(U_1951),U_1949),U_1950))
    | sP115(U_1949,U_1950,U_1951)
    | ~ dense_linorder(U_1951) ),
    inference(clausify,[status(thm)],[f_509_4]) ).

cnf(f_509_6,plain,
    ( hBOOL(hAPP(U_1951,bool,hAPP(U_1951,fun(U_1951,bool),ord_less(U_1951),sK70(U_1951,U_1950,U_1949)),U_1949))
    | ~ sP115(U_1949,U_1950,U_1951) ),
    inference(clausify,[status(thm)],[f_509_4]) ).

cnf(f_509_7,plain,
    ( ~ hBOOL(hAPP(U_1951,bool,hAPP(U_1951,fun(U_1951,bool),ord_less_eq(U_1951),sK70(U_1951,U_1950,U_1949)),U_1950))
    | ~ sP115(U_1949,U_1950,U_1951) ),
    inference(clausify,[status(thm)],[f_509_4]) ).

fof(f_510_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_3] :
              ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),W_3),Z))
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),W_3),Y))
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),W_3)) )
          | ~ 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_439_dense__le__bounded]) ).

fof(f_510_2,plain,
    ! [U_1956] :
      ( ! [U_1955,U_1954,U_1953] :
          ( hBOOL(hAPP(U_1956,bool,hAPP(U_1956,fun(U_1956,bool),ord_less_eq(U_1956),U_1953),U_1955))
          | ? [U_1952] :
              ( ~ hBOOL(hAPP(U_1956,bool,hAPP(U_1956,fun(U_1956,bool),ord_less_eq(U_1956),U_1952),U_1955))
              & hBOOL(hAPP(U_1956,bool,hAPP(U_1956,fun(U_1956,bool),ord_less(U_1956),U_1952),U_1953))
              & hBOOL(hAPP(U_1956,bool,hAPP(U_1956,fun(U_1956,bool),ord_less(U_1956),U_1954),U_1952)) )
          | ~ hBOOL(hAPP(U_1956,bool,hAPP(U_1956,fun(U_1956,bool),ord_less(U_1956),U_1954),U_1953)) )
      | ~ dense_linorder(U_1956) ),
    inference(variable_rename,[status(thm)],[f_510_1]) ).

fof(f_510_3,plain,
    ! [U_1956] :
      ( ! [U_1955,U_1954,U_1953] :
          ( hBOOL(hAPP(U_1956,bool,hAPP(U_1956,fun(U_1956,bool),ord_less_eq(U_1956),U_1953),U_1955))
          | ( ~ hBOOL(hAPP(U_1956,bool,hAPP(U_1956,fun(U_1956,bool),ord_less_eq(U_1956),sK71(U_1956,U_1955,U_1954,U_1953)),U_1955))
            & hBOOL(hAPP(U_1956,bool,hAPP(U_1956,fun(U_1956,bool),ord_less(U_1956),sK71(U_1956,U_1955,U_1954,U_1953)),U_1953))
            & hBOOL(hAPP(U_1956,bool,hAPP(U_1956,fun(U_1956,bool),ord_less(U_1956),U_1954),sK71(U_1956,U_1955,U_1954,U_1953))) )
          | ~ hBOOL(hAPP(U_1956,bool,hAPP(U_1956,fun(U_1956,bool),ord_less(U_1956),U_1954),U_1953)) )
      | ~ dense_linorder(U_1956) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK71]),skolemize(U_1952,sK71(U_1956,U_1955,U_1954,U_1953))],[f_510_2]) ).

fof(f_510_4,plain,
    ( ! [U_1953,U_1956,U_1954,U_1955] :
        ( ~ hBOOL(hAPP(U_1956,bool,hAPP(U_1956,fun(U_1956,bool),ord_less_eq(U_1956),sK71(U_1956,U_1955,U_1954,U_1953)),U_1955))
        | ~ sP116(U_1953,U_1956,U_1954,U_1955) )
    & ! [U_1953,U_1956,U_1954,U_1955] :
        ( hBOOL(hAPP(U_1956,bool,hAPP(U_1956,fun(U_1956,bool),ord_less(U_1956),sK71(U_1956,U_1955,U_1954,U_1953)),U_1953))
        | ~ sP116(U_1953,U_1956,U_1954,U_1955) )
    & ! [U_1953,U_1956,U_1954,U_1955] :
        ( hBOOL(hAPP(U_1956,bool,hAPP(U_1956,fun(U_1956,bool),ord_less(U_1956),U_1954),sK71(U_1956,U_1955,U_1954,U_1953)))
        | ~ sP116(U_1953,U_1956,U_1954,U_1955) )
    & ! [U_1953,U_1956,U_1954,U_1955] :
        ( hBOOL(hAPP(U_1956,bool,hAPP(U_1956,fun(U_1956,bool),ord_less_eq(U_1956),U_1953),U_1955))
        | sP116(U_1953,U_1956,U_1954,U_1955)
        | ~ hBOOL(hAPP(U_1956,bool,hAPP(U_1956,fun(U_1956,bool),ord_less(U_1956),U_1954),U_1953))
        | ~ dense_linorder(U_1956) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP116])],[f_510_3]) ).

cnf(f_510_5,plain,
    ( hBOOL(hAPP(U_1956,bool,hAPP(U_1956,fun(U_1956,bool),ord_less_eq(U_1956),U_1953),U_1955))
    | sP116(U_1953,U_1956,U_1954,U_1955)
    | ~ hBOOL(hAPP(U_1956,bool,hAPP(U_1956,fun(U_1956,bool),ord_less(U_1956),U_1954),U_1953))
    | ~ dense_linorder(U_1956) ),
    inference(clausify,[status(thm)],[f_510_4]) ).

cnf(f_510_6,plain,
    ( hBOOL(hAPP(U_1956,bool,hAPP(U_1956,fun(U_1956,bool),ord_less(U_1956),U_1954),sK71(U_1956,U_1955,U_1954,U_1953)))
    | ~ sP116(U_1953,U_1956,U_1954,U_1955) ),
    inference(clausify,[status(thm)],[f_510_4]) ).

cnf(f_510_7,plain,
    ( hBOOL(hAPP(U_1956,bool,hAPP(U_1956,fun(U_1956,bool),ord_less(U_1956),sK71(U_1956,U_1955,U_1954,U_1953)),U_1953))
    | ~ sP116(U_1953,U_1956,U_1954,U_1955) ),
    inference(clausify,[status(thm)],[f_510_4]) ).

cnf(f_510_8,plain,
    ( ~ hBOOL(hAPP(U_1956,bool,hAPP(U_1956,fun(U_1956,bool),ord_less_eq(U_1956),sK71(U_1956,U_1955,U_1954,U_1953)),U_1955))
    | ~ sP116(U_1953,U_1956,U_1954,U_1955) ),
    inference(clausify,[status(thm)],[f_510_4]) ).

fof(f_511_1,plain,
    ! [X_c,X_b] :
      ( ! [C_1,F,B_3,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_1] :
              ( ~ hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),hAPP(X_b,X_c,F,Y_1)),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_1),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_3)))
          | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),B_3),A_2)) )
      | ~ order(X_c)
      | ~ order(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_440_xt5]) ).

fof(f_511_2,plain,
    ! [U_1964,U_1963] :
      ( ! [U_1962,U_1961,U_1960,U_1959] :
          ( hBOOL(hAPP(U_1964,bool,hAPP(U_1964,fun(U_1964,bool),ord_less(U_1964),U_1962),hAPP(U_1963,U_1964,U_1961,U_1959)))
          | ? [U_1958,U_1957] :
              ( ~ hBOOL(hAPP(U_1964,bool,hAPP(U_1964,fun(U_1964,bool),ord_less(U_1964),hAPP(U_1963,U_1964,U_1961,U_1957)),hAPP(U_1963,U_1964,U_1961,U_1958)))
              & hBOOL(hAPP(U_1963,bool,hAPP(U_1963,fun(U_1963,bool),ord_less(U_1963),U_1957),U_1958)) )
          | ~ hBOOL(hAPP(U_1964,bool,hAPP(U_1964,fun(U_1964,bool),ord_less_eq(U_1964),U_1962),hAPP(U_1963,U_1964,U_1961,U_1960)))
          | ~ hBOOL(hAPP(U_1963,bool,hAPP(U_1963,fun(U_1963,bool),ord_less(U_1963),U_1960),U_1959)) )
      | ~ order(U_1964)
      | ~ order(U_1963) ),
    inference(variable_rename,[status(thm)],[f_511_1]) ).

fof(f_511_3,plain,
    ! [U_1964,U_1963] :
      ( ! [U_1962,U_1961,U_1960,U_1959] :
          ( hBOOL(hAPP(U_1964,bool,hAPP(U_1964,fun(U_1964,bool),ord_less(U_1964),U_1962),hAPP(U_1963,U_1964,U_1961,U_1959)))
          | ? [U_1957] :
              ( ~ hBOOL(hAPP(U_1964,bool,hAPP(U_1964,fun(U_1964,bool),ord_less(U_1964),hAPP(U_1963,U_1964,U_1961,U_1957)),hAPP(U_1963,U_1964,U_1961,sK72(U_1964,U_1963,U_1962,U_1961,U_1960,U_1959))))
              & hBOOL(hAPP(U_1963,bool,hAPP(U_1963,fun(U_1963,bool),ord_less(U_1963),U_1957),sK72(U_1964,U_1963,U_1962,U_1961,U_1960,U_1959))) )
          | ~ hBOOL(hAPP(U_1964,bool,hAPP(U_1964,fun(U_1964,bool),ord_less_eq(U_1964),U_1962),hAPP(U_1963,U_1964,U_1961,U_1960)))
          | ~ hBOOL(hAPP(U_1963,bool,hAPP(U_1963,fun(U_1963,bool),ord_less(U_1963),U_1960),U_1959)) )
      | ~ order(U_1964)
      | ~ order(U_1963) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK72]),skolemize(U_1958,sK72(U_1964,U_1963,U_1962,U_1961,U_1960,U_1959))],[f_511_2]) ).

fof(f_511_4,plain,
    ! [U_1964,U_1963] :
      ( ! [U_1962,U_1961,U_1960,U_1959] :
          ( hBOOL(hAPP(U_1964,bool,hAPP(U_1964,fun(U_1964,bool),ord_less(U_1964),U_1962),hAPP(U_1963,U_1964,U_1961,U_1959)))
          | ( ~ hBOOL(hAPP(U_1964,bool,hAPP(U_1964,fun(U_1964,bool),ord_less(U_1964),hAPP(U_1963,U_1964,U_1961,sK73(U_1964,U_1963,U_1962,U_1961,U_1960,U_1959))),hAPP(U_1963,U_1964,U_1961,sK72(U_1964,U_1963,U_1962,U_1961,U_1960,U_1959))))
            & hBOOL(hAPP(U_1963,bool,hAPP(U_1963,fun(U_1963,bool),ord_less(U_1963),sK73(U_1964,U_1963,U_1962,U_1961,U_1960,U_1959)),sK72(U_1964,U_1963,U_1962,U_1961,U_1960,U_1959))) )
          | ~ hBOOL(hAPP(U_1964,bool,hAPP(U_1964,fun(U_1964,bool),ord_less_eq(U_1964),U_1962),hAPP(U_1963,U_1964,U_1961,U_1960)))
          | ~ hBOOL(hAPP(U_1963,bool,hAPP(U_1963,fun(U_1963,bool),ord_less(U_1963),U_1960),U_1959)) )
      | ~ order(U_1964)
      | ~ order(U_1963) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK73]),skolemize(U_1957,sK73(U_1964,U_1963,U_1962,U_1961,U_1960,U_1959))],[f_511_3]) ).

fof(f_511_5,plain,
    ( ! [U_1961,U_1959,U_1960,U_1962,U_1963,U_1964] :
        ( ~ hBOOL(hAPP(U_1964,bool,hAPP(U_1964,fun(U_1964,bool),ord_less(U_1964),hAPP(U_1963,U_1964,U_1961,sK73(U_1964,U_1963,U_1962,U_1961,U_1960,U_1959))),hAPP(U_1963,U_1964,U_1961,sK72(U_1964,U_1963,U_1962,U_1961,U_1960,U_1959))))
        | ~ sP117(U_1961,U_1959,U_1960,U_1962,U_1963,U_1964) )
    & ! [U_1961,U_1959,U_1960,U_1962,U_1963,U_1964] :
        ( hBOOL(hAPP(U_1963,bool,hAPP(U_1963,fun(U_1963,bool),ord_less(U_1963),sK73(U_1964,U_1963,U_1962,U_1961,U_1960,U_1959)),sK72(U_1964,U_1963,U_1962,U_1961,U_1960,U_1959)))
        | ~ sP117(U_1961,U_1959,U_1960,U_1962,U_1963,U_1964) )
    & ! [U_1961,U_1959,U_1960,U_1962,U_1963,U_1964] :
        ( hBOOL(hAPP(U_1964,bool,hAPP(U_1964,fun(U_1964,bool),ord_less(U_1964),U_1962),hAPP(U_1963,U_1964,U_1961,U_1959)))
        | sP117(U_1961,U_1959,U_1960,U_1962,U_1963,U_1964)
        | ~ hBOOL(hAPP(U_1964,bool,hAPP(U_1964,fun(U_1964,bool),ord_less_eq(U_1964),U_1962),hAPP(U_1963,U_1964,U_1961,U_1960)))
        | ~ hBOOL(hAPP(U_1963,bool,hAPP(U_1963,fun(U_1963,bool),ord_less(U_1963),U_1960),U_1959))
        | ~ order(U_1964)
        | ~ order(U_1963) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP117])],[f_511_4]) ).

cnf(f_511_6,plain,
    ( hBOOL(hAPP(U_1964,bool,hAPP(U_1964,fun(U_1964,bool),ord_less(U_1964),U_1962),hAPP(U_1963,U_1964,U_1961,U_1959)))
    | sP117(U_1961,U_1959,U_1960,U_1962,U_1963,U_1964)
    | ~ hBOOL(hAPP(U_1964,bool,hAPP(U_1964,fun(U_1964,bool),ord_less_eq(U_1964),U_1962),hAPP(U_1963,U_1964,U_1961,U_1960)))
    | ~ hBOOL(hAPP(U_1963,bool,hAPP(U_1963,fun(U_1963,bool),ord_less(U_1963),U_1960),U_1959))
    | ~ order(U_1964)
    | ~ order(U_1963) ),
    inference(clausify,[status(thm)],[f_511_5]) ).

cnf(f_511_7,plain,
    ( hBOOL(hAPP(U_1963,bool,hAPP(U_1963,fun(U_1963,bool),ord_less(U_1963),sK73(U_1964,U_1963,U_1962,U_1961,U_1960,U_1959)),sK72(U_1964,U_1963,U_1962,U_1961,U_1960,U_1959)))
    | ~ sP117(U_1961,U_1959,U_1960,U_1962,U_1963,U_1964) ),
    inference(clausify,[status(thm)],[f_511_5]) ).

cnf(f_511_8,plain,
    ( ~ hBOOL(hAPP(U_1964,bool,hAPP(U_1964,fun(U_1964,bool),ord_less(U_1964),hAPP(U_1963,U_1964,U_1961,sK73(U_1964,U_1963,U_1962,U_1961,U_1960,U_1959))),hAPP(U_1963,U_1964,U_1961,sK72(U_1964,U_1963,U_1962,U_1961,U_1960,U_1959))))
    | ~ sP117(U_1961,U_1959,U_1960,U_1962,U_1963,U_1964) ),
    inference(clausify,[status(thm)],[f_511_5]) ).

fof(f_512_1,plain,
    ! [X_c,X_b] :
      ( ! [C_1,F,B_3,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_1] :
              ( ~ hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,Y_1)),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_1),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_3)))
          | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),B_3),A_2)) )
      | ~ order(X_c)
      | ~ order(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_441_xt7]) ).

fof(f_512_2,plain,
    ! [U_1972,U_1971] :
      ( ! [U_1970,U_1969,U_1968,U_1967] :
          ( hBOOL(hAPP(U_1972,bool,hAPP(U_1972,fun(U_1972,bool),ord_less(U_1972),U_1970),hAPP(U_1971,U_1972,U_1969,U_1967)))
          | ? [U_1966,U_1965] :
              ( ~ hBOOL(hAPP(U_1972,bool,hAPP(U_1972,fun(U_1972,bool),ord_less_eq(U_1972),hAPP(U_1971,U_1972,U_1969,U_1965)),hAPP(U_1971,U_1972,U_1969,U_1966)))
              & hBOOL(hAPP(U_1971,bool,hAPP(U_1971,fun(U_1971,bool),ord_less_eq(U_1971),U_1965),U_1966)) )
          | ~ hBOOL(hAPP(U_1972,bool,hAPP(U_1972,fun(U_1972,bool),ord_less(U_1972),U_1970),hAPP(U_1971,U_1972,U_1969,U_1968)))
          | ~ hBOOL(hAPP(U_1971,bool,hAPP(U_1971,fun(U_1971,bool),ord_less_eq(U_1971),U_1968),U_1967)) )
      | ~ order(U_1972)
      | ~ order(U_1971) ),
    inference(variable_rename,[status(thm)],[f_512_1]) ).

fof(f_512_3,plain,
    ! [U_1972,U_1971] :
      ( ! [U_1970,U_1969,U_1968,U_1967] :
          ( hBOOL(hAPP(U_1972,bool,hAPP(U_1972,fun(U_1972,bool),ord_less(U_1972),U_1970),hAPP(U_1971,U_1972,U_1969,U_1967)))
          | ? [U_1965] :
              ( ~ hBOOL(hAPP(U_1972,bool,hAPP(U_1972,fun(U_1972,bool),ord_less_eq(U_1972),hAPP(U_1971,U_1972,U_1969,U_1965)),hAPP(U_1971,U_1972,U_1969,sK74(U_1972,U_1971,U_1970,U_1969,U_1968,U_1967))))
              & hBOOL(hAPP(U_1971,bool,hAPP(U_1971,fun(U_1971,bool),ord_less_eq(U_1971),U_1965),sK74(U_1972,U_1971,U_1970,U_1969,U_1968,U_1967))) )
          | ~ hBOOL(hAPP(U_1972,bool,hAPP(U_1972,fun(U_1972,bool),ord_less(U_1972),U_1970),hAPP(U_1971,U_1972,U_1969,U_1968)))
          | ~ hBOOL(hAPP(U_1971,bool,hAPP(U_1971,fun(U_1971,bool),ord_less_eq(U_1971),U_1968),U_1967)) )
      | ~ order(U_1972)
      | ~ order(U_1971) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK74]),skolemize(U_1966,sK74(U_1972,U_1971,U_1970,U_1969,U_1968,U_1967))],[f_512_2]) ).

fof(f_512_4,plain,
    ! [U_1972,U_1971] :
      ( ! [U_1970,U_1969,U_1968,U_1967] :
          ( hBOOL(hAPP(U_1972,bool,hAPP(U_1972,fun(U_1972,bool),ord_less(U_1972),U_1970),hAPP(U_1971,U_1972,U_1969,U_1967)))
          | ( ~ hBOOL(hAPP(U_1972,bool,hAPP(U_1972,fun(U_1972,bool),ord_less_eq(U_1972),hAPP(U_1971,U_1972,U_1969,sK75(U_1972,U_1971,U_1970,U_1969,U_1968,U_1967))),hAPP(U_1971,U_1972,U_1969,sK74(U_1972,U_1971,U_1970,U_1969,U_1968,U_1967))))
            & hBOOL(hAPP(U_1971,bool,hAPP(U_1971,fun(U_1971,bool),ord_less_eq(U_1971),sK75(U_1972,U_1971,U_1970,U_1969,U_1968,U_1967)),sK74(U_1972,U_1971,U_1970,U_1969,U_1968,U_1967))) )
          | ~ hBOOL(hAPP(U_1972,bool,hAPP(U_1972,fun(U_1972,bool),ord_less(U_1972),U_1970),hAPP(U_1971,U_1972,U_1969,U_1968)))
          | ~ hBOOL(hAPP(U_1971,bool,hAPP(U_1971,fun(U_1971,bool),ord_less_eq(U_1971),U_1968),U_1967)) )
      | ~ order(U_1972)
      | ~ order(U_1971) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK75]),skolemize(U_1965,sK75(U_1972,U_1971,U_1970,U_1969,U_1968,U_1967))],[f_512_3]) ).

fof(f_512_5,plain,
    ( ! [U_1967,U_1968,U_1969,U_1971,U_1970,U_1972] :
        ( ~ hBOOL(hAPP(U_1972,bool,hAPP(U_1972,fun(U_1972,bool),ord_less_eq(U_1972),hAPP(U_1971,U_1972,U_1969,sK75(U_1972,U_1971,U_1970,U_1969,U_1968,U_1967))),hAPP(U_1971,U_1972,U_1969,sK74(U_1972,U_1971,U_1970,U_1969,U_1968,U_1967))))
        | ~ sP118(U_1967,U_1968,U_1969,U_1971,U_1970,U_1972) )
    & ! [U_1967,U_1968,U_1969,U_1971,U_1970,U_1972] :
        ( hBOOL(hAPP(U_1971,bool,hAPP(U_1971,fun(U_1971,bool),ord_less_eq(U_1971),sK75(U_1972,U_1971,U_1970,U_1969,U_1968,U_1967)),sK74(U_1972,U_1971,U_1970,U_1969,U_1968,U_1967)))
        | ~ sP118(U_1967,U_1968,U_1969,U_1971,U_1970,U_1972) )
    & ! [U_1967,U_1968,U_1969,U_1971,U_1970,U_1972] :
        ( hBOOL(hAPP(U_1972,bool,hAPP(U_1972,fun(U_1972,bool),ord_less(U_1972),U_1970),hAPP(U_1971,U_1972,U_1969,U_1967)))
        | sP118(U_1967,U_1968,U_1969,U_1971,U_1970,U_1972)
        | ~ hBOOL(hAPP(U_1972,bool,hAPP(U_1972,fun(U_1972,bool),ord_less(U_1972),U_1970),hAPP(U_1971,U_1972,U_1969,U_1968)))
        | ~ hBOOL(hAPP(U_1971,bool,hAPP(U_1971,fun(U_1971,bool),ord_less_eq(U_1971),U_1968),U_1967))
        | ~ order(U_1972)
        | ~ order(U_1971) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP118])],[f_512_4]) ).

cnf(f_512_6,plain,
    ( hBOOL(hAPP(U_1972,bool,hAPP(U_1972,fun(U_1972,bool),ord_less(U_1972),U_1970),hAPP(U_1971,U_1972,U_1969,U_1967)))
    | sP118(U_1967,U_1968,U_1969,U_1971,U_1970,U_1972)
    | ~ hBOOL(hAPP(U_1972,bool,hAPP(U_1972,fun(U_1972,bool),ord_less(U_1972),U_1970),hAPP(U_1971,U_1972,U_1969,U_1968)))
    | ~ hBOOL(hAPP(U_1971,bool,hAPP(U_1971,fun(U_1971,bool),ord_less_eq(U_1971),U_1968),U_1967))
    | ~ order(U_1972)
    | ~ order(U_1971) ),
    inference(clausify,[status(thm)],[f_512_5]) ).

cnf(f_512_7,plain,
    ( hBOOL(hAPP(U_1971,bool,hAPP(U_1971,fun(U_1971,bool),ord_less_eq(U_1971),sK75(U_1972,U_1971,U_1970,U_1969,U_1968,U_1967)),sK74(U_1972,U_1971,U_1970,U_1969,U_1968,U_1967)))
    | ~ sP118(U_1967,U_1968,U_1969,U_1971,U_1970,U_1972) ),
    inference(clausify,[status(thm)],[f_512_5]) ).

cnf(f_512_8,plain,
    ( ~ hBOOL(hAPP(U_1972,bool,hAPP(U_1972,fun(U_1972,bool),ord_less_eq(U_1972),hAPP(U_1971,U_1972,U_1969,sK75(U_1972,U_1971,U_1970,U_1969,U_1968,U_1967))),hAPP(U_1971,U_1972,U_1969,sK74(U_1972,U_1971,U_1970,U_1969,U_1968,U_1967))))
    | ~ sP118(U_1967,U_1968,U_1969,U_1971,U_1970,U_1972) ),
    inference(clausify,[status(thm)],[f_512_5]) ).

fof(f_513_1,plain,
    ! [X_b,X_c] :
      ( ! [F,C_1,A_2,B_3] :
          ( 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_1] :
              ( ~ 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_1)))
              & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_2),Y_1)) )
          | ~ hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),hAPP(X_b,X_c,F,B_3)),C_1))
          | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),B_3)) )
      | ~ order(X_b)
      | ~ order(X_c) ),
    inference(fof_nnf,[status(thm)],[fact_442_order__le__less__subst2]) ).

fof(f_513_2,plain,
    ! [U_1980,U_1979] :
      ( ! [U_1978,U_1977,U_1976,U_1975] :
          ( hBOOL(hAPP(U_1979,bool,hAPP(U_1979,fun(U_1979,bool),ord_less(U_1979),hAPP(U_1980,U_1979,U_1978,U_1976)),U_1977))
          | ? [U_1974,U_1973] :
              ( ~ hBOOL(hAPP(U_1979,bool,hAPP(U_1979,fun(U_1979,bool),ord_less_eq(U_1979),hAPP(U_1980,U_1979,U_1978,U_1974)),hAPP(U_1980,U_1979,U_1978,U_1973)))
              & hBOOL(hAPP(U_1980,bool,hAPP(U_1980,fun(U_1980,bool),ord_less_eq(U_1980),U_1974),U_1973)) )
          | ~ hBOOL(hAPP(U_1979,bool,hAPP(U_1979,fun(U_1979,bool),ord_less(U_1979),hAPP(U_1980,U_1979,U_1978,U_1975)),U_1977))
          | ~ hBOOL(hAPP(U_1980,bool,hAPP(U_1980,fun(U_1980,bool),ord_less_eq(U_1980),U_1976),U_1975)) )
      | ~ order(U_1980)
      | ~ order(U_1979) ),
    inference(variable_rename,[status(thm)],[f_513_1]) ).

fof(f_513_3,plain,
    ! [U_1980,U_1979] :
      ( ! [U_1978,U_1977,U_1976,U_1975] :
          ( hBOOL(hAPP(U_1979,bool,hAPP(U_1979,fun(U_1979,bool),ord_less(U_1979),hAPP(U_1980,U_1979,U_1978,U_1976)),U_1977))
          | ? [U_1973] :
              ( ~ hBOOL(hAPP(U_1979,bool,hAPP(U_1979,fun(U_1979,bool),ord_less_eq(U_1979),hAPP(U_1980,U_1979,U_1978,sK76(U_1980,U_1979,U_1978,U_1977,U_1976,U_1975))),hAPP(U_1980,U_1979,U_1978,U_1973)))
              & hBOOL(hAPP(U_1980,bool,hAPP(U_1980,fun(U_1980,bool),ord_less_eq(U_1980),sK76(U_1980,U_1979,U_1978,U_1977,U_1976,U_1975)),U_1973)) )
          | ~ hBOOL(hAPP(U_1979,bool,hAPP(U_1979,fun(U_1979,bool),ord_less(U_1979),hAPP(U_1980,U_1979,U_1978,U_1975)),U_1977))
          | ~ hBOOL(hAPP(U_1980,bool,hAPP(U_1980,fun(U_1980,bool),ord_less_eq(U_1980),U_1976),U_1975)) )
      | ~ order(U_1980)
      | ~ order(U_1979) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK76]),skolemize(U_1974,sK76(U_1980,U_1979,U_1978,U_1977,U_1976,U_1975))],[f_513_2]) ).

fof(f_513_4,plain,
    ! [U_1980,U_1979] :
      ( ! [U_1978,U_1977,U_1976,U_1975] :
          ( hBOOL(hAPP(U_1979,bool,hAPP(U_1979,fun(U_1979,bool),ord_less(U_1979),hAPP(U_1980,U_1979,U_1978,U_1976)),U_1977))
          | ( ~ hBOOL(hAPP(U_1979,bool,hAPP(U_1979,fun(U_1979,bool),ord_less_eq(U_1979),hAPP(U_1980,U_1979,U_1978,sK76(U_1980,U_1979,U_1978,U_1977,U_1976,U_1975))),hAPP(U_1980,U_1979,U_1978,sK77(U_1980,U_1979,U_1978,U_1977,U_1976,U_1975))))
            & hBOOL(hAPP(U_1980,bool,hAPP(U_1980,fun(U_1980,bool),ord_less_eq(U_1980),sK76(U_1980,U_1979,U_1978,U_1977,U_1976,U_1975)),sK77(U_1980,U_1979,U_1978,U_1977,U_1976,U_1975))) )
          | ~ hBOOL(hAPP(U_1979,bool,hAPP(U_1979,fun(U_1979,bool),ord_less(U_1979),hAPP(U_1980,U_1979,U_1978,U_1975)),U_1977))
          | ~ hBOOL(hAPP(U_1980,bool,hAPP(U_1980,fun(U_1980,bool),ord_less_eq(U_1980),U_1976),U_1975)) )
      | ~ order(U_1980)
      | ~ order(U_1979) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK77]),skolemize(U_1973,sK77(U_1980,U_1979,U_1978,U_1977,U_1976,U_1975))],[f_513_3]) ).

fof(f_513_5,plain,
    ( ! [U_1977,U_1976,U_1975,U_1979,U_1978,U_1980] :
        ( ~ hBOOL(hAPP(U_1979,bool,hAPP(U_1979,fun(U_1979,bool),ord_less_eq(U_1979),hAPP(U_1980,U_1979,U_1978,sK76(U_1980,U_1979,U_1978,U_1977,U_1976,U_1975))),hAPP(U_1980,U_1979,U_1978,sK77(U_1980,U_1979,U_1978,U_1977,U_1976,U_1975))))
        | ~ sP119(U_1977,U_1976,U_1975,U_1979,U_1978,U_1980) )
    & ! [U_1977,U_1976,U_1975,U_1979,U_1978,U_1980] :
        ( hBOOL(hAPP(U_1980,bool,hAPP(U_1980,fun(U_1980,bool),ord_less_eq(U_1980),sK76(U_1980,U_1979,U_1978,U_1977,U_1976,U_1975)),sK77(U_1980,U_1979,U_1978,U_1977,U_1976,U_1975)))
        | ~ sP119(U_1977,U_1976,U_1975,U_1979,U_1978,U_1980) )
    & ! [U_1977,U_1976,U_1975,U_1979,U_1978,U_1980] :
        ( hBOOL(hAPP(U_1979,bool,hAPP(U_1979,fun(U_1979,bool),ord_less(U_1979),hAPP(U_1980,U_1979,U_1978,U_1976)),U_1977))
        | sP119(U_1977,U_1976,U_1975,U_1979,U_1978,U_1980)
        | ~ hBOOL(hAPP(U_1979,bool,hAPP(U_1979,fun(U_1979,bool),ord_less(U_1979),hAPP(U_1980,U_1979,U_1978,U_1975)),U_1977))
        | ~ hBOOL(hAPP(U_1980,bool,hAPP(U_1980,fun(U_1980,bool),ord_less_eq(U_1980),U_1976),U_1975))
        | ~ order(U_1980)
        | ~ order(U_1979) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP119])],[f_513_4]) ).

cnf(f_513_6,plain,
    ( hBOOL(hAPP(U_1979,bool,hAPP(U_1979,fun(U_1979,bool),ord_less(U_1979),hAPP(U_1980,U_1979,U_1978,U_1976)),U_1977))
    | sP119(U_1977,U_1976,U_1975,U_1979,U_1978,U_1980)
    | ~ hBOOL(hAPP(U_1979,bool,hAPP(U_1979,fun(U_1979,bool),ord_less(U_1979),hAPP(U_1980,U_1979,U_1978,U_1975)),U_1977))
    | ~ hBOOL(hAPP(U_1980,bool,hAPP(U_1980,fun(U_1980,bool),ord_less_eq(U_1980),U_1976),U_1975))
    | ~ order(U_1980)
    | ~ order(U_1979) ),
    inference(clausify,[status(thm)],[f_513_5]) ).

cnf(f_513_7,plain,
    ( hBOOL(hAPP(U_1980,bool,hAPP(U_1980,fun(U_1980,bool),ord_less_eq(U_1980),sK76(U_1980,U_1979,U_1978,U_1977,U_1976,U_1975)),sK77(U_1980,U_1979,U_1978,U_1977,U_1976,U_1975)))
    | ~ sP119(U_1977,U_1976,U_1975,U_1979,U_1978,U_1980) ),
    inference(clausify,[status(thm)],[f_513_5]) ).

cnf(f_513_8,plain,
    ( ~ hBOOL(hAPP(U_1979,bool,hAPP(U_1979,fun(U_1979,bool),ord_less_eq(U_1979),hAPP(U_1980,U_1979,U_1978,sK76(U_1980,U_1979,U_1978,U_1977,U_1976,U_1975))),hAPP(U_1980,U_1979,U_1978,sK77(U_1980,U_1979,U_1978,U_1977,U_1976,U_1975))))
    | ~ sP119(U_1977,U_1976,U_1975,U_1979,U_1978,U_1980) ),
    inference(clausify,[status(thm)],[f_513_5]) ).

fof(f_514_1,plain,
    ! [X_b,X_c] :
      ( ! [F,C_1,A_2,B_3] :
          ( 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_1] :
              ( ~ 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_1)))
              & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_2),Y_1)) )
          | ~ hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,B_3)),C_1))
          | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_3)) )
      | ~ order(X_b)
      | ~ order(X_c) ),
    inference(fof_nnf,[status(thm)],[fact_443_order__less__le__subst2]) ).

fof(f_514_2,plain,
    ! [U_1988,U_1987] :
      ( ! [U_1986,U_1985,U_1984,U_1983] :
          ( hBOOL(hAPP(U_1987,bool,hAPP(U_1987,fun(U_1987,bool),ord_less(U_1987),hAPP(U_1988,U_1987,U_1986,U_1984)),U_1985))
          | ? [U_1982,U_1981] :
              ( ~ hBOOL(hAPP(U_1987,bool,hAPP(U_1987,fun(U_1987,bool),ord_less(U_1987),hAPP(U_1988,U_1987,U_1986,U_1982)),hAPP(U_1988,U_1987,U_1986,U_1981)))
              & hBOOL(hAPP(U_1988,bool,hAPP(U_1988,fun(U_1988,bool),ord_less(U_1988),U_1982),U_1981)) )
          | ~ hBOOL(hAPP(U_1987,bool,hAPP(U_1987,fun(U_1987,bool),ord_less_eq(U_1987),hAPP(U_1988,U_1987,U_1986,U_1983)),U_1985))
          | ~ hBOOL(hAPP(U_1988,bool,hAPP(U_1988,fun(U_1988,bool),ord_less(U_1988),U_1984),U_1983)) )
      | ~ order(U_1988)
      | ~ order(U_1987) ),
    inference(variable_rename,[status(thm)],[f_514_1]) ).

fof(f_514_3,plain,
    ! [U_1988,U_1987] :
      ( ! [U_1986,U_1985,U_1984,U_1983] :
          ( hBOOL(hAPP(U_1987,bool,hAPP(U_1987,fun(U_1987,bool),ord_less(U_1987),hAPP(U_1988,U_1987,U_1986,U_1984)),U_1985))
          | ? [U_1981] :
              ( ~ hBOOL(hAPP(U_1987,bool,hAPP(U_1987,fun(U_1987,bool),ord_less(U_1987),hAPP(U_1988,U_1987,U_1986,sK78(U_1988,U_1987,U_1986,U_1985,U_1984,U_1983))),hAPP(U_1988,U_1987,U_1986,U_1981)))
              & hBOOL(hAPP(U_1988,bool,hAPP(U_1988,fun(U_1988,bool),ord_less(U_1988),sK78(U_1988,U_1987,U_1986,U_1985,U_1984,U_1983)),U_1981)) )
          | ~ hBOOL(hAPP(U_1987,bool,hAPP(U_1987,fun(U_1987,bool),ord_less_eq(U_1987),hAPP(U_1988,U_1987,U_1986,U_1983)),U_1985))
          | ~ hBOOL(hAPP(U_1988,bool,hAPP(U_1988,fun(U_1988,bool),ord_less(U_1988),U_1984),U_1983)) )
      | ~ order(U_1988)
      | ~ order(U_1987) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK78]),skolemize(U_1982,sK78(U_1988,U_1987,U_1986,U_1985,U_1984,U_1983))],[f_514_2]) ).

fof(f_514_4,plain,
    ! [U_1988,U_1987] :
      ( ! [U_1986,U_1985,U_1984,U_1983] :
          ( hBOOL(hAPP(U_1987,bool,hAPP(U_1987,fun(U_1987,bool),ord_less(U_1987),hAPP(U_1988,U_1987,U_1986,U_1984)),U_1985))
          | ( ~ hBOOL(hAPP(U_1987,bool,hAPP(U_1987,fun(U_1987,bool),ord_less(U_1987),hAPP(U_1988,U_1987,U_1986,sK78(U_1988,U_1987,U_1986,U_1985,U_1984,U_1983))),hAPP(U_1988,U_1987,U_1986,sK79(U_1988,U_1987,U_1986,U_1985,U_1984,U_1983))))
            & hBOOL(hAPP(U_1988,bool,hAPP(U_1988,fun(U_1988,bool),ord_less(U_1988),sK78(U_1988,U_1987,U_1986,U_1985,U_1984,U_1983)),sK79(U_1988,U_1987,U_1986,U_1985,U_1984,U_1983))) )
          | ~ hBOOL(hAPP(U_1987,bool,hAPP(U_1987,fun(U_1987,bool),ord_less_eq(U_1987),hAPP(U_1988,U_1987,U_1986,U_1983)),U_1985))
          | ~ hBOOL(hAPP(U_1988,bool,hAPP(U_1988,fun(U_1988,bool),ord_less(U_1988),U_1984),U_1983)) )
      | ~ order(U_1988)
      | ~ order(U_1987) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK79]),skolemize(U_1981,sK79(U_1988,U_1987,U_1986,U_1985,U_1984,U_1983))],[f_514_3]) ).

fof(f_514_5,plain,
    ( ! [U_1984,U_1985,U_1983,U_1987,U_1986,U_1988] :
        ( ~ hBOOL(hAPP(U_1987,bool,hAPP(U_1987,fun(U_1987,bool),ord_less(U_1987),hAPP(U_1988,U_1987,U_1986,sK78(U_1988,U_1987,U_1986,U_1985,U_1984,U_1983))),hAPP(U_1988,U_1987,U_1986,sK79(U_1988,U_1987,U_1986,U_1985,U_1984,U_1983))))
        | ~ sP120(U_1984,U_1985,U_1983,U_1987,U_1986,U_1988) )
    & ! [U_1984,U_1985,U_1983,U_1987,U_1986,U_1988] :
        ( hBOOL(hAPP(U_1988,bool,hAPP(U_1988,fun(U_1988,bool),ord_less(U_1988),sK78(U_1988,U_1987,U_1986,U_1985,U_1984,U_1983)),sK79(U_1988,U_1987,U_1986,U_1985,U_1984,U_1983)))
        | ~ sP120(U_1984,U_1985,U_1983,U_1987,U_1986,U_1988) )
    & ! [U_1984,U_1985,U_1983,U_1987,U_1986,U_1988] :
        ( hBOOL(hAPP(U_1987,bool,hAPP(U_1987,fun(U_1987,bool),ord_less(U_1987),hAPP(U_1988,U_1987,U_1986,U_1984)),U_1985))
        | sP120(U_1984,U_1985,U_1983,U_1987,U_1986,U_1988)
        | ~ hBOOL(hAPP(U_1987,bool,hAPP(U_1987,fun(U_1987,bool),ord_less_eq(U_1987),hAPP(U_1988,U_1987,U_1986,U_1983)),U_1985))
        | ~ hBOOL(hAPP(U_1988,bool,hAPP(U_1988,fun(U_1988,bool),ord_less(U_1988),U_1984),U_1983))
        | ~ order(U_1988)
        | ~ order(U_1987) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP120])],[f_514_4]) ).

cnf(f_514_6,plain,
    ( hBOOL(hAPP(U_1987,bool,hAPP(U_1987,fun(U_1987,bool),ord_less(U_1987),hAPP(U_1988,U_1987,U_1986,U_1984)),U_1985))
    | sP120(U_1984,U_1985,U_1983,U_1987,U_1986,U_1988)
    | ~ hBOOL(hAPP(U_1987,bool,hAPP(U_1987,fun(U_1987,bool),ord_less_eq(U_1987),hAPP(U_1988,U_1987,U_1986,U_1983)),U_1985))
    | ~ hBOOL(hAPP(U_1988,bool,hAPP(U_1988,fun(U_1988,bool),ord_less(U_1988),U_1984),U_1983))
    | ~ order(U_1988)
    | ~ order(U_1987) ),
    inference(clausify,[status(thm)],[f_514_5]) ).

cnf(f_514_7,plain,
    ( hBOOL(hAPP(U_1988,bool,hAPP(U_1988,fun(U_1988,bool),ord_less(U_1988),sK78(U_1988,U_1987,U_1986,U_1985,U_1984,U_1983)),sK79(U_1988,U_1987,U_1986,U_1985,U_1984,U_1983)))
    | ~ sP120(U_1984,U_1985,U_1983,U_1987,U_1986,U_1988) ),
    inference(clausify,[status(thm)],[f_514_5]) ).

cnf(f_514_8,plain,
    ( ~ hBOOL(hAPP(U_1987,bool,hAPP(U_1987,fun(U_1987,bool),ord_less(U_1987),hAPP(U_1988,U_1987,U_1986,sK78(U_1988,U_1987,U_1986,U_1985,U_1984,U_1983))),hAPP(U_1988,U_1987,U_1986,sK79(U_1988,U_1987,U_1986,U_1985,U_1984,U_1983))))
    | ~ sP120(U_1984,U_1985,U_1983,U_1987,U_1986,U_1988) ),
    inference(clausify,[status(thm)],[f_514_5]) ).

fof(f_515_1,plain,
    ! [X_c,X_b,B_1,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_1)) = 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_1))
      | ~ hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),B_1))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) ),
    inference(fof_nnf,[status(thm)],[fact_444_card__Plus]) ).

fof(f_515_2,plain,
    ! [U_1992,U_1991,U_1990,U_1989] :
      ( hAPP(fun(sum_sum(U_1991,U_1992),bool),nat,finite_card(sum_sum(U_1991,U_1992)),hAPP(fun(U_1992,bool),fun(sum_sum(U_1991,U_1992),bool),hAPP(fun(U_1991,bool),fun(fun(U_1992,bool),fun(sum_sum(U_1991,U_1992),bool)),sum_Plus(U_1991,U_1992),U_1989),U_1990)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(U_1991,bool),nat,finite_card(U_1991),U_1989)),hAPP(fun(U_1992,bool),nat,finite_card(U_1992),U_1990))
      | ~ hBOOL(hAPP(fun(U_1992,bool),bool,finite_finite(U_1992),U_1990))
      | ~ hBOOL(hAPP(fun(U_1991,bool),bool,finite_finite(U_1991),U_1989)) ),
    inference(variable_rename,[status(thm)],[f_515_1]) ).

fof(f_515_3,plain,
    ! [U_1992,U_1991,U_1990,U_1989] :
      ( hAPP(fun(sum_sum(U_1991,U_1992),bool),nat,finite_card(sum_sum(U_1991,U_1992)),hAPP(fun(U_1992,bool),fun(sum_sum(U_1991,U_1992),bool),hAPP(fun(U_1991,bool),fun(fun(U_1992,bool),fun(sum_sum(U_1991,U_1992),bool)),sum_Plus(U_1991,U_1992),U_1989),U_1990)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(U_1991,bool),nat,finite_card(U_1991),U_1989)),hAPP(fun(U_1992,bool),nat,finite_card(U_1992),U_1990))
      | ~ hBOOL(hAPP(fun(U_1992,bool),bool,finite_finite(U_1992),U_1990))
      | ~ hBOOL(hAPP(fun(U_1991,bool),bool,finite_finite(U_1991),U_1989)) ),
    inference(definitional_conversion,[status(esa)],[f_515_2]) ).

cnf(f_515_4,plain,
    ( hAPP(fun(sum_sum(U_1991,U_1992),bool),nat,finite_card(sum_sum(U_1991,U_1992)),hAPP(fun(U_1992,bool),fun(sum_sum(U_1991,U_1992),bool),hAPP(fun(U_1991,bool),fun(fun(U_1992,bool),fun(sum_sum(U_1991,U_1992),bool)),sum_Plus(U_1991,U_1992),U_1989),U_1990)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(U_1991,bool),nat,finite_card(U_1991),U_1989)),hAPP(fun(U_1992,bool),nat,finite_card(U_1992),U_1990))
    | ~ hBOOL(hAPP(fun(U_1992,bool),bool,finite_finite(U_1992),U_1990))
    | ~ hBOOL(hAPP(fun(U_1991,bool),bool,finite_finite(U_1991),U_1989)) ),
    inference(clausify,[status(thm)],[f_515_3]) ).

fof(f_516_1,plain,
    ! [X_c,X_b,F,G,M_3,N_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),M_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),G),N_2)
      | ? [X_2] :
          ( hAPP(X_b,X_c,F,X_2) != hAPP(X_b,X_c,G,X_2)
          & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),N_2)) )
      | ti(fun(X_b,bool),M_3) != ti(fun(X_b,bool),N_2) ),
    inference(fof_nnf,[status(thm)],[fact_445_image__cong]) ).

fof(f_516_2,plain,
    ! [U_1999,U_1998,U_1997,U_1996,U_1995,U_1994] :
      ( hAPP(fun(U_1998,bool),fun(U_1999,bool),hAPP(fun(U_1998,U_1999),fun(fun(U_1998,bool),fun(U_1999,bool)),image(U_1998,U_1999),U_1997),U_1995) = hAPP(fun(U_1998,bool),fun(U_1999,bool),hAPP(fun(U_1998,U_1999),fun(fun(U_1998,bool),fun(U_1999,bool)),image(U_1998,U_1999),U_1996),U_1994)
      | ? [U_1993] :
          ( hAPP(U_1998,U_1999,U_1997,U_1993) != hAPP(U_1998,U_1999,U_1996,U_1993)
          & hBOOL(hAPP(fun(U_1998,bool),bool,hAPP(U_1998,fun(fun(U_1998,bool),bool),member(U_1998),U_1993),U_1994)) )
      | ti(fun(U_1998,bool),U_1995) != ti(fun(U_1998,bool),U_1994) ),
    inference(variable_rename,[status(thm)],[f_516_1]) ).

fof(f_516_3,plain,
    ! [U_1999,U_1998,U_1997,U_1996,U_1995,U_1994] :
      ( hAPP(fun(U_1998,bool),fun(U_1999,bool),hAPP(fun(U_1998,U_1999),fun(fun(U_1998,bool),fun(U_1999,bool)),image(U_1998,U_1999),U_1997),U_1995) = hAPP(fun(U_1998,bool),fun(U_1999,bool),hAPP(fun(U_1998,U_1999),fun(fun(U_1998,bool),fun(U_1999,bool)),image(U_1998,U_1999),U_1996),U_1994)
      | ( hAPP(U_1998,U_1999,U_1997,sK80(U_1999,U_1998,U_1997,U_1996,U_1995,U_1994)) != hAPP(U_1998,U_1999,U_1996,sK80(U_1999,U_1998,U_1997,U_1996,U_1995,U_1994))
        & hBOOL(hAPP(fun(U_1998,bool),bool,hAPP(U_1998,fun(fun(U_1998,bool),bool),member(U_1998),sK80(U_1999,U_1998,U_1997,U_1996,U_1995,U_1994)),U_1994)) )
      | ti(fun(U_1998,bool),U_1995) != ti(fun(U_1998,bool),U_1994) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK80]),skolemize(U_1993,sK80(U_1999,U_1998,U_1997,U_1996,U_1995,U_1994))],[f_516_2]) ).

fof(f_516_4,plain,
    ( ! [U_1994,U_1995,U_1996,U_1997,U_1998,U_1999] :
        ( hAPP(U_1998,U_1999,U_1997,sK80(U_1999,U_1998,U_1997,U_1996,U_1995,U_1994)) != hAPP(U_1998,U_1999,U_1996,sK80(U_1999,U_1998,U_1997,U_1996,U_1995,U_1994))
        | ~ sP121(U_1994,U_1995,U_1996,U_1997,U_1998,U_1999) )
    & ! [U_1994,U_1995,U_1996,U_1997,U_1998,U_1999] :
        ( hBOOL(hAPP(fun(U_1998,bool),bool,hAPP(U_1998,fun(fun(U_1998,bool),bool),member(U_1998),sK80(U_1999,U_1998,U_1997,U_1996,U_1995,U_1994)),U_1994))
        | ~ sP121(U_1994,U_1995,U_1996,U_1997,U_1998,U_1999) )
    & ! [U_1994,U_1995,U_1996,U_1997,U_1998,U_1999] :
        ( hAPP(fun(U_1998,bool),fun(U_1999,bool),hAPP(fun(U_1998,U_1999),fun(fun(U_1998,bool),fun(U_1999,bool)),image(U_1998,U_1999),U_1997),U_1995) = hAPP(fun(U_1998,bool),fun(U_1999,bool),hAPP(fun(U_1998,U_1999),fun(fun(U_1998,bool),fun(U_1999,bool)),image(U_1998,U_1999),U_1996),U_1994)
        | sP121(U_1994,U_1995,U_1996,U_1997,U_1998,U_1999)
        | ti(fun(U_1998,bool),U_1995) != ti(fun(U_1998,bool),U_1994) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP121])],[f_516_3]) ).

cnf(f_516_5,plain,
    ( hAPP(fun(U_1998,bool),fun(U_1999,bool),hAPP(fun(U_1998,U_1999),fun(fun(U_1998,bool),fun(U_1999,bool)),image(U_1998,U_1999),U_1997),U_1995) = hAPP(fun(U_1998,bool),fun(U_1999,bool),hAPP(fun(U_1998,U_1999),fun(fun(U_1998,bool),fun(U_1999,bool)),image(U_1998,U_1999),U_1996),U_1994)
    | sP121(U_1994,U_1995,U_1996,U_1997,U_1998,U_1999)
    | ti(fun(U_1998,bool),U_1995) != ti(fun(U_1998,bool),U_1994) ),
    inference(clausify,[status(thm)],[f_516_4]) ).

cnf(f_516_6,plain,
    ( hBOOL(hAPP(fun(U_1998,bool),bool,hAPP(U_1998,fun(fun(U_1998,bool),bool),member(U_1998),sK80(U_1999,U_1998,U_1997,U_1996,U_1995,U_1994)),U_1994))
    | ~ sP121(U_1994,U_1995,U_1996,U_1997,U_1998,U_1999) ),
    inference(clausify,[status(thm)],[f_516_4]) ).

cnf(f_516_7,plain,
    ( hAPP(U_1998,U_1999,U_1997,sK80(U_1999,U_1998,U_1997,U_1996,U_1995,U_1994)) != hAPP(U_1998,U_1999,U_1996,sK80(U_1999,U_1998,U_1997,U_1996,U_1995,U_1994))
    | ~ sP121(U_1994,U_1995,U_1996,U_1997,U_1998,U_1999) ),
    inference(clausify,[status(thm)],[f_516_4]) ).

fof(f_517_1,plain,
    ! [X_b,X_c,A_3,B_1] :
      ( hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),B_1))
      | ~ 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_1))) ),
    inference(fof_nnf,[status(thm)],[fact_446_finite__PlusD_I2_J]) ).

fof(f_517_2,plain,
    ! [U_2003,U_2002,U_2001,U_2000] :
      ( hBOOL(hAPP(fun(U_2002,bool),bool,finite_finite(U_2002),U_2000))
      | ~ hBOOL(hAPP(fun(sum_sum(U_2003,U_2002),bool),bool,finite_finite(sum_sum(U_2003,U_2002)),hAPP(fun(U_2002,bool),fun(sum_sum(U_2003,U_2002),bool),hAPP(fun(U_2003,bool),fun(fun(U_2002,bool),fun(sum_sum(U_2003,U_2002),bool)),sum_Plus(U_2003,U_2002),U_2001),U_2000))) ),
    inference(variable_rename,[status(thm)],[f_517_1]) ).

fof(f_517_3,plain,
    ! [U_2003,U_2002,U_2000,U_2001] :
      ( hBOOL(hAPP(fun(U_2002,bool),bool,finite_finite(U_2002),U_2000))
      | ~ hBOOL(hAPP(fun(sum_sum(U_2003,U_2002),bool),bool,finite_finite(sum_sum(U_2003,U_2002)),hAPP(fun(U_2002,bool),fun(sum_sum(U_2003,U_2002),bool),hAPP(fun(U_2003,bool),fun(fun(U_2002,bool),fun(sum_sum(U_2003,U_2002),bool)),sum_Plus(U_2003,U_2002),U_2001),U_2000))) ),
    inference(definitional_conversion,[status(esa)],[f_517_2]) ).

cnf(f_517_4,plain,
    ( hBOOL(hAPP(fun(U_2002,bool),bool,finite_finite(U_2002),U_2000))
    | ~ hBOOL(hAPP(fun(sum_sum(U_2003,U_2002),bool),bool,finite_finite(sum_sum(U_2003,U_2002)),hAPP(fun(U_2002,bool),fun(sum_sum(U_2003,U_2002),bool),hAPP(fun(U_2003,bool),fun(fun(U_2002,bool),fun(sum_sum(U_2003,U_2002),bool)),sum_Plus(U_2003,U_2002),U_2001),U_2000))) ),
    inference(clausify,[status(thm)],[f_517_3]) ).

fof(f_518_1,plain,
    ! [X_b,X_c,A_3,B_1] :
      ( 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_1))) ),
    inference(fof_nnf,[status(thm)],[fact_447_finite__PlusD_I1_J]) ).

fof(f_518_2,plain,
    ! [U_2007,U_2006,U_2005,U_2004] :
      ( hBOOL(hAPP(fun(U_2007,bool),bool,finite_finite(U_2007),U_2005))
      | ~ hBOOL(hAPP(fun(sum_sum(U_2007,U_2006),bool),bool,finite_finite(sum_sum(U_2007,U_2006)),hAPP(fun(U_2006,bool),fun(sum_sum(U_2007,U_2006),bool),hAPP(fun(U_2007,bool),fun(fun(U_2006,bool),fun(sum_sum(U_2007,U_2006),bool)),sum_Plus(U_2007,U_2006),U_2005),U_2004))) ),
    inference(variable_rename,[status(thm)],[f_518_1]) ).

fof(f_518_3,plain,
    ! [U_2007,U_2006,U_2005] :
      ( ! [U_2004] : ~ hBOOL(hAPP(fun(sum_sum(U_2007,U_2006),bool),bool,finite_finite(sum_sum(U_2007,U_2006)),hAPP(fun(U_2006,bool),fun(sum_sum(U_2007,U_2006),bool),hAPP(fun(U_2007,bool),fun(fun(U_2006,bool),fun(sum_sum(U_2007,U_2006),bool)),sum_Plus(U_2007,U_2006),U_2005),U_2004)))
      | hBOOL(hAPP(fun(U_2007,bool),bool,finite_finite(U_2007),U_2005)) ),
    inference(miniscope,[status(thm)],[f_518_2]) ).

fof(f_518_4,plain,
    ! [U_2004,U_2006,U_2005,U_2007] :
      ( ~ hBOOL(hAPP(fun(sum_sum(U_2007,U_2006),bool),bool,finite_finite(sum_sum(U_2007,U_2006)),hAPP(fun(U_2006,bool),fun(sum_sum(U_2007,U_2006),bool),hAPP(fun(U_2007,bool),fun(fun(U_2006,bool),fun(sum_sum(U_2007,U_2006),bool)),sum_Plus(U_2007,U_2006),U_2005),U_2004)))
      | hBOOL(hAPP(fun(U_2007,bool),bool,finite_finite(U_2007),U_2005)) ),
    inference(definitional_conversion,[status(esa)],[f_518_3]) ).

cnf(f_518_5,plain,
    ( ~ hBOOL(hAPP(fun(sum_sum(U_2007,U_2006),bool),bool,finite_finite(sum_sum(U_2007,U_2006)),hAPP(fun(U_2006,bool),fun(sum_sum(U_2007,U_2006),bool),hAPP(fun(U_2007,bool),fun(fun(U_2006,bool),fun(sum_sum(U_2007,U_2006),bool)),sum_Plus(U_2007,U_2006),U_2005),U_2004)))
    | hBOOL(hAPP(fun(U_2007,bool),bool,finite_finite(U_2007),U_2005)) ),
    inference(clausify,[status(thm)],[f_518_4]) ).

fof(f_519_1,plain,
    ! [X_c,X_b,B_1,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_1)))
      | ~ hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),B_1))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) ),
    inference(fof_nnf,[status(thm)],[fact_448_finite__Plus]) ).

fof(f_519_2,plain,
    ! [U_2011,U_2010,U_2009,U_2008] :
      ( hBOOL(hAPP(fun(sum_sum(U_2010,U_2011),bool),bool,finite_finite(sum_sum(U_2010,U_2011)),hAPP(fun(U_2011,bool),fun(sum_sum(U_2010,U_2011),bool),hAPP(fun(U_2010,bool),fun(fun(U_2011,bool),fun(sum_sum(U_2010,U_2011),bool)),sum_Plus(U_2010,U_2011),U_2008),U_2009)))
      | ~ hBOOL(hAPP(fun(U_2011,bool),bool,finite_finite(U_2011),U_2009))
      | ~ hBOOL(hAPP(fun(U_2010,bool),bool,finite_finite(U_2010),U_2008)) ),
    inference(variable_rename,[status(thm)],[f_519_1]) ).

fof(f_519_3,plain,
    ! [U_2009,U_2008,U_2010,U_2011] :
      ( hBOOL(hAPP(fun(sum_sum(U_2010,U_2011),bool),bool,finite_finite(sum_sum(U_2010,U_2011)),hAPP(fun(U_2011,bool),fun(sum_sum(U_2010,U_2011),bool),hAPP(fun(U_2010,bool),fun(fun(U_2011,bool),fun(sum_sum(U_2010,U_2011),bool)),sum_Plus(U_2010,U_2011),U_2008),U_2009)))
      | ~ hBOOL(hAPP(fun(U_2011,bool),bool,finite_finite(U_2011),U_2009))
      | ~ hBOOL(hAPP(fun(U_2010,bool),bool,finite_finite(U_2010),U_2008)) ),
    inference(definitional_conversion,[status(esa)],[f_519_2]) ).

cnf(f_519_4,plain,
    ( hBOOL(hAPP(fun(sum_sum(U_2010,U_2011),bool),bool,finite_finite(sum_sum(U_2010,U_2011)),hAPP(fun(U_2011,bool),fun(sum_sum(U_2010,U_2011),bool),hAPP(fun(U_2010,bool),fun(fun(U_2011,bool),fun(sum_sum(U_2010,U_2011),bool)),sum_Plus(U_2010,U_2011),U_2008),U_2009)))
    | ~ hBOOL(hAPP(fun(U_2011,bool),bool,finite_finite(U_2011),U_2009))
    | ~ hBOOL(hAPP(fun(U_2010,bool),bool,finite_finite(U_2010),U_2008)) ),
    inference(clausify,[status(thm)],[f_519_3]) ).

fof(f_520_1,plain,
    ! [X_b,X_c,A_3,B_1] :
      ( ( 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_1)))
        | ~ hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),B_1))
        | ~ 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_1))
          & 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_1))) ) ),
    inference(fof_nnf,[status(thm)],[fact_449_finite__Plus__iff]) ).

fof(f_520_2,plain,
    ! [U_2015,U_2014,U_2013,U_2012] :
      ( ( hBOOL(hAPP(fun(sum_sum(U_2015,U_2014),bool),bool,finite_finite(sum_sum(U_2015,U_2014)),hAPP(fun(U_2014,bool),fun(sum_sum(U_2015,U_2014),bool),hAPP(fun(U_2015,bool),fun(fun(U_2014,bool),fun(sum_sum(U_2015,U_2014),bool)),sum_Plus(U_2015,U_2014),U_2013),U_2012)))
        | ~ hBOOL(hAPP(fun(U_2014,bool),bool,finite_finite(U_2014),U_2012))
        | ~ hBOOL(hAPP(fun(U_2015,bool),bool,finite_finite(U_2015),U_2013)) )
      & ( ( hBOOL(hAPP(fun(U_2014,bool),bool,finite_finite(U_2014),U_2012))
          & hBOOL(hAPP(fun(U_2015,bool),bool,finite_finite(U_2015),U_2013)) )
        | ~ hBOOL(hAPP(fun(sum_sum(U_2015,U_2014),bool),bool,finite_finite(sum_sum(U_2015,U_2014)),hAPP(fun(U_2014,bool),fun(sum_sum(U_2015,U_2014),bool),hAPP(fun(U_2015,bool),fun(fun(U_2014,bool),fun(sum_sum(U_2015,U_2014),bool)),sum_Plus(U_2015,U_2014),U_2013),U_2012))) ) ),
    inference(variable_rename,[status(thm)],[f_520_1]) ).

fof(f_520_3,plain,
    ( ! [U_2023,U_2021,U_2019,U_2017] :
        ( hBOOL(hAPP(fun(sum_sum(U_2023,U_2021),bool),bool,finite_finite(sum_sum(U_2023,U_2021)),hAPP(fun(U_2021,bool),fun(sum_sum(U_2023,U_2021),bool),hAPP(fun(U_2023,bool),fun(fun(U_2021,bool),fun(sum_sum(U_2023,U_2021),bool)),sum_Plus(U_2023,U_2021),U_2019),U_2017)))
        | ~ hBOOL(hAPP(fun(U_2021,bool),bool,finite_finite(U_2021),U_2017))
        | ~ hBOOL(hAPP(fun(U_2023,bool),bool,finite_finite(U_2023),U_2019)) )
    & ! [U_2022,U_2020,U_2018,U_2016] :
        ( ( hBOOL(hAPP(fun(U_2020,bool),bool,finite_finite(U_2020),U_2016))
          & hBOOL(hAPP(fun(U_2022,bool),bool,finite_finite(U_2022),U_2018)) )
        | ~ hBOOL(hAPP(fun(sum_sum(U_2022,U_2020),bool),bool,finite_finite(sum_sum(U_2022,U_2020)),hAPP(fun(U_2020,bool),fun(sum_sum(U_2022,U_2020),bool),hAPP(fun(U_2022,bool),fun(fun(U_2020,bool),fun(sum_sum(U_2022,U_2020),bool)),sum_Plus(U_2022,U_2020),U_2018),U_2016))) ) ),
    inference(miniscope,[status(thm)],[f_520_2]) ).

fof(f_520_4,plain,
    ( ! [U_2018,U_2016,U_2020,U_2022] :
        ( hBOOL(hAPP(fun(U_2020,bool),bool,finite_finite(U_2020),U_2016))
        | ~ sP122(U_2018,U_2016,U_2020,U_2022) )
    & ! [U_2018,U_2016,U_2020,U_2022] :
        ( hBOOL(hAPP(fun(U_2022,bool),bool,finite_finite(U_2022),U_2018))
        | ~ sP122(U_2018,U_2016,U_2020,U_2022) )
    & ! [U_2021,U_2017,U_2019,U_2023] :
        ( hBOOL(hAPP(fun(sum_sum(U_2023,U_2021),bool),bool,finite_finite(sum_sum(U_2023,U_2021)),hAPP(fun(U_2021,bool),fun(sum_sum(U_2023,U_2021),bool),hAPP(fun(U_2023,bool),fun(fun(U_2021,bool),fun(sum_sum(U_2023,U_2021),bool)),sum_Plus(U_2023,U_2021),U_2019),U_2017)))
        | ~ hBOOL(hAPP(fun(U_2021,bool),bool,finite_finite(U_2021),U_2017))
        | ~ hBOOL(hAPP(fun(U_2023,bool),bool,finite_finite(U_2023),U_2019)) )
    & ! [U_2018,U_2016,U_2020,U_2022] :
        ( sP122(U_2018,U_2016,U_2020,U_2022)
        | ~ hBOOL(hAPP(fun(sum_sum(U_2022,U_2020),bool),bool,finite_finite(sum_sum(U_2022,U_2020)),hAPP(fun(U_2020,bool),fun(sum_sum(U_2022,U_2020),bool),hAPP(fun(U_2022,bool),fun(fun(U_2020,bool),fun(sum_sum(U_2022,U_2020),bool)),sum_Plus(U_2022,U_2020),U_2018),U_2016))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP122])],[f_520_3]) ).

cnf(f_520_5,plain,
    ( sP122(U_2018,U_2016,U_2020,U_2022)
    | ~ hBOOL(hAPP(fun(sum_sum(U_2022,U_2020),bool),bool,finite_finite(sum_sum(U_2022,U_2020)),hAPP(fun(U_2020,bool),fun(sum_sum(U_2022,U_2020),bool),hAPP(fun(U_2022,bool),fun(fun(U_2020,bool),fun(sum_sum(U_2022,U_2020),bool)),sum_Plus(U_2022,U_2020),U_2018),U_2016))) ),
    inference(clausify,[status(thm)],[f_520_4]) ).

cnf(f_520_6,plain,
    ( hBOOL(hAPP(fun(sum_sum(U_2023,U_2021),bool),bool,finite_finite(sum_sum(U_2023,U_2021)),hAPP(fun(U_2021,bool),fun(sum_sum(U_2023,U_2021),bool),hAPP(fun(U_2023,bool),fun(fun(U_2021,bool),fun(sum_sum(U_2023,U_2021),bool)),sum_Plus(U_2023,U_2021),U_2019),U_2017)))
    | ~ hBOOL(hAPP(fun(U_2021,bool),bool,finite_finite(U_2021),U_2017))
    | ~ hBOOL(hAPP(fun(U_2023,bool),bool,finite_finite(U_2023),U_2019)) ),
    inference(clausify,[status(thm)],[f_520_4]) ).

cnf(f_520_7,plain,
    ( hBOOL(hAPP(fun(U_2022,bool),bool,finite_finite(U_2022),U_2018))
    | ~ sP122(U_2018,U_2016,U_2020,U_2022) ),
    inference(clausify,[status(thm)],[f_520_4]) ).

cnf(f_520_8,plain,
    ( hBOOL(hAPP(fun(U_2020,bool),bool,finite_finite(U_2020),U_2016))
    | ~ sP122(U_2018,U_2016,U_2020,U_2022) ),
    inference(clausify,[status(thm)],[f_520_4]) ).

fof(f_521_1,plain,
    ! [X_c,X_b,A_3,B_1] :
      ( ( 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_1) = bot_bot(fun(sum_sum(X_b,X_c),bool))
        | ti(fun(X_c,bool),B_1) != 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_1) = 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_1) != bot_bot(fun(sum_sum(X_b,X_c),bool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_450_Plus__eq__empty__conv]) ).

fof(f_521_2,plain,
    ! [U_2027,U_2026,U_2025,U_2024] :
      ( ( hAPP(fun(U_2027,bool),fun(sum_sum(U_2026,U_2027),bool),hAPP(fun(U_2026,bool),fun(fun(U_2027,bool),fun(sum_sum(U_2026,U_2027),bool)),sum_Plus(U_2026,U_2027),U_2025),U_2024) = bot_bot(fun(sum_sum(U_2026,U_2027),bool))
        | ti(fun(U_2027,bool),U_2024) != bot_bot(fun(U_2027,bool))
        | ti(fun(U_2026,bool),U_2025) != bot_bot(fun(U_2026,bool)) )
      & ( ( ti(fun(U_2027,bool),U_2024) = bot_bot(fun(U_2027,bool))
          & ti(fun(U_2026,bool),U_2025) = bot_bot(fun(U_2026,bool)) )
        | hAPP(fun(U_2027,bool),fun(sum_sum(U_2026,U_2027),bool),hAPP(fun(U_2026,bool),fun(fun(U_2027,bool),fun(sum_sum(U_2026,U_2027),bool)),sum_Plus(U_2026,U_2027),U_2025),U_2024) != bot_bot(fun(sum_sum(U_2026,U_2027),bool)) ) ),
    inference(variable_rename,[status(thm)],[f_521_1]) ).

fof(f_521_3,plain,
    ( ! [U_2035,U_2033,U_2031,U_2029] :
        ( hAPP(fun(U_2035,bool),fun(sum_sum(U_2033,U_2035),bool),hAPP(fun(U_2033,bool),fun(fun(U_2035,bool),fun(sum_sum(U_2033,U_2035),bool)),sum_Plus(U_2033,U_2035),U_2031),U_2029) = bot_bot(fun(sum_sum(U_2033,U_2035),bool))
        | ti(fun(U_2035,bool),U_2029) != bot_bot(fun(U_2035,bool))
        | ti(fun(U_2033,bool),U_2031) != bot_bot(fun(U_2033,bool)) )
    & ! [U_2034,U_2032,U_2030,U_2028] :
        ( ( ti(fun(U_2034,bool),U_2028) = bot_bot(fun(U_2034,bool))
          & ti(fun(U_2032,bool),U_2030) = bot_bot(fun(U_2032,bool)) )
        | hAPP(fun(U_2034,bool),fun(sum_sum(U_2032,U_2034),bool),hAPP(fun(U_2032,bool),fun(fun(U_2034,bool),fun(sum_sum(U_2032,U_2034),bool)),sum_Plus(U_2032,U_2034),U_2030),U_2028) != bot_bot(fun(sum_sum(U_2032,U_2034),bool)) ) ),
    inference(miniscope,[status(thm)],[f_521_2]) ).

fof(f_521_4,plain,
    ( ! [U_2028,U_2030,U_2032,U_2034] :
        ( ti(fun(U_2034,bool),U_2028) = bot_bot(fun(U_2034,bool))
        | ~ sP123(U_2028,U_2030,U_2032,U_2034) )
    & ! [U_2028,U_2030,U_2032,U_2034] :
        ( ti(fun(U_2032,bool),U_2030) = bot_bot(fun(U_2032,bool))
        | ~ sP123(U_2028,U_2030,U_2032,U_2034) )
    & ! [U_2029,U_2031,U_2033,U_2035] :
        ( hAPP(fun(U_2035,bool),fun(sum_sum(U_2033,U_2035),bool),hAPP(fun(U_2033,bool),fun(fun(U_2035,bool),fun(sum_sum(U_2033,U_2035),bool)),sum_Plus(U_2033,U_2035),U_2031),U_2029) = bot_bot(fun(sum_sum(U_2033,U_2035),bool))
        | ti(fun(U_2035,bool),U_2029) != bot_bot(fun(U_2035,bool))
        | ti(fun(U_2033,bool),U_2031) != bot_bot(fun(U_2033,bool)) )
    & ! [U_2028,U_2030,U_2032,U_2034] :
        ( sP123(U_2028,U_2030,U_2032,U_2034)
        | hAPP(fun(U_2034,bool),fun(sum_sum(U_2032,U_2034),bool),hAPP(fun(U_2032,bool),fun(fun(U_2034,bool),fun(sum_sum(U_2032,U_2034),bool)),sum_Plus(U_2032,U_2034),U_2030),U_2028) != bot_bot(fun(sum_sum(U_2032,U_2034),bool)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP123])],[f_521_3]) ).

cnf(f_521_5,plain,
    ( sP123(U_2028,U_2030,U_2032,U_2034)
    | hAPP(fun(U_2034,bool),fun(sum_sum(U_2032,U_2034),bool),hAPP(fun(U_2032,bool),fun(fun(U_2034,bool),fun(sum_sum(U_2032,U_2034),bool)),sum_Plus(U_2032,U_2034),U_2030),U_2028) != bot_bot(fun(sum_sum(U_2032,U_2034),bool)) ),
    inference(clausify,[status(thm)],[f_521_4]) ).

cnf(f_521_6,plain,
    ( hAPP(fun(U_2035,bool),fun(sum_sum(U_2033,U_2035),bool),hAPP(fun(U_2033,bool),fun(fun(U_2035,bool),fun(sum_sum(U_2033,U_2035),bool)),sum_Plus(U_2033,U_2035),U_2031),U_2029) = bot_bot(fun(sum_sum(U_2033,U_2035),bool))
    | ti(fun(U_2035,bool),U_2029) != bot_bot(fun(U_2035,bool))
    | ti(fun(U_2033,bool),U_2031) != bot_bot(fun(U_2033,bool)) ),
    inference(clausify,[status(thm)],[f_521_4]) ).

cnf(f_521_7,plain,
    ( ti(fun(U_2032,bool),U_2030) = bot_bot(fun(U_2032,bool))
    | ~ sP123(U_2028,U_2030,U_2032,U_2034) ),
    inference(clausify,[status(thm)],[f_521_4]) ).

cnf(f_521_8,plain,
    ( ti(fun(U_2034,bool),U_2028) = bot_bot(fun(U_2034,bool))
    | ~ sP123(U_2028,U_2030,U_2032,U_2034) ),
    inference(clausify,[status(thm)],[f_521_4]) ).

fof(f_522_1,plain,
    ! [X_c,X_b,B_1,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_1)) = zero_zero(nat)
        | ( hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),B_1))
          & 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_1)) = 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_1))
        | ~ hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),B_1))
        | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) ) ),
    inference(fof_nnf,[status(thm)],[fact_451_card__Plus__conv__if]) ).

fof(f_522_2,plain,
    ! [U_2039,U_2038,U_2037,U_2036] :
      ( ( hAPP(fun(sum_sum(U_2038,U_2039),bool),nat,finite_card(sum_sum(U_2038,U_2039)),hAPP(fun(U_2039,bool),fun(sum_sum(U_2038,U_2039),bool),hAPP(fun(U_2038,bool),fun(fun(U_2039,bool),fun(sum_sum(U_2038,U_2039),bool)),sum_Plus(U_2038,U_2039),U_2036),U_2037)) = zero_zero(nat)
        | ( hBOOL(hAPP(fun(U_2039,bool),bool,finite_finite(U_2039),U_2037))
          & hBOOL(hAPP(fun(U_2038,bool),bool,finite_finite(U_2038),U_2036)) ) )
      & ( hAPP(fun(sum_sum(U_2038,U_2039),bool),nat,finite_card(sum_sum(U_2038,U_2039)),hAPP(fun(U_2039,bool),fun(sum_sum(U_2038,U_2039),bool),hAPP(fun(U_2038,bool),fun(fun(U_2039,bool),fun(sum_sum(U_2038,U_2039),bool)),sum_Plus(U_2038,U_2039),U_2036),U_2037)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(U_2038,bool),nat,finite_card(U_2038),U_2036)),hAPP(fun(U_2039,bool),nat,finite_card(U_2039),U_2037))
        | ~ hBOOL(hAPP(fun(U_2039,bool),bool,finite_finite(U_2039),U_2037))
        | ~ hBOOL(hAPP(fun(U_2038,bool),bool,finite_finite(U_2038),U_2036)) ) ),
    inference(variable_rename,[status(thm)],[f_522_1]) ).

fof(f_522_3,plain,
    ( ! [U_2047,U_2045,U_2043,U_2041] :
        ( hAPP(fun(sum_sum(U_2045,U_2047),bool),nat,finite_card(sum_sum(U_2045,U_2047)),hAPP(fun(U_2047,bool),fun(sum_sum(U_2045,U_2047),bool),hAPP(fun(U_2045,bool),fun(fun(U_2047,bool),fun(sum_sum(U_2045,U_2047),bool)),sum_Plus(U_2045,U_2047),U_2041),U_2043)) = zero_zero(nat)
        | ( hBOOL(hAPP(fun(U_2047,bool),bool,finite_finite(U_2047),U_2043))
          & hBOOL(hAPP(fun(U_2045,bool),bool,finite_finite(U_2045),U_2041)) ) )
    & ! [U_2046,U_2044,U_2042,U_2040] :
        ( hAPP(fun(sum_sum(U_2044,U_2046),bool),nat,finite_card(sum_sum(U_2044,U_2046)),hAPP(fun(U_2046,bool),fun(sum_sum(U_2044,U_2046),bool),hAPP(fun(U_2044,bool),fun(fun(U_2046,bool),fun(sum_sum(U_2044,U_2046),bool)),sum_Plus(U_2044,U_2046),U_2040),U_2042)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(U_2044,bool),nat,finite_card(U_2044),U_2040)),hAPP(fun(U_2046,bool),nat,finite_card(U_2046),U_2042))
        | ~ hBOOL(hAPP(fun(U_2046,bool),bool,finite_finite(U_2046),U_2042))
        | ~ hBOOL(hAPP(fun(U_2044,bool),bool,finite_finite(U_2044),U_2040)) ) ),
    inference(miniscope,[status(thm)],[f_522_2]) ).

fof(f_522_4,plain,
    ( ! [U_2045,U_2043,U_2041,U_2047] :
        ( hBOOL(hAPP(fun(U_2047,bool),bool,finite_finite(U_2047),U_2043))
        | ~ sP124(U_2045,U_2043,U_2041,U_2047) )
    & ! [U_2045,U_2043,U_2041,U_2047] :
        ( hBOOL(hAPP(fun(U_2045,bool),bool,finite_finite(U_2045),U_2041))
        | ~ sP124(U_2045,U_2043,U_2041,U_2047) )
    & ! [U_2045,U_2043,U_2041,U_2047] :
        ( hAPP(fun(sum_sum(U_2045,U_2047),bool),nat,finite_card(sum_sum(U_2045,U_2047)),hAPP(fun(U_2047,bool),fun(sum_sum(U_2045,U_2047),bool),hAPP(fun(U_2045,bool),fun(fun(U_2047,bool),fun(sum_sum(U_2045,U_2047),bool)),sum_Plus(U_2045,U_2047),U_2041),U_2043)) = zero_zero(nat)
        | sP124(U_2045,U_2043,U_2041,U_2047) )
    & ! [U_2040,U_2044,U_2042,U_2046] :
        ( hAPP(fun(sum_sum(U_2044,U_2046),bool),nat,finite_card(sum_sum(U_2044,U_2046)),hAPP(fun(U_2046,bool),fun(sum_sum(U_2044,U_2046),bool),hAPP(fun(U_2044,bool),fun(fun(U_2046,bool),fun(sum_sum(U_2044,U_2046),bool)),sum_Plus(U_2044,U_2046),U_2040),U_2042)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(U_2044,bool),nat,finite_card(U_2044),U_2040)),hAPP(fun(U_2046,bool),nat,finite_card(U_2046),U_2042))
        | ~ hBOOL(hAPP(fun(U_2046,bool),bool,finite_finite(U_2046),U_2042))
        | ~ hBOOL(hAPP(fun(U_2044,bool),bool,finite_finite(U_2044),U_2040)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP124])],[f_522_3]) ).

cnf(f_522_5,plain,
    ( hAPP(fun(sum_sum(U_2044,U_2046),bool),nat,finite_card(sum_sum(U_2044,U_2046)),hAPP(fun(U_2046,bool),fun(sum_sum(U_2044,U_2046),bool),hAPP(fun(U_2044,bool),fun(fun(U_2046,bool),fun(sum_sum(U_2044,U_2046),bool)),sum_Plus(U_2044,U_2046),U_2040),U_2042)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(U_2044,bool),nat,finite_card(U_2044),U_2040)),hAPP(fun(U_2046,bool),nat,finite_card(U_2046),U_2042))
    | ~ hBOOL(hAPP(fun(U_2046,bool),bool,finite_finite(U_2046),U_2042))
    | ~ hBOOL(hAPP(fun(U_2044,bool),bool,finite_finite(U_2044),U_2040)) ),
    inference(clausify,[status(thm)],[f_522_4]) ).

cnf(f_522_6,plain,
    ( hAPP(fun(sum_sum(U_2045,U_2047),bool),nat,finite_card(sum_sum(U_2045,U_2047)),hAPP(fun(U_2047,bool),fun(sum_sum(U_2045,U_2047),bool),hAPP(fun(U_2045,bool),fun(fun(U_2047,bool),fun(sum_sum(U_2045,U_2047),bool)),sum_Plus(U_2045,U_2047),U_2041),U_2043)) = zero_zero(nat)
    | sP124(U_2045,U_2043,U_2041,U_2047) ),
    inference(clausify,[status(thm)],[f_522_4]) ).

cnf(f_522_7,plain,
    ( hBOOL(hAPP(fun(U_2045,bool),bool,finite_finite(U_2045),U_2041))
    | ~ sP124(U_2045,U_2043,U_2041,U_2047) ),
    inference(clausify,[status(thm)],[f_522_4]) ).

cnf(f_522_8,plain,
    ( hBOOL(hAPP(fun(U_2047,bool),bool,finite_finite(U_2047),U_2043))
    | ~ sP124(U_2045,U_2043,U_2041,U_2047) ),
    inference(clausify,[status(thm)],[f_522_4]) ).

fof(f_523_1,plain,
    ! [X_b,R_1,S] :
      ( ( 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,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)),R_1)),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)),S)))
        | ~ 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)),R_1),S)) )
      & ( 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)),R_1),S))
        | ~ 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,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)),R_1)),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)),S))) ) ),
    inference(fof_nnf,[status(thm)],[fact_452_pred__subset__eq]) ).

fof(f_523_2,plain,
    ! [U_2050,U_2049,U_2048] :
      ( ( hBOOL(hAPP(fun(U_2050,bool),bool,hAPP(fun(U_2050,bool),fun(fun(U_2050,bool),bool),ord_less_eq(fun(U_2050,bool)),hAPP(fun(U_2050,bool),fun(U_2050,bool),hAPP(fun(U_2050,fun(fun(U_2050,bool),bool)),fun(fun(U_2050,bool),fun(U_2050,bool)),combc(U_2050,fun(U_2050,bool),bool),member(U_2050)),U_2049)),hAPP(fun(U_2050,bool),fun(U_2050,bool),hAPP(fun(U_2050,fun(fun(U_2050,bool),bool)),fun(fun(U_2050,bool),fun(U_2050,bool)),combc(U_2050,fun(U_2050,bool),bool),member(U_2050)),U_2048)))
        | ~ hBOOL(hAPP(fun(U_2050,bool),bool,hAPP(fun(U_2050,bool),fun(fun(U_2050,bool),bool),ord_less_eq(fun(U_2050,bool)),U_2049),U_2048)) )
      & ( hBOOL(hAPP(fun(U_2050,bool),bool,hAPP(fun(U_2050,bool),fun(fun(U_2050,bool),bool),ord_less_eq(fun(U_2050,bool)),U_2049),U_2048))
        | ~ hBOOL(hAPP(fun(U_2050,bool),bool,hAPP(fun(U_2050,bool),fun(fun(U_2050,bool),bool),ord_less_eq(fun(U_2050,bool)),hAPP(fun(U_2050,bool),fun(U_2050,bool),hAPP(fun(U_2050,fun(fun(U_2050,bool),bool)),fun(fun(U_2050,bool),fun(U_2050,bool)),combc(U_2050,fun(U_2050,bool),bool),member(U_2050)),U_2049)),hAPP(fun(U_2050,bool),fun(U_2050,bool),hAPP(fun(U_2050,fun(fun(U_2050,bool),bool)),fun(fun(U_2050,bool),fun(U_2050,bool)),combc(U_2050,fun(U_2050,bool),bool),member(U_2050)),U_2048))) ) ),
    inference(variable_rename,[status(thm)],[f_523_1]) ).

fof(f_523_3,plain,
    ( ! [U_2056,U_2054,U_2052] :
        ( hBOOL(hAPP(fun(U_2056,bool),bool,hAPP(fun(U_2056,bool),fun(fun(U_2056,bool),bool),ord_less_eq(fun(U_2056,bool)),hAPP(fun(U_2056,bool),fun(U_2056,bool),hAPP(fun(U_2056,fun(fun(U_2056,bool),bool)),fun(fun(U_2056,bool),fun(U_2056,bool)),combc(U_2056,fun(U_2056,bool),bool),member(U_2056)),U_2054)),hAPP(fun(U_2056,bool),fun(U_2056,bool),hAPP(fun(U_2056,fun(fun(U_2056,bool),bool)),fun(fun(U_2056,bool),fun(U_2056,bool)),combc(U_2056,fun(U_2056,bool),bool),member(U_2056)),U_2052)))
        | ~ hBOOL(hAPP(fun(U_2056,bool),bool,hAPP(fun(U_2056,bool),fun(fun(U_2056,bool),bool),ord_less_eq(fun(U_2056,bool)),U_2054),U_2052)) )
    & ! [U_2055,U_2053,U_2051] :
        ( hBOOL(hAPP(fun(U_2055,bool),bool,hAPP(fun(U_2055,bool),fun(fun(U_2055,bool),bool),ord_less_eq(fun(U_2055,bool)),U_2053),U_2051))
        | ~ hBOOL(hAPP(fun(U_2055,bool),bool,hAPP(fun(U_2055,bool),fun(fun(U_2055,bool),bool),ord_less_eq(fun(U_2055,bool)),hAPP(fun(U_2055,bool),fun(U_2055,bool),hAPP(fun(U_2055,fun(fun(U_2055,bool),bool)),fun(fun(U_2055,bool),fun(U_2055,bool)),combc(U_2055,fun(U_2055,bool),bool),member(U_2055)),U_2053)),hAPP(fun(U_2055,bool),fun(U_2055,bool),hAPP(fun(U_2055,fun(fun(U_2055,bool),bool)),fun(fun(U_2055,bool),fun(U_2055,bool)),combc(U_2055,fun(U_2055,bool),bool),member(U_2055)),U_2051))) ) ),
    inference(miniscope,[status(thm)],[f_523_2]) ).

fof(f_523_4,plain,
    ( ! [U_2056,U_2052,U_2054] :
        ( hBOOL(hAPP(fun(U_2056,bool),bool,hAPP(fun(U_2056,bool),fun(fun(U_2056,bool),bool),ord_less_eq(fun(U_2056,bool)),hAPP(fun(U_2056,bool),fun(U_2056,bool),hAPP(fun(U_2056,fun(fun(U_2056,bool),bool)),fun(fun(U_2056,bool),fun(U_2056,bool)),combc(U_2056,fun(U_2056,bool),bool),member(U_2056)),U_2054)),hAPP(fun(U_2056,bool),fun(U_2056,bool),hAPP(fun(U_2056,fun(fun(U_2056,bool),bool)),fun(fun(U_2056,bool),fun(U_2056,bool)),combc(U_2056,fun(U_2056,bool),bool),member(U_2056)),U_2052)))
        | ~ hBOOL(hAPP(fun(U_2056,bool),bool,hAPP(fun(U_2056,bool),fun(fun(U_2056,bool),bool),ord_less_eq(fun(U_2056,bool)),U_2054),U_2052)) )
    & ! [U_2053,U_2051,U_2055] :
        ( hBOOL(hAPP(fun(U_2055,bool),bool,hAPP(fun(U_2055,bool),fun(fun(U_2055,bool),bool),ord_less_eq(fun(U_2055,bool)),U_2053),U_2051))
        | ~ hBOOL(hAPP(fun(U_2055,bool),bool,hAPP(fun(U_2055,bool),fun(fun(U_2055,bool),bool),ord_less_eq(fun(U_2055,bool)),hAPP(fun(U_2055,bool),fun(U_2055,bool),hAPP(fun(U_2055,fun(fun(U_2055,bool),bool)),fun(fun(U_2055,bool),fun(U_2055,bool)),combc(U_2055,fun(U_2055,bool),bool),member(U_2055)),U_2053)),hAPP(fun(U_2055,bool),fun(U_2055,bool),hAPP(fun(U_2055,fun(fun(U_2055,bool),bool)),fun(fun(U_2055,bool),fun(U_2055,bool)),combc(U_2055,fun(U_2055,bool),bool),member(U_2055)),U_2051))) ) ),
    inference(definitional_conversion,[status(esa)],[f_523_3]) ).

cnf(f_523_5,plain,
    ( hBOOL(hAPP(fun(U_2055,bool),bool,hAPP(fun(U_2055,bool),fun(fun(U_2055,bool),bool),ord_less_eq(fun(U_2055,bool)),U_2053),U_2051))
    | ~ hBOOL(hAPP(fun(U_2055,bool),bool,hAPP(fun(U_2055,bool),fun(fun(U_2055,bool),bool),ord_less_eq(fun(U_2055,bool)),hAPP(fun(U_2055,bool),fun(U_2055,bool),hAPP(fun(U_2055,fun(fun(U_2055,bool),bool)),fun(fun(U_2055,bool),fun(U_2055,bool)),combc(U_2055,fun(U_2055,bool),bool),member(U_2055)),U_2053)),hAPP(fun(U_2055,bool),fun(U_2055,bool),hAPP(fun(U_2055,fun(fun(U_2055,bool),bool)),fun(fun(U_2055,bool),fun(U_2055,bool)),combc(U_2055,fun(U_2055,bool),bool),member(U_2055)),U_2051))) ),
    inference(clausify,[status(thm)],[f_523_4]) ).

cnf(f_523_6,plain,
    ( hBOOL(hAPP(fun(U_2056,bool),bool,hAPP(fun(U_2056,bool),fun(fun(U_2056,bool),bool),ord_less_eq(fun(U_2056,bool)),hAPP(fun(U_2056,bool),fun(U_2056,bool),hAPP(fun(U_2056,fun(fun(U_2056,bool),bool)),fun(fun(U_2056,bool),fun(U_2056,bool)),combc(U_2056,fun(U_2056,bool),bool),member(U_2056)),U_2054)),hAPP(fun(U_2056,bool),fun(U_2056,bool),hAPP(fun(U_2056,fun(fun(U_2056,bool),bool)),fun(fun(U_2056,bool),fun(U_2056,bool)),combc(U_2056,fun(U_2056,bool),bool),member(U_2056)),U_2052)))
    | ~ hBOOL(hAPP(fun(U_2056,bool),bool,hAPP(fun(U_2056,bool),fun(fun(U_2056,bool),bool),ord_less_eq(fun(U_2056,bool)),U_2054),U_2052)) ),
    inference(clausify,[status(thm)],[f_523_4]) ).

fof(f_524_1,plain,
    ! [X_b,Q_3,Pa] :
      ( 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),collect(X_b),Pa)),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Q_3)))
      | ? [X_2] :
          ( ~ hBOOL(hAPP(X_b,bool,Q_3,X_2))
          & hBOOL(hAPP(X_b,bool,Pa,X_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_453_Collect__mono]) ).

fof(f_524_2,plain,
    ! [U_2060,U_2059,U_2058] :
      ( hBOOL(hAPP(fun(U_2060,bool),bool,hAPP(fun(U_2060,bool),fun(fun(U_2060,bool),bool),ord_less_eq(fun(U_2060,bool)),hAPP(fun(U_2060,bool),fun(U_2060,bool),collect(U_2060),U_2058)),hAPP(fun(U_2060,bool),fun(U_2060,bool),collect(U_2060),U_2059)))
      | ? [U_2057] :
          ( ~ hBOOL(hAPP(U_2060,bool,U_2059,U_2057))
          & hBOOL(hAPP(U_2060,bool,U_2058,U_2057)) ) ),
    inference(variable_rename,[status(thm)],[f_524_1]) ).

fof(f_524_3,plain,
    ! [U_2060,U_2059,U_2058] :
      ( hBOOL(hAPP(fun(U_2060,bool),bool,hAPP(fun(U_2060,bool),fun(fun(U_2060,bool),bool),ord_less_eq(fun(U_2060,bool)),hAPP(fun(U_2060,bool),fun(U_2060,bool),collect(U_2060),U_2058)),hAPP(fun(U_2060,bool),fun(U_2060,bool),collect(U_2060),U_2059)))
      | ( ~ hBOOL(hAPP(U_2060,bool,U_2059,sK81(U_2060,U_2059,U_2058)))
        & hBOOL(hAPP(U_2060,bool,U_2058,sK81(U_2060,U_2059,U_2058))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK81]),skolemize(U_2057,sK81(U_2060,U_2059,U_2058))],[f_524_2]) ).

fof(f_524_4,plain,
    ( ! [U_2058,U_2060,U_2059] :
        ( ~ hBOOL(hAPP(U_2060,bool,U_2059,sK81(U_2060,U_2059,U_2058)))
        | ~ sP125(U_2058,U_2060,U_2059) )
    & ! [U_2058,U_2060,U_2059] :
        ( hBOOL(hAPP(U_2060,bool,U_2058,sK81(U_2060,U_2059,U_2058)))
        | ~ sP125(U_2058,U_2060,U_2059) )
    & ! [U_2058,U_2060,U_2059] :
        ( hBOOL(hAPP(fun(U_2060,bool),bool,hAPP(fun(U_2060,bool),fun(fun(U_2060,bool),bool),ord_less_eq(fun(U_2060,bool)),hAPP(fun(U_2060,bool),fun(U_2060,bool),collect(U_2060),U_2058)),hAPP(fun(U_2060,bool),fun(U_2060,bool),collect(U_2060),U_2059)))
        | sP125(U_2058,U_2060,U_2059) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP125])],[f_524_3]) ).

cnf(f_524_5,plain,
    ( hBOOL(hAPP(fun(U_2060,bool),bool,hAPP(fun(U_2060,bool),fun(fun(U_2060,bool),bool),ord_less_eq(fun(U_2060,bool)),hAPP(fun(U_2060,bool),fun(U_2060,bool),collect(U_2060),U_2058)),hAPP(fun(U_2060,bool),fun(U_2060,bool),collect(U_2060),U_2059)))
    | sP125(U_2058,U_2060,U_2059) ),
    inference(clausify,[status(thm)],[f_524_4]) ).

cnf(f_524_6,plain,
    ( hBOOL(hAPP(U_2060,bool,U_2058,sK81(U_2060,U_2059,U_2058)))
    | ~ sP125(U_2058,U_2060,U_2059) ),
    inference(clausify,[status(thm)],[f_524_4]) ).

cnf(f_524_7,plain,
    ( ~ hBOOL(hAPP(U_2060,bool,U_2059,sK81(U_2060,U_2059,U_2058)))
    | ~ sP125(U_2058,U_2060,U_2059) ),
    inference(clausify,[status(thm)],[f_524_4]) ).

fof(f_525_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_454_less__zeroE]) ).

fof(f_525_2,plain,
    ! [U_2061] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2061),zero_zero(nat))),
    inference(variable_rename,[status(thm)],[f_525_1]) ).

fof(f_525_3,plain,
    ! [U_2061] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2061),zero_zero(nat))),
    inference(definitional_conversion,[status(esa)],[f_525_2]) ).

cnf(f_525_4,plain,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2061),zero_zero(nat))),
    inference(clausify,[status(thm)],[f_525_3]) ).

fof(f_526_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_455_le0]) ).

fof(f_526_2,plain,
    ! [U_2062] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),U_2062)),
    inference(variable_rename,[status(thm)],[f_526_1]) ).

fof(f_526_3,plain,
    ! [U_2062] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),U_2062)),
    inference(definitional_conversion,[status(esa)],[f_526_2]) ).

cnf(f_526_4,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),U_2062)),
    inference(clausify,[status(thm)],[f_526_3]) ).

fof(f_527_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_456_zero__less__Suc]) ).

fof(f_527_2,plain,
    ! [U_2063] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,U_2063))),
    inference(variable_rename,[status(thm)],[f_527_1]) ).

fof(f_527_3,plain,
    ! [U_2063] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,U_2063))),
    inference(definitional_conversion,[status(esa)],[f_527_2]) ).

cnf(f_527_4,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,U_2063))),
    inference(clausify,[status(thm)],[f_527_3]) ).

fof(f_528_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_457_le__0__eq]) ).

fof(f_528_2,plain,
    ! [U_2064] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2064),zero_zero(nat)))
        | U_2064 != zero_zero(nat) )
      & ( U_2064 = zero_zero(nat)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2064),zero_zero(nat))) ) ),
    inference(variable_rename,[status(thm)],[f_528_1]) ).

fof(f_528_3,plain,
    ( ! [U_2066] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2066),zero_zero(nat)))
        | U_2066 != zero_zero(nat) )
    & ! [U_2065] :
        ( U_2065 = zero_zero(nat)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2065),zero_zero(nat))) ) ),
    inference(miniscope,[status(thm)],[f_528_2]) ).

fof(f_528_4,plain,
    ( ! [U_2066] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2066),zero_zero(nat)))
        | U_2066 != zero_zero(nat) )
    & ! [U_2065] :
        ( U_2065 = zero_zero(nat)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2065),zero_zero(nat))) ) ),
    inference(definitional_conversion,[status(esa)],[f_528_3]) ).

cnf(f_528_5,plain,
    ( U_2065 = zero_zero(nat)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2065),zero_zero(nat))) ),
    inference(clausify,[status(thm)],[f_528_4]) ).

cnf(f_528_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2066),zero_zero(nat)))
    | U_2066 != zero_zero(nat) ),
    inference(clausify,[status(thm)],[f_528_4]) ).

fof(f_529_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_458_less__eq__nat_Osimps_I1_J]) ).

fof(f_529_2,plain,
    ! [U_2067] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),U_2067)),
    inference(variable_rename,[status(thm)],[f_529_1]) ).

fof(f_529_3,plain,
    ! [U_2067] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),U_2067)),
    inference(definitional_conversion,[status(esa)],[f_529_2]) ).

cnf(f_529_4,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),U_2067)),
    inference(clausify,[status(thm)],[f_529_3]) ).

fof(f_530_1,plain,
    ! [M_1,N] :
      ( M_1 = N
      | hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),M_1) != zero_zero(nat)
      | hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N) != zero_zero(nat) ),
    inference(fof_nnf,[status(thm)],[fact_459_diffs0__imp__equal]) ).

fof(f_530_2,plain,
    ! [U_2069,U_2068] :
      ( U_2069 = U_2068
      | hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2068),U_2069) != zero_zero(nat)
      | hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2069),U_2068) != zero_zero(nat) ),
    inference(variable_rename,[status(thm)],[f_530_1]) ).

fof(f_530_3,plain,
    ! [U_2069,U_2068] :
      ( U_2069 = U_2068
      | hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2068),U_2069) != zero_zero(nat)
      | hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2069),U_2068) != zero_zero(nat) ),
    inference(definitional_conversion,[status(esa)],[f_530_2]) ).

cnf(f_530_4,plain,
    ( U_2069 = U_2068
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2068),U_2069) != zero_zero(nat)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2069),U_2068) != zero_zero(nat) ),
    inference(clausify,[status(thm)],[f_530_3]) ).

fof(f_531_1,plain,
    ! [M_1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),M_1) = zero_zero(nat),
    inference(fof_nnf,[status(thm)],[fact_460_diff__self__eq__0]) ).

fof(f_531_2,plain,
    ! [U_2070] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2070),U_2070) = zero_zero(nat),
    inference(variable_rename,[status(thm)],[f_531_1]) ).

fof(f_531_3,plain,
    ! [U_2070] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2070),U_2070) = zero_zero(nat),
    inference(definitional_conversion,[status(esa)],[f_531_2]) ).

cnf(f_531_4,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2070),U_2070) = zero_zero(nat),
    inference(clausify,[status(thm)],[f_531_3]) ).

fof(f_532_1,plain,
    ! [M_1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),zero_zero(nat)) = M_1,
    inference(fof_nnf,[status(thm)],[fact_461_minus__nat_Odiff__0]) ).

fof(f_532_2,plain,
    ! [U_2071] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2071),zero_zero(nat)) = U_2071,
    inference(variable_rename,[status(thm)],[f_532_1]) ).

fof(f_532_3,plain,
    ! [U_2071] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2071),zero_zero(nat)) = U_2071,
    inference(definitional_conversion,[status(esa)],[f_532_2]) ).

cnf(f_532_4,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2071),zero_zero(nat)) = U_2071,
    inference(clausify,[status(thm)],[f_532_3]) ).

fof(f_533_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_462_diff__0__eq__0]) ).

fof(f_533_2,plain,
    ! [U_2072] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),zero_zero(nat)),U_2072) = zero_zero(nat),
    inference(variable_rename,[status(thm)],[f_533_1]) ).

fof(f_533_3,plain,
    ! [U_2072] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),zero_zero(nat)),U_2072) = zero_zero(nat),
    inference(definitional_conversion,[status(esa)],[f_533_2]) ).

cnf(f_533_4,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),zero_zero(nat)),U_2072) = zero_zero(nat),
    inference(clausify,[status(thm)],[f_533_3]) ).

fof(f_534_1,plain,
    ! [X_a] :
      ( one_one(X_a) != zero_zero(X_a)
      | ~ zero_neq_one(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_463_one__neq__zero]) ).

fof(f_534_2,plain,
    ! [U_2073] :
      ( one_one(U_2073) != zero_zero(U_2073)
      | ~ zero_neq_one(U_2073) ),
    inference(variable_rename,[status(thm)],[f_534_1]) ).

fof(f_534_3,plain,
    ! [U_2073] :
      ( one_one(U_2073) != zero_zero(U_2073)
      | ~ zero_neq_one(U_2073) ),
    inference(definitional_conversion,[status(esa)],[f_534_2]) ).

cnf(f_534_4,plain,
    ( one_one(U_2073) != zero_zero(U_2073)
    | ~ zero_neq_one(U_2073) ),
    inference(clausify,[status(thm)],[f_534_3]) ).

fof(f_535_1,plain,
    ! [X_a] :
      ( zero_zero(X_a) != one_one(X_a)
      | ~ zero_neq_one(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_464_zero__neq__one]) ).

fof(f_535_2,plain,
    ! [U_2074] :
      ( zero_zero(U_2074) != one_one(U_2074)
      | ~ zero_neq_one(U_2074) ),
    inference(variable_rename,[status(thm)],[f_535_1]) ).

fof(f_535_3,plain,
    ! [U_2074] :
      ( zero_zero(U_2074) != one_one(U_2074)
      | ~ zero_neq_one(U_2074) ),
    inference(definitional_conversion,[status(esa)],[f_535_2]) ).

cnf(f_535_4,plain,
    ( zero_zero(U_2074) != one_one(U_2074)
    | ~ zero_neq_one(U_2074) ),
    inference(clausify,[status(thm)],[f_535_3]) ).

fof(f_536_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_465_add_Ocomm__neutral]) ).

fof(f_536_2,plain,
    ! [U_2076] :
      ( ! [U_2075] : hAPP(U_2076,U_2076,hAPP(U_2076,fun(U_2076,U_2076),plus_plus(U_2076),U_2075),zero_zero(U_2076)) = ti(U_2076,U_2075)
      | ~ comm_monoid_add(U_2076) ),
    inference(variable_rename,[status(thm)],[f_536_1]) ).

fof(f_536_3,plain,
    ! [U_2076,U_2075] :
      ( hAPP(U_2076,U_2076,hAPP(U_2076,fun(U_2076,U_2076),plus_plus(U_2076),U_2075),zero_zero(U_2076)) = ti(U_2076,U_2075)
      | ~ comm_monoid_add(U_2076) ),
    inference(definitional_conversion,[status(esa)],[f_536_2]) ).

cnf(f_536_4,plain,
    ( hAPP(U_2076,U_2076,hAPP(U_2076,fun(U_2076,U_2076),plus_plus(U_2076),U_2075),zero_zero(U_2076)) = ti(U_2076,U_2075)
    | ~ comm_monoid_add(U_2076) ),
    inference(clausify,[status(thm)],[f_536_3]) ).

fof(f_537_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_466_add__0__right]) ).

fof(f_537_2,plain,
    ! [U_2078] :
      ( ! [U_2077] : hAPP(U_2078,U_2078,hAPP(U_2078,fun(U_2078,U_2078),plus_plus(U_2078),U_2077),zero_zero(U_2078)) = ti(U_2078,U_2077)
      | ~ monoid_add(U_2078) ),
    inference(variable_rename,[status(thm)],[f_537_1]) ).

fof(f_537_3,plain,
    ! [U_2077,U_2078] :
      ( hAPP(U_2078,U_2078,hAPP(U_2078,fun(U_2078,U_2078),plus_plus(U_2078),U_2077),zero_zero(U_2078)) = ti(U_2078,U_2077)
      | ~ monoid_add(U_2078) ),
    inference(definitional_conversion,[status(esa)],[f_537_2]) ).

cnf(f_537_4,plain,
    ( hAPP(U_2078,U_2078,hAPP(U_2078,fun(U_2078,U_2078),plus_plus(U_2078),U_2077),zero_zero(U_2078)) = ti(U_2078,U_2077)
    | ~ monoid_add(U_2078) ),
    inference(clausify,[status(thm)],[f_537_3]) ).

fof(f_538_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_467_double__zero__sym]) ).

fof(f_538_2,plain,
    ! [U_2080] :
      ( ! [U_2079] :
          ( ( zero_zero(U_2080) = hAPP(U_2080,U_2080,hAPP(U_2080,fun(U_2080,U_2080),plus_plus(U_2080),U_2079),U_2079)
            | ti(U_2080,U_2079) != zero_zero(U_2080) )
          & ( ti(U_2080,U_2079) = zero_zero(U_2080)
            | zero_zero(U_2080) != hAPP(U_2080,U_2080,hAPP(U_2080,fun(U_2080,U_2080),plus_plus(U_2080),U_2079),U_2079) ) )
      | ~ linord219039673up_add(U_2080) ),
    inference(variable_rename,[status(thm)],[f_538_1]) ).

fof(f_538_3,plain,
    ! [U_2080] :
      ( ( ! [U_2082] :
            ( zero_zero(U_2080) = hAPP(U_2080,U_2080,hAPP(U_2080,fun(U_2080,U_2080),plus_plus(U_2080),U_2082),U_2082)
            | ti(U_2080,U_2082) != zero_zero(U_2080) )
        & ! [U_2081] :
            ( ti(U_2080,U_2081) = zero_zero(U_2080)
            | zero_zero(U_2080) != hAPP(U_2080,U_2080,hAPP(U_2080,fun(U_2080,U_2080),plus_plus(U_2080),U_2081),U_2081) ) )
      | ~ linord219039673up_add(U_2080) ),
    inference(miniscope,[status(thm)],[f_538_2]) ).

fof(f_538_4,plain,
    ( ! [U_2080,U_2082,U_2081] :
        ( zero_zero(U_2080) = hAPP(U_2080,U_2080,hAPP(U_2080,fun(U_2080,U_2080),plus_plus(U_2080),U_2082),U_2082)
        | ti(U_2080,U_2082) != zero_zero(U_2080)
        | ~ sP126(U_2080,U_2082,U_2081) )
    & ! [U_2080,U_2082,U_2081] :
        ( ti(U_2080,U_2081) = zero_zero(U_2080)
        | zero_zero(U_2080) != hAPP(U_2080,U_2080,hAPP(U_2080,fun(U_2080,U_2080),plus_plus(U_2080),U_2081),U_2081)
        | ~ sP126(U_2080,U_2082,U_2081) )
    & ! [U_2080,U_2082,U_2081] :
        ( sP126(U_2080,U_2082,U_2081)
        | ~ linord219039673up_add(U_2080) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP126])],[f_538_3]) ).

cnf(f_538_5,plain,
    ( sP126(U_2080,U_2082,U_2081)
    | ~ linord219039673up_add(U_2080) ),
    inference(clausify,[status(thm)],[f_538_4]) ).

cnf(f_538_6,plain,
    ( ti(U_2080,U_2081) = zero_zero(U_2080)
    | zero_zero(U_2080) != hAPP(U_2080,U_2080,hAPP(U_2080,fun(U_2080,U_2080),plus_plus(U_2080),U_2081),U_2081)
    | ~ sP126(U_2080,U_2082,U_2081) ),
    inference(clausify,[status(thm)],[f_538_4]) ).

cnf(f_538_7,plain,
    ( zero_zero(U_2080) = hAPP(U_2080,U_2080,hAPP(U_2080,fun(U_2080,U_2080),plus_plus(U_2080),U_2082),U_2082)
    | ti(U_2080,U_2082) != zero_zero(U_2080)
    | ~ sP126(U_2080,U_2082,U_2081) ),
    inference(clausify,[status(thm)],[f_538_4]) ).

fof(f_539_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_468_add__0]) ).

fof(f_539_2,plain,
    ! [U_2084] :
      ( ! [U_2083] : hAPP(U_2084,U_2084,hAPP(U_2084,fun(U_2084,U_2084),plus_plus(U_2084),zero_zero(U_2084)),U_2083) = ti(U_2084,U_2083)
      | ~ comm_monoid_add(U_2084) ),
    inference(variable_rename,[status(thm)],[f_539_1]) ).

fof(f_539_3,plain,
    ! [U_2084,U_2083] :
      ( hAPP(U_2084,U_2084,hAPP(U_2084,fun(U_2084,U_2084),plus_plus(U_2084),zero_zero(U_2084)),U_2083) = ti(U_2084,U_2083)
      | ~ comm_monoid_add(U_2084) ),
    inference(definitional_conversion,[status(esa)],[f_539_2]) ).

cnf(f_539_4,plain,
    ( hAPP(U_2084,U_2084,hAPP(U_2084,fun(U_2084,U_2084),plus_plus(U_2084),zero_zero(U_2084)),U_2083) = ti(U_2084,U_2083)
    | ~ comm_monoid_add(U_2084) ),
    inference(clausify,[status(thm)],[f_539_3]) ).

fof(f_540_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_469_add__0__left]) ).

fof(f_540_2,plain,
    ! [U_2086] :
      ( ! [U_2085] : hAPP(U_2086,U_2086,hAPP(U_2086,fun(U_2086,U_2086),plus_plus(U_2086),zero_zero(U_2086)),U_2085) = ti(U_2086,U_2085)
      | ~ monoid_add(U_2086) ),
    inference(variable_rename,[status(thm)],[f_540_1]) ).

fof(f_540_3,plain,
    ! [U_2085,U_2086] :
      ( hAPP(U_2086,U_2086,hAPP(U_2086,fun(U_2086,U_2086),plus_plus(U_2086),zero_zero(U_2086)),U_2085) = ti(U_2086,U_2085)
      | ~ monoid_add(U_2086) ),
    inference(definitional_conversion,[status(esa)],[f_540_2]) ).

cnf(f_540_4,plain,
    ( hAPP(U_2086,U_2086,hAPP(U_2086,fun(U_2086,U_2086),plus_plus(U_2086),zero_zero(U_2086)),U_2085) = ti(U_2086,U_2085)
    | ~ monoid_add(U_2086) ),
    inference(clausify,[status(thm)],[f_540_3]) ).

fof(f_541_1,plain,
    ! [X_b] :
      ( ! [A_2,B_3] :
          ( ( hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3) = zero_zero(X_b)
            | ti(X_b,A_2) != ti(X_b,B_3) )
          & ( ti(X_b,A_2) = ti(X_b,B_3)
            | hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3) != zero_zero(X_b) ) )
      | ~ group_add(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_470_right__minus__eq]) ).

fof(f_541_2,plain,
    ! [U_2089] :
      ( ! [U_2088,U_2087] :
          ( ( hAPP(U_2089,U_2089,hAPP(U_2089,fun(U_2089,U_2089),minus_minus(U_2089),U_2088),U_2087) = zero_zero(U_2089)
            | ti(U_2089,U_2088) != ti(U_2089,U_2087) )
          & ( ti(U_2089,U_2088) = ti(U_2089,U_2087)
            | hAPP(U_2089,U_2089,hAPP(U_2089,fun(U_2089,U_2089),minus_minus(U_2089),U_2088),U_2087) != zero_zero(U_2089) ) )
      | ~ group_add(U_2089) ),
    inference(variable_rename,[status(thm)],[f_541_1]) ).

fof(f_541_3,plain,
    ! [U_2089] :
      ( ( ! [U_2093,U_2091] :
            ( hAPP(U_2089,U_2089,hAPP(U_2089,fun(U_2089,U_2089),minus_minus(U_2089),U_2093),U_2091) = zero_zero(U_2089)
            | ti(U_2089,U_2093) != ti(U_2089,U_2091) )
        & ! [U_2092,U_2090] :
            ( ti(U_2089,U_2092) = ti(U_2089,U_2090)
            | hAPP(U_2089,U_2089,hAPP(U_2089,fun(U_2089,U_2089),minus_minus(U_2089),U_2092),U_2090) != zero_zero(U_2089) ) )
      | ~ group_add(U_2089) ),
    inference(miniscope,[status(thm)],[f_541_2]) ).

fof(f_541_4,plain,
    ( ! [U_2093,U_2089,U_2091,U_2090,U_2092] :
        ( hAPP(U_2089,U_2089,hAPP(U_2089,fun(U_2089,U_2089),minus_minus(U_2089),U_2093),U_2091) = zero_zero(U_2089)
        | ti(U_2089,U_2093) != ti(U_2089,U_2091)
        | ~ sP127(U_2093,U_2089,U_2091,U_2090,U_2092) )
    & ! [U_2093,U_2089,U_2091,U_2090,U_2092] :
        ( ti(U_2089,U_2092) = ti(U_2089,U_2090)
        | hAPP(U_2089,U_2089,hAPP(U_2089,fun(U_2089,U_2089),minus_minus(U_2089),U_2092),U_2090) != zero_zero(U_2089)
        | ~ sP127(U_2093,U_2089,U_2091,U_2090,U_2092) )
    & ! [U_2093,U_2089,U_2091,U_2090,U_2092] :
        ( sP127(U_2093,U_2089,U_2091,U_2090,U_2092)
        | ~ group_add(U_2089) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP127])],[f_541_3]) ).

cnf(f_541_5,plain,
    ( sP127(U_2093,U_2089,U_2091,U_2090,U_2092)
    | ~ group_add(U_2089) ),
    inference(clausify,[status(thm)],[f_541_4]) ).

cnf(f_541_6,plain,
    ( ti(U_2089,U_2092) = ti(U_2089,U_2090)
    | hAPP(U_2089,U_2089,hAPP(U_2089,fun(U_2089,U_2089),minus_minus(U_2089),U_2092),U_2090) != zero_zero(U_2089)
    | ~ sP127(U_2093,U_2089,U_2091,U_2090,U_2092) ),
    inference(clausify,[status(thm)],[f_541_4]) ).

cnf(f_541_7,plain,
    ( hAPP(U_2089,U_2089,hAPP(U_2089,fun(U_2089,U_2089),minus_minus(U_2089),U_2093),U_2091) = zero_zero(U_2089)
    | ti(U_2089,U_2093) != ti(U_2089,U_2091)
    | ~ sP127(U_2093,U_2089,U_2091,U_2090,U_2092) ),
    inference(clausify,[status(thm)],[f_541_4]) ).

fof(f_542_1,plain,
    ! [X_b] :
      ( ! [A_2,B_3] :
          ( ( ti(X_b,A_2) = ti(X_b,B_3)
            | hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3) != zero_zero(X_b) )
          & ( hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3) = zero_zero(X_b)
            | ti(X_b,A_2) != ti(X_b,B_3) ) )
      | ~ ab_group_add(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_471_eq__iff__diff__eq__0]) ).

fof(f_542_2,plain,
    ! [U_2096] :
      ( ! [U_2095,U_2094] :
          ( ( ti(U_2096,U_2095) = ti(U_2096,U_2094)
            | hAPP(U_2096,U_2096,hAPP(U_2096,fun(U_2096,U_2096),minus_minus(U_2096),U_2095),U_2094) != zero_zero(U_2096) )
          & ( hAPP(U_2096,U_2096,hAPP(U_2096,fun(U_2096,U_2096),minus_minus(U_2096),U_2095),U_2094) = zero_zero(U_2096)
            | ti(U_2096,U_2095) != ti(U_2096,U_2094) ) )
      | ~ ab_group_add(U_2096) ),
    inference(variable_rename,[status(thm)],[f_542_1]) ).

fof(f_542_3,plain,
    ! [U_2096] :
      ( ( ! [U_2100,U_2098] :
            ( ti(U_2096,U_2100) = ti(U_2096,U_2098)
            | hAPP(U_2096,U_2096,hAPP(U_2096,fun(U_2096,U_2096),minus_minus(U_2096),U_2100),U_2098) != zero_zero(U_2096) )
        & ! [U_2099,U_2097] :
            ( hAPP(U_2096,U_2096,hAPP(U_2096,fun(U_2096,U_2096),minus_minus(U_2096),U_2099),U_2097) = zero_zero(U_2096)
            | ti(U_2096,U_2099) != ti(U_2096,U_2097) ) )
      | ~ ab_group_add(U_2096) ),
    inference(miniscope,[status(thm)],[f_542_2]) ).

fof(f_542_4,plain,
    ( ! [U_2100,U_2096,U_2097,U_2098,U_2099] :
        ( ti(U_2096,U_2100) = ti(U_2096,U_2098)
        | hAPP(U_2096,U_2096,hAPP(U_2096,fun(U_2096,U_2096),minus_minus(U_2096),U_2100),U_2098) != zero_zero(U_2096)
        | ~ sP128(U_2100,U_2096,U_2097,U_2098,U_2099) )
    & ! [U_2100,U_2096,U_2097,U_2098,U_2099] :
        ( hAPP(U_2096,U_2096,hAPP(U_2096,fun(U_2096,U_2096),minus_minus(U_2096),U_2099),U_2097) = zero_zero(U_2096)
        | ti(U_2096,U_2099) != ti(U_2096,U_2097)
        | ~ sP128(U_2100,U_2096,U_2097,U_2098,U_2099) )
    & ! [U_2100,U_2096,U_2097,U_2098,U_2099] :
        ( sP128(U_2100,U_2096,U_2097,U_2098,U_2099)
        | ~ ab_group_add(U_2096) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP128])],[f_542_3]) ).

cnf(f_542_5,plain,
    ( sP128(U_2100,U_2096,U_2097,U_2098,U_2099)
    | ~ ab_group_add(U_2096) ),
    inference(clausify,[status(thm)],[f_542_4]) ).

cnf(f_542_6,plain,
    ( hAPP(U_2096,U_2096,hAPP(U_2096,fun(U_2096,U_2096),minus_minus(U_2096),U_2099),U_2097) = zero_zero(U_2096)
    | ti(U_2096,U_2099) != ti(U_2096,U_2097)
    | ~ sP128(U_2100,U_2096,U_2097,U_2098,U_2099) ),
    inference(clausify,[status(thm)],[f_542_4]) ).

cnf(f_542_7,plain,
    ( ti(U_2096,U_2100) = ti(U_2096,U_2098)
    | hAPP(U_2096,U_2096,hAPP(U_2096,fun(U_2096,U_2096),minus_minus(U_2096),U_2100),U_2098) != zero_zero(U_2096)
    | ~ sP128(U_2100,U_2096,U_2097,U_2098,U_2099) ),
    inference(clausify,[status(thm)],[f_542_4]) ).

fof(f_543_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_472_diff__self]) ).

fof(f_543_2,plain,
    ! [U_2102] :
      ( ! [U_2101] : hAPP(U_2102,U_2102,hAPP(U_2102,fun(U_2102,U_2102),minus_minus(U_2102),U_2101),U_2101) = zero_zero(U_2102)
      | ~ group_add(U_2102) ),
    inference(variable_rename,[status(thm)],[f_543_1]) ).

fof(f_543_3,plain,
    ! [U_2102,U_2101] :
      ( hAPP(U_2102,U_2102,hAPP(U_2102,fun(U_2102,U_2102),minus_minus(U_2102),U_2101),U_2101) = zero_zero(U_2102)
      | ~ group_add(U_2102) ),
    inference(definitional_conversion,[status(esa)],[f_543_2]) ).

cnf(f_543_4,plain,
    ( hAPP(U_2102,U_2102,hAPP(U_2102,fun(U_2102,U_2102),minus_minus(U_2102),U_2101),U_2101) = zero_zero(U_2102)
    | ~ group_add(U_2102) ),
    inference(clausify,[status(thm)],[f_543_3]) ).

fof(f_544_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_473_diff__0__right]) ).

fof(f_544_2,plain,
    ! [U_2104] :
      ( ! [U_2103] : hAPP(U_2104,U_2104,hAPP(U_2104,fun(U_2104,U_2104),minus_minus(U_2104),U_2103),zero_zero(U_2104)) = ti(U_2104,U_2103)
      | ~ group_add(U_2104) ),
    inference(variable_rename,[status(thm)],[f_544_1]) ).

fof(f_544_3,plain,
    ! [U_2103,U_2104] :
      ( hAPP(U_2104,U_2104,hAPP(U_2104,fun(U_2104,U_2104),minus_minus(U_2104),U_2103),zero_zero(U_2104)) = ti(U_2104,U_2103)
      | ~ group_add(U_2104) ),
    inference(definitional_conversion,[status(esa)],[f_544_2]) ).

cnf(f_544_4,plain,
    ( hAPP(U_2104,U_2104,hAPP(U_2104,fun(U_2104,U_2104),minus_minus(U_2104),U_2103),zero_zero(U_2104)) = ti(U_2104,U_2103)
    | ~ group_add(U_2104) ),
    inference(clausify,[status(thm)],[f_544_3]) ).

fof(f_545_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_474_zero__reorient]) ).

fof(f_545_2,plain,
    ! [U_2106] :
      ( ! [U_2105] :
          ( ( zero_zero(U_2106) = ti(U_2106,U_2105)
            | ti(U_2106,U_2105) != zero_zero(U_2106) )
          & ( ti(U_2106,U_2105) = zero_zero(U_2106)
            | zero_zero(U_2106) != ti(U_2106,U_2105) ) )
      | ~ zero(U_2106) ),
    inference(variable_rename,[status(thm)],[f_545_1]) ).

fof(f_545_3,plain,
    ! [U_2106] :
      ( ( ! [U_2108] :
            ( zero_zero(U_2106) = ti(U_2106,U_2108)
            | ti(U_2106,U_2108) != zero_zero(U_2106) )
        & ! [U_2107] :
            ( ti(U_2106,U_2107) = zero_zero(U_2106)
            | zero_zero(U_2106) != ti(U_2106,U_2107) ) )
      | ~ zero(U_2106) ),
    inference(miniscope,[status(thm)],[f_545_2]) ).

fof(f_545_4,plain,
    ( ! [U_2106,U_2108,U_2107] :
        ( zero_zero(U_2106) = ti(U_2106,U_2108)
        | ti(U_2106,U_2108) != zero_zero(U_2106)
        | ~ sP129(U_2106,U_2108,U_2107) )
    & ! [U_2106,U_2108,U_2107] :
        ( ti(U_2106,U_2107) = zero_zero(U_2106)
        | zero_zero(U_2106) != ti(U_2106,U_2107)
        | ~ sP129(U_2106,U_2108,U_2107) )
    & ! [U_2106,U_2108,U_2107] :
        ( sP129(U_2106,U_2108,U_2107)
        | ~ zero(U_2106) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP129])],[f_545_3]) ).

cnf(f_545_5,plain,
    ( sP129(U_2106,U_2108,U_2107)
    | ~ zero(U_2106) ),
    inference(clausify,[status(thm)],[f_545_4]) ).

cnf(f_545_6,plain,
    ( ti(U_2106,U_2107) = zero_zero(U_2106)
    | zero_zero(U_2106) != ti(U_2106,U_2107)
    | ~ sP129(U_2106,U_2108,U_2107) ),
    inference(clausify,[status(thm)],[f_545_4]) ).

cnf(f_545_7,plain,
    ( zero_zero(U_2106) = ti(U_2106,U_2108)
    | ti(U_2106,U_2108) != zero_zero(U_2106)
    | ~ sP129(U_2106,U_2108,U_2107) ),
    inference(clausify,[status(thm)],[f_545_4]) ).

fof(f_546_1,plain,
    bot_bot(nat) = zero_zero(nat),
    inference(fof_nnf,[status(thm)],[fact_475_bot__nat__def]) ).

fof(f_546_2,plain,
    bot_bot(nat) = zero_zero(nat),
    inference(definitional_conversion,[status(esa)],[f_546_1]) ).

cnf(f_546_3,plain,
    bot_bot(nat) = zero_zero(nat),
    inference(clausify,[status(thm)],[f_546_2]) ).

fof(f_547_1,plain,
    ! [M_1,N] :
      ( N = zero_zero(nat)
      | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N) != M_1 ),
    inference(fof_nnf,[status(thm)],[fact_476_add__eq__self__zero]) ).

fof(f_547_2,plain,
    ! [U_2110,U_2109] :
      ( U_2109 = zero_zero(nat)
      | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2110),U_2109) != U_2110 ),
    inference(variable_rename,[status(thm)],[f_547_1]) ).

fof(f_547_3,plain,
    ! [U_2109,U_2110] :
      ( U_2109 = zero_zero(nat)
      | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2110),U_2109) != U_2110 ),
    inference(definitional_conversion,[status(esa)],[f_547_2]) ).

cnf(f_547_4,plain,
    ( U_2109 = zero_zero(nat)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2110),U_2109) != U_2110 ),
    inference(clausify,[status(thm)],[f_547_3]) ).

fof(f_548_1,plain,
    ! [M,Na] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),Na) = zero_zero(nat)
        | Na != zero_zero(nat)
        | M != zero_zero(nat) )
      & ( ( Na = zero_zero(nat)
          & M = zero_zero(nat) )
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),Na) != zero_zero(nat) ) ),
    inference(fof_nnf,[status(thm)],[fact_477_add__is__0]) ).

fof(f_548_2,plain,
    ! [U_2112,U_2111] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2112),U_2111) = zero_zero(nat)
        | U_2111 != zero_zero(nat)
        | U_2112 != zero_zero(nat) )
      & ( ( U_2111 = zero_zero(nat)
          & U_2112 = zero_zero(nat) )
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2112),U_2111) != zero_zero(nat) ) ),
    inference(variable_rename,[status(thm)],[f_548_1]) ).

fof(f_548_3,plain,
    ( ! [U_2116,U_2114] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2116),U_2114) = zero_zero(nat)
        | U_2114 != zero_zero(nat)
        | U_2116 != zero_zero(nat) )
    & ! [U_2115,U_2113] :
        ( ( U_2113 = zero_zero(nat)
          & U_2115 = zero_zero(nat) )
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2115),U_2113) != zero_zero(nat) ) ),
    inference(miniscope,[status(thm)],[f_548_2]) ).

fof(f_548_4,plain,
    ( ! [U_2113,U_2115] :
        ( U_2113 = zero_zero(nat)
        | ~ sP130(U_2113,U_2115) )
    & ! [U_2113,U_2115] :
        ( U_2115 = zero_zero(nat)
        | ~ sP130(U_2113,U_2115) )
    & ! [U_2116,U_2114] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2116),U_2114) = zero_zero(nat)
        | U_2114 != zero_zero(nat)
        | U_2116 != zero_zero(nat) )
    & ! [U_2113,U_2115] :
        ( sP130(U_2113,U_2115)
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2115),U_2113) != zero_zero(nat) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP130])],[f_548_3]) ).

cnf(f_548_5,plain,
    ( sP130(U_2113,U_2115)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2115),U_2113) != zero_zero(nat) ),
    inference(clausify,[status(thm)],[f_548_4]) ).

cnf(f_548_6,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2116),U_2114) = zero_zero(nat)
    | U_2114 != zero_zero(nat)
    | U_2116 != zero_zero(nat) ),
    inference(clausify,[status(thm)],[f_548_4]) ).

cnf(f_548_7,plain,
    ( U_2115 = zero_zero(nat)
    | ~ sP130(U_2113,U_2115) ),
    inference(clausify,[status(thm)],[f_548_4]) ).

cnf(f_548_8,plain,
    ( U_2113 = zero_zero(nat)
    | ~ sP130(U_2113,U_2115) ),
    inference(clausify,[status(thm)],[f_548_4]) ).

fof(f_549_1,plain,
    ! [M_1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),zero_zero(nat)) = M_1,
    inference(fof_nnf,[status(thm)],[fact_478_Nat_Oadd__0__right]) ).

fof(f_549_2,plain,
    ! [U_2117] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2117),zero_zero(nat)) = U_2117,
    inference(variable_rename,[status(thm)],[f_549_1]) ).

fof(f_549_3,plain,
    ! [U_2117] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2117),zero_zero(nat)) = U_2117,
    inference(definitional_conversion,[status(esa)],[f_549_2]) ).

cnf(f_549_4,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2117),zero_zero(nat)) = U_2117,
    inference(clausify,[status(thm)],[f_549_3]) ).

fof(f_550_1,plain,
    ! [N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),N) = N,
    inference(fof_nnf,[status(thm)],[fact_479_plus__nat_Oadd__0]) ).

fof(f_550_2,plain,
    ! [U_2118] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),U_2118) = U_2118,
    inference(variable_rename,[status(thm)],[f_550_1]) ).

fof(f_550_3,plain,
    ! [U_2118] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),U_2118) = U_2118,
    inference(definitional_conversion,[status(esa)],[f_550_2]) ).

cnf(f_550_4,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),U_2118) = U_2118,
    inference(clausify,[status(thm)],[f_550_3]) ).

fof(f_551_1,plain,
    ! [N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))
      | N = zero_zero(nat) ),
    inference(fof_nnf,[status(thm)],[fact_480_gr0I]) ).

fof(f_551_2,plain,
    ! [U_2119] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2119))
      | U_2119 = zero_zero(nat) ),
    inference(variable_rename,[status(thm)],[f_551_1]) ).

fof(f_551_3,plain,
    ! [U_2119] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2119))
      | U_2119 = zero_zero(nat) ),
    inference(definitional_conversion,[status(esa)],[f_551_2]) ).

cnf(f_551_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2119))
    | U_2119 = zero_zero(nat) ),
    inference(clausify,[status(thm)],[f_551_3]) ).

fof(f_552_1,plain,
    ! [M_1,N] :
      ( N != zero_zero(nat)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)) ),
    inference(fof_nnf,[status(thm)],[fact_481_gr__implies__not0]) ).

fof(f_552_2,plain,
    ! [U_2121,U_2120] :
      ( U_2120 != zero_zero(nat)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2121),U_2120)) ),
    inference(variable_rename,[status(thm)],[f_552_1]) ).

fof(f_552_3,plain,
    ! [U_2121,U_2120] :
      ( U_2120 != zero_zero(nat)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2121),U_2120)) ),
    inference(definitional_conversion,[status(esa)],[f_552_2]) ).

cnf(f_552_4,plain,
    ( U_2120 != zero_zero(nat)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2121),U_2120)) ),
    inference(clausify,[status(thm)],[f_552_3]) ).

fof(f_553_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_482_less__nat__zero__code]) ).

fof(f_553_2,plain,
    ! [U_2122] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2122),zero_zero(nat))),
    inference(variable_rename,[status(thm)],[f_553_1]) ).

fof(f_553_3,plain,
    ! [U_2122] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2122),zero_zero(nat))),
    inference(definitional_conversion,[status(esa)],[f_553_2]) ).

cnf(f_553_4,plain,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2122),zero_zero(nat))),
    inference(clausify,[status(thm)],[f_553_3]) ).

fof(f_554_1,plain,
    ! [Na] :
      ( ( Na != zero_zero(nat)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na))
        | Na = zero_zero(nat) ) ),
    inference(fof_nnf,[status(thm)],[fact_483_neq0__conv]) ).

fof(f_554_2,plain,
    ! [U_2123] :
      ( ( U_2123 != zero_zero(nat)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2123)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2123))
        | U_2123 = zero_zero(nat) ) ),
    inference(variable_rename,[status(thm)],[f_554_1]) ).

fof(f_554_3,plain,
    ( ! [U_2125] :
        ( U_2125 != zero_zero(nat)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2125)) )
    & ! [U_2124] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2124))
        | U_2124 = zero_zero(nat) ) ),
    inference(miniscope,[status(thm)],[f_554_2]) ).

fof(f_554_4,plain,
    ( ! [U_2125] :
        ( U_2125 != zero_zero(nat)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2125)) )
    & ! [U_2124] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2124))
        | U_2124 = zero_zero(nat) ) ),
    inference(definitional_conversion,[status(esa)],[f_554_3]) ).

cnf(f_554_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2124))
    | U_2124 = zero_zero(nat) ),
    inference(clausify,[status(thm)],[f_554_4]) ).

cnf(f_554_6,plain,
    ( U_2125 != zero_zero(nat)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2125)) ),
    inference(clausify,[status(thm)],[f_554_4]) ).

fof(f_555_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_484_not__less0]) ).

fof(f_555_2,plain,
    ! [U_2126] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2126),zero_zero(nat))),
    inference(variable_rename,[status(thm)],[f_555_1]) ).

fof(f_555_3,plain,
    ! [U_2126] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2126),zero_zero(nat))),
    inference(definitional_conversion,[status(esa)],[f_555_2]) ).

cnf(f_555_4,plain,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2126),zero_zero(nat))),
    inference(clausify,[status(thm)],[f_555_3]) ).

fof(f_556_1,plain,
    ! [M_1] : hAPP(nat,nat,suc,M_1) != zero_zero(nat),
    inference(fof_nnf,[status(thm)],[fact_485_Suc__neq__Zero]) ).

fof(f_556_2,plain,
    ! [U_2127] : hAPP(nat,nat,suc,U_2127) != zero_zero(nat),
    inference(variable_rename,[status(thm)],[f_556_1]) ).

fof(f_556_3,plain,
    ! [U_2127] : hAPP(nat,nat,suc,U_2127) != zero_zero(nat),
    inference(definitional_conversion,[status(esa)],[f_556_2]) ).

cnf(f_556_4,plain,
    hAPP(nat,nat,suc,U_2127) != zero_zero(nat),
    inference(clausify,[status(thm)],[f_556_3]) ).

fof(f_557_1,plain,
    ! [M_1] : zero_zero(nat) != hAPP(nat,nat,suc,M_1),
    inference(fof_nnf,[status(thm)],[fact_486_Zero__neq__Suc]) ).

fof(f_557_2,plain,
    ! [U_2128] : zero_zero(nat) != hAPP(nat,nat,suc,U_2128),
    inference(variable_rename,[status(thm)],[f_557_1]) ).

fof(f_557_3,plain,
    ! [U_2128] : zero_zero(nat) != hAPP(nat,nat,suc,U_2128),
    inference(definitional_conversion,[status(esa)],[f_557_2]) ).

cnf(f_557_4,plain,
    zero_zero(nat) != hAPP(nat,nat,suc,U_2128),
    inference(clausify,[status(thm)],[f_557_3]) ).

fof(f_558_1,plain,
    ! [Nat_2] : hAPP(nat,nat,suc,Nat_2) != zero_zero(nat),
    inference(fof_nnf,[status(thm)],[fact_487_nat_Osimps_I3_J]) ).

fof(f_558_2,plain,
    ! [U_2129] : hAPP(nat,nat,suc,U_2129) != zero_zero(nat),
    inference(variable_rename,[status(thm)],[f_558_1]) ).

fof(f_558_3,plain,
    ! [U_2129] : hAPP(nat,nat,suc,U_2129) != zero_zero(nat),
    inference(definitional_conversion,[status(esa)],[f_558_2]) ).

cnf(f_558_4,plain,
    hAPP(nat,nat,suc,U_2129) != zero_zero(nat),
    inference(clausify,[status(thm)],[f_558_3]) ).

fof(f_559_1,plain,
    ! [M_1] : hAPP(nat,nat,suc,M_1) != zero_zero(nat),
    inference(fof_nnf,[status(thm)],[fact_488_Suc__not__Zero]) ).

fof(f_559_2,plain,
    ! [U_2130] : hAPP(nat,nat,suc,U_2130) != zero_zero(nat),
    inference(variable_rename,[status(thm)],[f_559_1]) ).

fof(f_559_3,plain,
    ! [U_2130] : hAPP(nat,nat,suc,U_2130) != zero_zero(nat),
    inference(definitional_conversion,[status(esa)],[f_559_2]) ).

cnf(f_559_4,plain,
    hAPP(nat,nat,suc,U_2130) != zero_zero(nat),
    inference(clausify,[status(thm)],[f_559_3]) ).

fof(f_560_1,plain,
    ! [Nat_1] : zero_zero(nat) != hAPP(nat,nat,suc,Nat_1),
    inference(fof_nnf,[status(thm)],[fact_489_nat_Osimps_I2_J]) ).

fof(f_560_2,plain,
    ! [U_2131] : zero_zero(nat) != hAPP(nat,nat,suc,U_2131),
    inference(variable_rename,[status(thm)],[f_560_1]) ).

fof(f_560_3,plain,
    ! [U_2131] : zero_zero(nat) != hAPP(nat,nat,suc,U_2131),
    inference(definitional_conversion,[status(esa)],[f_560_2]) ).

cnf(f_560_4,plain,
    zero_zero(nat) != hAPP(nat,nat,suc,U_2131),
    inference(clausify,[status(thm)],[f_560_3]) ).

fof(f_561_1,plain,
    ! [M_1] : zero_zero(nat) != hAPP(nat,nat,suc,M_1),
    inference(fof_nnf,[status(thm)],[fact_490_Zero__not__Suc]) ).

fof(f_561_2,plain,
    ! [U_2132] : zero_zero(nat) != hAPP(nat,nat,suc,U_2132),
    inference(variable_rename,[status(thm)],[f_561_1]) ).

fof(f_561_3,plain,
    ! [U_2132] : zero_zero(nat) != hAPP(nat,nat,suc,U_2132),
    inference(definitional_conversion,[status(esa)],[f_561_2]) ).

cnf(f_561_4,plain,
    zero_zero(nat) != hAPP(nat,nat,suc,U_2132),
    inference(clausify,[status(thm)],[f_561_3]) ).

fof(f_562_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_562_2,plain,
    ! [U_2135,U_2134,U_2133] : hAPP(nat,U_2135,hAPP(fun(nat,U_2135),fun(nat,U_2135),hAPP(U_2135,fun(fun(nat,U_2135),fun(nat,U_2135)),nat_case(U_2135),U_2134),U_2133),zero_zero(nat)) = ti(U_2135,U_2134),
    inference(variable_rename,[status(thm)],[f_562_1]) ).

fof(f_562_3,plain,
    ! [U_2133,U_2134,U_2135] : hAPP(nat,U_2135,hAPP(fun(nat,U_2135),fun(nat,U_2135),hAPP(U_2135,fun(fun(nat,U_2135),fun(nat,U_2135)),nat_case(U_2135),U_2134),U_2133),zero_zero(nat)) = ti(U_2135,U_2134),
    inference(definitional_conversion,[status(esa)],[f_562_2]) ).

cnf(f_562_4,plain,
    hAPP(nat,U_2135,hAPP(fun(nat,U_2135),fun(nat,U_2135),hAPP(U_2135,fun(fun(nat,U_2135),fun(nat,U_2135)),nat_case(U_2135),U_2134),U_2133),zero_zero(nat)) = ti(U_2135,U_2134),
    inference(clausify,[status(thm)],[f_562_3]) ).

fof(f_563_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_492_zero__le__double__add__iff__zero__le__single__add]) ).

fof(f_563_2,plain,
    ! [U_2137] :
      ( ! [U_2136] :
          ( ( hBOOL(hAPP(U_2137,bool,hAPP(U_2137,fun(U_2137,bool),ord_less_eq(U_2137),zero_zero(U_2137)),hAPP(U_2137,U_2137,hAPP(U_2137,fun(U_2137,U_2137),plus_plus(U_2137),U_2136),U_2136)))
            | ~ hBOOL(hAPP(U_2137,bool,hAPP(U_2137,fun(U_2137,bool),ord_less_eq(U_2137),zero_zero(U_2137)),U_2136)) )
          & ( hBOOL(hAPP(U_2137,bool,hAPP(U_2137,fun(U_2137,bool),ord_less_eq(U_2137),zero_zero(U_2137)),U_2136))
            | ~ hBOOL(hAPP(U_2137,bool,hAPP(U_2137,fun(U_2137,bool),ord_less_eq(U_2137),zero_zero(U_2137)),hAPP(U_2137,U_2137,hAPP(U_2137,fun(U_2137,U_2137),plus_plus(U_2137),U_2136),U_2136))) ) )
      | ~ linord219039673up_add(U_2137) ),
    inference(variable_rename,[status(thm)],[f_563_1]) ).

fof(f_563_3,plain,
    ! [U_2137] :
      ( ( ! [U_2139] :
            ( hBOOL(hAPP(U_2137,bool,hAPP(U_2137,fun(U_2137,bool),ord_less_eq(U_2137),zero_zero(U_2137)),hAPP(U_2137,U_2137,hAPP(U_2137,fun(U_2137,U_2137),plus_plus(U_2137),U_2139),U_2139)))
            | ~ hBOOL(hAPP(U_2137,bool,hAPP(U_2137,fun(U_2137,bool),ord_less_eq(U_2137),zero_zero(U_2137)),U_2139)) )
        & ! [U_2138] :
            ( hBOOL(hAPP(U_2137,bool,hAPP(U_2137,fun(U_2137,bool),ord_less_eq(U_2137),zero_zero(U_2137)),U_2138))
            | ~ hBOOL(hAPP(U_2137,bool,hAPP(U_2137,fun(U_2137,bool),ord_less_eq(U_2137),zero_zero(U_2137)),hAPP(U_2137,U_2137,hAPP(U_2137,fun(U_2137,U_2137),plus_plus(U_2137),U_2138),U_2138))) ) )
      | ~ linord219039673up_add(U_2137) ),
    inference(miniscope,[status(thm)],[f_563_2]) ).

fof(f_563_4,plain,
    ( ! [U_2137,U_2138,U_2139] :
        ( hBOOL(hAPP(U_2137,bool,hAPP(U_2137,fun(U_2137,bool),ord_less_eq(U_2137),zero_zero(U_2137)),hAPP(U_2137,U_2137,hAPP(U_2137,fun(U_2137,U_2137),plus_plus(U_2137),U_2139),U_2139)))
        | ~ hBOOL(hAPP(U_2137,bool,hAPP(U_2137,fun(U_2137,bool),ord_less_eq(U_2137),zero_zero(U_2137)),U_2139))
        | ~ sP131(U_2137,U_2138,U_2139) )
    & ! [U_2137,U_2138,U_2139] :
        ( hBOOL(hAPP(U_2137,bool,hAPP(U_2137,fun(U_2137,bool),ord_less_eq(U_2137),zero_zero(U_2137)),U_2138))
        | ~ hBOOL(hAPP(U_2137,bool,hAPP(U_2137,fun(U_2137,bool),ord_less_eq(U_2137),zero_zero(U_2137)),hAPP(U_2137,U_2137,hAPP(U_2137,fun(U_2137,U_2137),plus_plus(U_2137),U_2138),U_2138)))
        | ~ sP131(U_2137,U_2138,U_2139) )
    & ! [U_2137,U_2138,U_2139] :
        ( sP131(U_2137,U_2138,U_2139)
        | ~ linord219039673up_add(U_2137) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP131])],[f_563_3]) ).

cnf(f_563_5,plain,
    ( sP131(U_2137,U_2138,U_2139)
    | ~ linord219039673up_add(U_2137) ),
    inference(clausify,[status(thm)],[f_563_4]) ).

cnf(f_563_6,plain,
    ( hBOOL(hAPP(U_2137,bool,hAPP(U_2137,fun(U_2137,bool),ord_less_eq(U_2137),zero_zero(U_2137)),U_2138))
    | ~ hBOOL(hAPP(U_2137,bool,hAPP(U_2137,fun(U_2137,bool),ord_less_eq(U_2137),zero_zero(U_2137)),hAPP(U_2137,U_2137,hAPP(U_2137,fun(U_2137,U_2137),plus_plus(U_2137),U_2138),U_2138)))
    | ~ sP131(U_2137,U_2138,U_2139) ),
    inference(clausify,[status(thm)],[f_563_4]) ).

cnf(f_563_7,plain,
    ( hBOOL(hAPP(U_2137,bool,hAPP(U_2137,fun(U_2137,bool),ord_less_eq(U_2137),zero_zero(U_2137)),hAPP(U_2137,U_2137,hAPP(U_2137,fun(U_2137,U_2137),plus_plus(U_2137),U_2139),U_2139)))
    | ~ hBOOL(hAPP(U_2137,bool,hAPP(U_2137,fun(U_2137,bool),ord_less_eq(U_2137),zero_zero(U_2137)),U_2139))
    | ~ sP131(U_2137,U_2138,U_2139) ),
    inference(clausify,[status(thm)],[f_563_4]) ).

fof(f_564_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_493_double__add__le__zero__iff__single__add__le__zero]) ).

fof(f_564_2,plain,
    ! [U_2141] :
      ( ! [U_2140] :
          ( ( hBOOL(hAPP(U_2141,bool,hAPP(U_2141,fun(U_2141,bool),ord_less_eq(U_2141),hAPP(U_2141,U_2141,hAPP(U_2141,fun(U_2141,U_2141),plus_plus(U_2141),U_2140),U_2140)),zero_zero(U_2141)))
            | ~ hBOOL(hAPP(U_2141,bool,hAPP(U_2141,fun(U_2141,bool),ord_less_eq(U_2141),U_2140),zero_zero(U_2141))) )
          & ( hBOOL(hAPP(U_2141,bool,hAPP(U_2141,fun(U_2141,bool),ord_less_eq(U_2141),U_2140),zero_zero(U_2141)))
            | ~ hBOOL(hAPP(U_2141,bool,hAPP(U_2141,fun(U_2141,bool),ord_less_eq(U_2141),hAPP(U_2141,U_2141,hAPP(U_2141,fun(U_2141,U_2141),plus_plus(U_2141),U_2140),U_2140)),zero_zero(U_2141))) ) )
      | ~ linord219039673up_add(U_2141) ),
    inference(variable_rename,[status(thm)],[f_564_1]) ).

fof(f_564_3,plain,
    ! [U_2141] :
      ( ( ! [U_2143] :
            ( hBOOL(hAPP(U_2141,bool,hAPP(U_2141,fun(U_2141,bool),ord_less_eq(U_2141),hAPP(U_2141,U_2141,hAPP(U_2141,fun(U_2141,U_2141),plus_plus(U_2141),U_2143),U_2143)),zero_zero(U_2141)))
            | ~ hBOOL(hAPP(U_2141,bool,hAPP(U_2141,fun(U_2141,bool),ord_less_eq(U_2141),U_2143),zero_zero(U_2141))) )
        & ! [U_2142] :
            ( hBOOL(hAPP(U_2141,bool,hAPP(U_2141,fun(U_2141,bool),ord_less_eq(U_2141),U_2142),zero_zero(U_2141)))
            | ~ hBOOL(hAPP(U_2141,bool,hAPP(U_2141,fun(U_2141,bool),ord_less_eq(U_2141),hAPP(U_2141,U_2141,hAPP(U_2141,fun(U_2141,U_2141),plus_plus(U_2141),U_2142),U_2142)),zero_zero(U_2141))) ) )
      | ~ linord219039673up_add(U_2141) ),
    inference(miniscope,[status(thm)],[f_564_2]) ).

fof(f_564_4,plain,
    ( ! [U_2143,U_2141,U_2142] :
        ( hBOOL(hAPP(U_2141,bool,hAPP(U_2141,fun(U_2141,bool),ord_less_eq(U_2141),hAPP(U_2141,U_2141,hAPP(U_2141,fun(U_2141,U_2141),plus_plus(U_2141),U_2143),U_2143)),zero_zero(U_2141)))
        | ~ hBOOL(hAPP(U_2141,bool,hAPP(U_2141,fun(U_2141,bool),ord_less_eq(U_2141),U_2143),zero_zero(U_2141)))
        | ~ sP132(U_2143,U_2141,U_2142) )
    & ! [U_2143,U_2141,U_2142] :
        ( hBOOL(hAPP(U_2141,bool,hAPP(U_2141,fun(U_2141,bool),ord_less_eq(U_2141),U_2142),zero_zero(U_2141)))
        | ~ hBOOL(hAPP(U_2141,bool,hAPP(U_2141,fun(U_2141,bool),ord_less_eq(U_2141),hAPP(U_2141,U_2141,hAPP(U_2141,fun(U_2141,U_2141),plus_plus(U_2141),U_2142),U_2142)),zero_zero(U_2141)))
        | ~ sP132(U_2143,U_2141,U_2142) )
    & ! [U_2143,U_2141,U_2142] :
        ( sP132(U_2143,U_2141,U_2142)
        | ~ linord219039673up_add(U_2141) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP132])],[f_564_3]) ).

cnf(f_564_5,plain,
    ( sP132(U_2143,U_2141,U_2142)
    | ~ linord219039673up_add(U_2141) ),
    inference(clausify,[status(thm)],[f_564_4]) ).

cnf(f_564_6,plain,
    ( hBOOL(hAPP(U_2141,bool,hAPP(U_2141,fun(U_2141,bool),ord_less_eq(U_2141),U_2142),zero_zero(U_2141)))
    | ~ hBOOL(hAPP(U_2141,bool,hAPP(U_2141,fun(U_2141,bool),ord_less_eq(U_2141),hAPP(U_2141,U_2141,hAPP(U_2141,fun(U_2141,U_2141),plus_plus(U_2141),U_2142),U_2142)),zero_zero(U_2141)))
    | ~ sP132(U_2143,U_2141,U_2142) ),
    inference(clausify,[status(thm)],[f_564_4]) ).

cnf(f_564_7,plain,
    ( hBOOL(hAPP(U_2141,bool,hAPP(U_2141,fun(U_2141,bool),ord_less_eq(U_2141),hAPP(U_2141,U_2141,hAPP(U_2141,fun(U_2141,U_2141),plus_plus(U_2141),U_2143),U_2143)),zero_zero(U_2141)))
    | ~ hBOOL(hAPP(U_2141,bool,hAPP(U_2141,fun(U_2141,bool),ord_less_eq(U_2141),U_2143),zero_zero(U_2141)))
    | ~ sP132(U_2143,U_2141,U_2142) ),
    inference(clausify,[status(thm)],[f_564_4]) ).

fof(f_565_1,plain,
    ! [X_a] :
      ( ! [B,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)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B))
          | ~ 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_494_add__nonneg__nonneg]) ).

fof(f_565_2,plain,
    ! [U_2146] :
      ( ! [U_2145,U_2144] :
          ( hBOOL(hAPP(U_2146,bool,hAPP(U_2146,fun(U_2146,bool),ord_less_eq(U_2146),zero_zero(U_2146)),hAPP(U_2146,U_2146,hAPP(U_2146,fun(U_2146,U_2146),plus_plus(U_2146),U_2144),U_2145)))
          | ~ hBOOL(hAPP(U_2146,bool,hAPP(U_2146,fun(U_2146,bool),ord_less_eq(U_2146),zero_zero(U_2146)),U_2145))
          | ~ hBOOL(hAPP(U_2146,bool,hAPP(U_2146,fun(U_2146,bool),ord_less_eq(U_2146),zero_zero(U_2146)),U_2144)) )
      | ~ ordere216010020id_add(U_2146) ),
    inference(variable_rename,[status(thm)],[f_565_1]) ).

fof(f_565_3,plain,
    ! [U_2144,U_2146,U_2145] :
      ( hBOOL(hAPP(U_2146,bool,hAPP(U_2146,fun(U_2146,bool),ord_less_eq(U_2146),zero_zero(U_2146)),hAPP(U_2146,U_2146,hAPP(U_2146,fun(U_2146,U_2146),plus_plus(U_2146),U_2144),U_2145)))
      | ~ hBOOL(hAPP(U_2146,bool,hAPP(U_2146,fun(U_2146,bool),ord_less_eq(U_2146),zero_zero(U_2146)),U_2145))
      | ~ hBOOL(hAPP(U_2146,bool,hAPP(U_2146,fun(U_2146,bool),ord_less_eq(U_2146),zero_zero(U_2146)),U_2144))
      | ~ ordere216010020id_add(U_2146) ),
    inference(definitional_conversion,[status(esa)],[f_565_2]) ).

cnf(f_565_4,plain,
    ( hBOOL(hAPP(U_2146,bool,hAPP(U_2146,fun(U_2146,bool),ord_less_eq(U_2146),zero_zero(U_2146)),hAPP(U_2146,U_2146,hAPP(U_2146,fun(U_2146,U_2146),plus_plus(U_2146),U_2144),U_2145)))
    | ~ hBOOL(hAPP(U_2146,bool,hAPP(U_2146,fun(U_2146,bool),ord_less_eq(U_2146),zero_zero(U_2146)),U_2145))
    | ~ hBOOL(hAPP(U_2146,bool,hAPP(U_2146,fun(U_2146,bool),ord_less_eq(U_2146),zero_zero(U_2146)),U_2144))
    | ~ ordere216010020id_add(U_2146) ),
    inference(clausify,[status(thm)],[f_565_3]) ).

fof(f_566_1,plain,
    ! [X_b] :
      ( ! [Y_2,X_1] :
          ( ( ( hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),X_1),Y_2) = zero_zero(X_b)
              | ti(X_b,Y_2) != zero_zero(X_b)
              | ti(X_b,X_1) != zero_zero(X_b) )
            & ( ( ti(X_b,Y_2) = 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_2) != 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_2))
          | ~ 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_495_add__nonneg__eq__0__iff]) ).

fof(f_566_2,plain,
    ! [U_2149] :
      ( ! [U_2148,U_2147] :
          ( ( ( hAPP(U_2149,U_2149,hAPP(U_2149,fun(U_2149,U_2149),plus_plus(U_2149),U_2147),U_2148) = zero_zero(U_2149)
              | ti(U_2149,U_2148) != zero_zero(U_2149)
              | ti(U_2149,U_2147) != zero_zero(U_2149) )
            & ( ( ti(U_2149,U_2148) = zero_zero(U_2149)
                & ti(U_2149,U_2147) = zero_zero(U_2149) )
              | hAPP(U_2149,U_2149,hAPP(U_2149,fun(U_2149,U_2149),plus_plus(U_2149),U_2147),U_2148) != zero_zero(U_2149) ) )
          | ~ hBOOL(hAPP(U_2149,bool,hAPP(U_2149,fun(U_2149,bool),ord_less_eq(U_2149),zero_zero(U_2149)),U_2148))
          | ~ hBOOL(hAPP(U_2149,bool,hAPP(U_2149,fun(U_2149,bool),ord_less_eq(U_2149),zero_zero(U_2149)),U_2147)) )
      | ~ ordere216010020id_add(U_2149) ),
    inference(variable_rename,[status(thm)],[f_566_1]) ).

fof(f_566_3,plain,
    ( ! [U_2149,U_2148,U_2147] :
        ( ti(U_2149,U_2148) = zero_zero(U_2149)
        | ~ sP133(U_2149,U_2148,U_2147) )
    & ! [U_2149,U_2148,U_2147] :
        ( ti(U_2149,U_2147) = zero_zero(U_2149)
        | ~ sP133(U_2149,U_2148,U_2147) )
    & ! [U_2149,U_2148,U_2147] :
        ( hAPP(U_2149,U_2149,hAPP(U_2149,fun(U_2149,U_2149),plus_plus(U_2149),U_2147),U_2148) = zero_zero(U_2149)
        | ti(U_2149,U_2148) != zero_zero(U_2149)
        | ti(U_2149,U_2147) != zero_zero(U_2149)
        | ~ sP134(U_2149,U_2148,U_2147) )
    & ! [U_2149,U_2148,U_2147] :
        ( sP133(U_2149,U_2148,U_2147)
        | hAPP(U_2149,U_2149,hAPP(U_2149,fun(U_2149,U_2149),plus_plus(U_2149),U_2147),U_2148) != zero_zero(U_2149)
        | ~ sP134(U_2149,U_2148,U_2147) )
    & ! [U_2149,U_2148,U_2147] :
        ( sP134(U_2149,U_2148,U_2147)
        | ~ hBOOL(hAPP(U_2149,bool,hAPP(U_2149,fun(U_2149,bool),ord_less_eq(U_2149),zero_zero(U_2149)),U_2148))
        | ~ hBOOL(hAPP(U_2149,bool,hAPP(U_2149,fun(U_2149,bool),ord_less_eq(U_2149),zero_zero(U_2149)),U_2147))
        | ~ ordere216010020id_add(U_2149) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP133,sP134])],[f_566_2]) ).

cnf(f_566_4,plain,
    ( sP134(U_2149,U_2148,U_2147)
    | ~ hBOOL(hAPP(U_2149,bool,hAPP(U_2149,fun(U_2149,bool),ord_less_eq(U_2149),zero_zero(U_2149)),U_2148))
    | ~ hBOOL(hAPP(U_2149,bool,hAPP(U_2149,fun(U_2149,bool),ord_less_eq(U_2149),zero_zero(U_2149)),U_2147))
    | ~ ordere216010020id_add(U_2149) ),
    inference(clausify,[status(thm)],[f_566_3]) ).

cnf(f_566_5,plain,
    ( sP133(U_2149,U_2148,U_2147)
    | hAPP(U_2149,U_2149,hAPP(U_2149,fun(U_2149,U_2149),plus_plus(U_2149),U_2147),U_2148) != zero_zero(U_2149)
    | ~ sP134(U_2149,U_2148,U_2147) ),
    inference(clausify,[status(thm)],[f_566_3]) ).

cnf(f_566_6,plain,
    ( hAPP(U_2149,U_2149,hAPP(U_2149,fun(U_2149,U_2149),plus_plus(U_2149),U_2147),U_2148) = zero_zero(U_2149)
    | ti(U_2149,U_2148) != zero_zero(U_2149)
    | ti(U_2149,U_2147) != zero_zero(U_2149)
    | ~ sP134(U_2149,U_2148,U_2147) ),
    inference(clausify,[status(thm)],[f_566_3]) ).

cnf(f_566_7,plain,
    ( ti(U_2149,U_2147) = zero_zero(U_2149)
    | ~ sP133(U_2149,U_2148,U_2147) ),
    inference(clausify,[status(thm)],[f_566_3]) ).

cnf(f_566_8,plain,
    ( ti(U_2149,U_2148) = zero_zero(U_2149)
    | ~ sP133(U_2149,U_2148,U_2147) ),
    inference(clausify,[status(thm)],[f_566_3]) ).

fof(f_567_1,plain,
    ! [X_a] :
      ( ! [B,C,A_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),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),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_496_add__increasing]) ).

fof(f_567_2,plain,
    ! [U_2153] :
      ( ! [U_2152,U_2151,U_2150] :
          ( hBOOL(hAPP(U_2153,bool,hAPP(U_2153,fun(U_2153,bool),ord_less_eq(U_2153),U_2152),hAPP(U_2153,U_2153,hAPP(U_2153,fun(U_2153,U_2153),plus_plus(U_2153),U_2150),U_2151)))
          | ~ hBOOL(hAPP(U_2153,bool,hAPP(U_2153,fun(U_2153,bool),ord_less_eq(U_2153),U_2152),U_2151))
          | ~ hBOOL(hAPP(U_2153,bool,hAPP(U_2153,fun(U_2153,bool),ord_less_eq(U_2153),zero_zero(U_2153)),U_2150)) )
      | ~ ordere216010020id_add(U_2153) ),
    inference(variable_rename,[status(thm)],[f_567_1]) ).

fof(f_567_3,plain,
    ! [U_2150,U_2152,U_2153,U_2151] :
      ( hBOOL(hAPP(U_2153,bool,hAPP(U_2153,fun(U_2153,bool),ord_less_eq(U_2153),U_2152),hAPP(U_2153,U_2153,hAPP(U_2153,fun(U_2153,U_2153),plus_plus(U_2153),U_2150),U_2151)))
      | ~ hBOOL(hAPP(U_2153,bool,hAPP(U_2153,fun(U_2153,bool),ord_less_eq(U_2153),U_2152),U_2151))
      | ~ hBOOL(hAPP(U_2153,bool,hAPP(U_2153,fun(U_2153,bool),ord_less_eq(U_2153),zero_zero(U_2153)),U_2150))
      | ~ ordere216010020id_add(U_2153) ),
    inference(definitional_conversion,[status(esa)],[f_567_2]) ).

cnf(f_567_4,plain,
    ( hBOOL(hAPP(U_2153,bool,hAPP(U_2153,fun(U_2153,bool),ord_less_eq(U_2153),U_2152),hAPP(U_2153,U_2153,hAPP(U_2153,fun(U_2153,U_2153),plus_plus(U_2153),U_2150),U_2151)))
    | ~ hBOOL(hAPP(U_2153,bool,hAPP(U_2153,fun(U_2153,bool),ord_less_eq(U_2153),U_2152),U_2151))
    | ~ hBOOL(hAPP(U_2153,bool,hAPP(U_2153,fun(U_2153,bool),ord_less_eq(U_2153),zero_zero(U_2153)),U_2150))
    | ~ ordere216010020id_add(U_2153) ),
    inference(clausify,[status(thm)],[f_567_3]) ).

fof(f_568_1,plain,
    ! [X_a] :
      ( ! [B,A_1,C] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),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),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_497_add__increasing2]) ).

fof(f_568_2,plain,
    ! [U_2157] :
      ( ! [U_2156,U_2155,U_2154] :
          ( hBOOL(hAPP(U_2157,bool,hAPP(U_2157,fun(U_2157,bool),ord_less_eq(U_2157),U_2156),hAPP(U_2157,U_2157,hAPP(U_2157,fun(U_2157,U_2157),plus_plus(U_2157),U_2155),U_2154)))
          | ~ hBOOL(hAPP(U_2157,bool,hAPP(U_2157,fun(U_2157,bool),ord_less_eq(U_2157),U_2156),U_2155))
          | ~ hBOOL(hAPP(U_2157,bool,hAPP(U_2157,fun(U_2157,bool),ord_less_eq(U_2157),zero_zero(U_2157)),U_2154)) )
      | ~ ordere216010020id_add(U_2157) ),
    inference(variable_rename,[status(thm)],[f_568_1]) ).

fof(f_568_3,plain,
    ! [U_2157,U_2154,U_2155,U_2156] :
      ( hBOOL(hAPP(U_2157,bool,hAPP(U_2157,fun(U_2157,bool),ord_less_eq(U_2157),U_2156),hAPP(U_2157,U_2157,hAPP(U_2157,fun(U_2157,U_2157),plus_plus(U_2157),U_2155),U_2154)))
      | ~ hBOOL(hAPP(U_2157,bool,hAPP(U_2157,fun(U_2157,bool),ord_less_eq(U_2157),U_2156),U_2155))
      | ~ hBOOL(hAPP(U_2157,bool,hAPP(U_2157,fun(U_2157,bool),ord_less_eq(U_2157),zero_zero(U_2157)),U_2154))
      | ~ ordere216010020id_add(U_2157) ),
    inference(definitional_conversion,[status(esa)],[f_568_2]) ).

cnf(f_568_4,plain,
    ( hBOOL(hAPP(U_2157,bool,hAPP(U_2157,fun(U_2157,bool),ord_less_eq(U_2157),U_2156),hAPP(U_2157,U_2157,hAPP(U_2157,fun(U_2157,U_2157),plus_plus(U_2157),U_2155),U_2154)))
    | ~ hBOOL(hAPP(U_2157,bool,hAPP(U_2157,fun(U_2157,bool),ord_less_eq(U_2157),U_2156),U_2155))
    | ~ hBOOL(hAPP(U_2157,bool,hAPP(U_2157,fun(U_2157,bool),ord_less_eq(U_2157),zero_zero(U_2157)),U_2154))
    | ~ ordere216010020id_add(U_2157) ),
    inference(clausify,[status(thm)],[f_568_3]) ).

fof(f_569_1,plain,
    ! [X_a] :
      ( ! [B,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)),zero_zero(X_a)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),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_498_add__nonpos__nonpos]) ).

fof(f_569_2,plain,
    ! [U_2160] :
      ( ! [U_2159,U_2158] :
          ( hBOOL(hAPP(U_2160,bool,hAPP(U_2160,fun(U_2160,bool),ord_less_eq(U_2160),hAPP(U_2160,U_2160,hAPP(U_2160,fun(U_2160,U_2160),plus_plus(U_2160),U_2158),U_2159)),zero_zero(U_2160)))
          | ~ hBOOL(hAPP(U_2160,bool,hAPP(U_2160,fun(U_2160,bool),ord_less_eq(U_2160),U_2159),zero_zero(U_2160)))
          | ~ hBOOL(hAPP(U_2160,bool,hAPP(U_2160,fun(U_2160,bool),ord_less_eq(U_2160),U_2158),zero_zero(U_2160))) )
      | ~ ordere216010020id_add(U_2160) ),
    inference(variable_rename,[status(thm)],[f_569_1]) ).

fof(f_569_3,plain,
    ! [U_2159,U_2160,U_2158] :
      ( hBOOL(hAPP(U_2160,bool,hAPP(U_2160,fun(U_2160,bool),ord_less_eq(U_2160),hAPP(U_2160,U_2160,hAPP(U_2160,fun(U_2160,U_2160),plus_plus(U_2160),U_2158),U_2159)),zero_zero(U_2160)))
      | ~ hBOOL(hAPP(U_2160,bool,hAPP(U_2160,fun(U_2160,bool),ord_less_eq(U_2160),U_2159),zero_zero(U_2160)))
      | ~ hBOOL(hAPP(U_2160,bool,hAPP(U_2160,fun(U_2160,bool),ord_less_eq(U_2160),U_2158),zero_zero(U_2160)))
      | ~ ordere216010020id_add(U_2160) ),
    inference(definitional_conversion,[status(esa)],[f_569_2]) ).

cnf(f_569_4,plain,
    ( hBOOL(hAPP(U_2160,bool,hAPP(U_2160,fun(U_2160,bool),ord_less_eq(U_2160),hAPP(U_2160,U_2160,hAPP(U_2160,fun(U_2160,U_2160),plus_plus(U_2160),U_2158),U_2159)),zero_zero(U_2160)))
    | ~ hBOOL(hAPP(U_2160,bool,hAPP(U_2160,fun(U_2160,bool),ord_less_eq(U_2160),U_2159),zero_zero(U_2160)))
    | ~ hBOOL(hAPP(U_2160,bool,hAPP(U_2160,fun(U_2160,bool),ord_less_eq(U_2160),U_2158),zero_zero(U_2160)))
    | ~ ordere216010020id_add(U_2160) ),
    inference(clausify,[status(thm)],[f_569_3]) ).

fof(f_570_1,plain,
    ! [X_b] :
      ( ! [A_2] :
          ( ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(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(X_b),zero_zero(X_b)),A_2)) )
          & ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),A_2))
            | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(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_499_zero__less__double__add__iff__zero__less__single__add]) ).

fof(f_570_2,plain,
    ! [U_2162] :
      ( ! [U_2161] :
          ( ( hBOOL(hAPP(U_2162,bool,hAPP(U_2162,fun(U_2162,bool),ord_less(U_2162),zero_zero(U_2162)),hAPP(U_2162,U_2162,hAPP(U_2162,fun(U_2162,U_2162),plus_plus(U_2162),U_2161),U_2161)))
            | ~ hBOOL(hAPP(U_2162,bool,hAPP(U_2162,fun(U_2162,bool),ord_less(U_2162),zero_zero(U_2162)),U_2161)) )
          & ( hBOOL(hAPP(U_2162,bool,hAPP(U_2162,fun(U_2162,bool),ord_less(U_2162),zero_zero(U_2162)),U_2161))
            | ~ hBOOL(hAPP(U_2162,bool,hAPP(U_2162,fun(U_2162,bool),ord_less(U_2162),zero_zero(U_2162)),hAPP(U_2162,U_2162,hAPP(U_2162,fun(U_2162,U_2162),plus_plus(U_2162),U_2161),U_2161))) ) )
      | ~ linord219039673up_add(U_2162) ),
    inference(variable_rename,[status(thm)],[f_570_1]) ).

fof(f_570_3,plain,
    ! [U_2162] :
      ( ( ! [U_2164] :
            ( hBOOL(hAPP(U_2162,bool,hAPP(U_2162,fun(U_2162,bool),ord_less(U_2162),zero_zero(U_2162)),hAPP(U_2162,U_2162,hAPP(U_2162,fun(U_2162,U_2162),plus_plus(U_2162),U_2164),U_2164)))
            | ~ hBOOL(hAPP(U_2162,bool,hAPP(U_2162,fun(U_2162,bool),ord_less(U_2162),zero_zero(U_2162)),U_2164)) )
        & ! [U_2163] :
            ( hBOOL(hAPP(U_2162,bool,hAPP(U_2162,fun(U_2162,bool),ord_less(U_2162),zero_zero(U_2162)),U_2163))
            | ~ hBOOL(hAPP(U_2162,bool,hAPP(U_2162,fun(U_2162,bool),ord_less(U_2162),zero_zero(U_2162)),hAPP(U_2162,U_2162,hAPP(U_2162,fun(U_2162,U_2162),plus_plus(U_2162),U_2163),U_2163))) ) )
      | ~ linord219039673up_add(U_2162) ),
    inference(miniscope,[status(thm)],[f_570_2]) ).

fof(f_570_4,plain,
    ( ! [U_2162,U_2164,U_2163] :
        ( hBOOL(hAPP(U_2162,bool,hAPP(U_2162,fun(U_2162,bool),ord_less(U_2162),zero_zero(U_2162)),hAPP(U_2162,U_2162,hAPP(U_2162,fun(U_2162,U_2162),plus_plus(U_2162),U_2164),U_2164)))
        | ~ hBOOL(hAPP(U_2162,bool,hAPP(U_2162,fun(U_2162,bool),ord_less(U_2162),zero_zero(U_2162)),U_2164))
        | ~ sP135(U_2162,U_2164,U_2163) )
    & ! [U_2162,U_2164,U_2163] :
        ( hBOOL(hAPP(U_2162,bool,hAPP(U_2162,fun(U_2162,bool),ord_less(U_2162),zero_zero(U_2162)),U_2163))
        | ~ hBOOL(hAPP(U_2162,bool,hAPP(U_2162,fun(U_2162,bool),ord_less(U_2162),zero_zero(U_2162)),hAPP(U_2162,U_2162,hAPP(U_2162,fun(U_2162,U_2162),plus_plus(U_2162),U_2163),U_2163)))
        | ~ sP135(U_2162,U_2164,U_2163) )
    & ! [U_2162,U_2164,U_2163] :
        ( sP135(U_2162,U_2164,U_2163)
        | ~ linord219039673up_add(U_2162) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP135])],[f_570_3]) ).

cnf(f_570_5,plain,
    ( sP135(U_2162,U_2164,U_2163)
    | ~ linord219039673up_add(U_2162) ),
    inference(clausify,[status(thm)],[f_570_4]) ).

cnf(f_570_6,plain,
    ( hBOOL(hAPP(U_2162,bool,hAPP(U_2162,fun(U_2162,bool),ord_less(U_2162),zero_zero(U_2162)),U_2163))
    | ~ hBOOL(hAPP(U_2162,bool,hAPP(U_2162,fun(U_2162,bool),ord_less(U_2162),zero_zero(U_2162)),hAPP(U_2162,U_2162,hAPP(U_2162,fun(U_2162,U_2162),plus_plus(U_2162),U_2163),U_2163)))
    | ~ sP135(U_2162,U_2164,U_2163) ),
    inference(clausify,[status(thm)],[f_570_4]) ).

cnf(f_570_7,plain,
    ( hBOOL(hAPP(U_2162,bool,hAPP(U_2162,fun(U_2162,bool),ord_less(U_2162),zero_zero(U_2162)),hAPP(U_2162,U_2162,hAPP(U_2162,fun(U_2162,U_2162),plus_plus(U_2162),U_2164),U_2164)))
    | ~ hBOOL(hAPP(U_2162,bool,hAPP(U_2162,fun(U_2162,bool),ord_less(U_2162),zero_zero(U_2162)),U_2164))
    | ~ sP135(U_2162,U_2164,U_2163) ),
    inference(clausify,[status(thm)],[f_570_4]) ).

fof(f_571_1,plain,
    ! [X_b] :
      ( ! [A_2] :
          ( ( 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),A_2)),zero_zero(X_b)))
            | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),zero_zero(X_b))) )
          & ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),zero_zero(X_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),A_2)),zero_zero(X_b))) ) )
      | ~ linord219039673up_add(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_500_double__add__less__zero__iff__single__add__less__zero]) ).

fof(f_571_2,plain,
    ! [U_2166] :
      ( ! [U_2165] :
          ( ( hBOOL(hAPP(U_2166,bool,hAPP(U_2166,fun(U_2166,bool),ord_less(U_2166),hAPP(U_2166,U_2166,hAPP(U_2166,fun(U_2166,U_2166),plus_plus(U_2166),U_2165),U_2165)),zero_zero(U_2166)))
            | ~ hBOOL(hAPP(U_2166,bool,hAPP(U_2166,fun(U_2166,bool),ord_less(U_2166),U_2165),zero_zero(U_2166))) )
          & ( hBOOL(hAPP(U_2166,bool,hAPP(U_2166,fun(U_2166,bool),ord_less(U_2166),U_2165),zero_zero(U_2166)))
            | ~ hBOOL(hAPP(U_2166,bool,hAPP(U_2166,fun(U_2166,bool),ord_less(U_2166),hAPP(U_2166,U_2166,hAPP(U_2166,fun(U_2166,U_2166),plus_plus(U_2166),U_2165),U_2165)),zero_zero(U_2166))) ) )
      | ~ linord219039673up_add(U_2166) ),
    inference(variable_rename,[status(thm)],[f_571_1]) ).

fof(f_571_3,plain,
    ! [U_2166] :
      ( ( ! [U_2168] :
            ( hBOOL(hAPP(U_2166,bool,hAPP(U_2166,fun(U_2166,bool),ord_less(U_2166),hAPP(U_2166,U_2166,hAPP(U_2166,fun(U_2166,U_2166),plus_plus(U_2166),U_2168),U_2168)),zero_zero(U_2166)))
            | ~ hBOOL(hAPP(U_2166,bool,hAPP(U_2166,fun(U_2166,bool),ord_less(U_2166),U_2168),zero_zero(U_2166))) )
        & ! [U_2167] :
            ( hBOOL(hAPP(U_2166,bool,hAPP(U_2166,fun(U_2166,bool),ord_less(U_2166),U_2167),zero_zero(U_2166)))
            | ~ hBOOL(hAPP(U_2166,bool,hAPP(U_2166,fun(U_2166,bool),ord_less(U_2166),hAPP(U_2166,U_2166,hAPP(U_2166,fun(U_2166,U_2166),plus_plus(U_2166),U_2167),U_2167)),zero_zero(U_2166))) ) )
      | ~ linord219039673up_add(U_2166) ),
    inference(miniscope,[status(thm)],[f_571_2]) ).

fof(f_571_4,plain,
    ( ! [U_2166,U_2168,U_2167] :
        ( hBOOL(hAPP(U_2166,bool,hAPP(U_2166,fun(U_2166,bool),ord_less(U_2166),hAPP(U_2166,U_2166,hAPP(U_2166,fun(U_2166,U_2166),plus_plus(U_2166),U_2168),U_2168)),zero_zero(U_2166)))
        | ~ hBOOL(hAPP(U_2166,bool,hAPP(U_2166,fun(U_2166,bool),ord_less(U_2166),U_2168),zero_zero(U_2166)))
        | ~ sP136(U_2166,U_2168,U_2167) )
    & ! [U_2166,U_2168,U_2167] :
        ( hBOOL(hAPP(U_2166,bool,hAPP(U_2166,fun(U_2166,bool),ord_less(U_2166),U_2167),zero_zero(U_2166)))
        | ~ hBOOL(hAPP(U_2166,bool,hAPP(U_2166,fun(U_2166,bool),ord_less(U_2166),hAPP(U_2166,U_2166,hAPP(U_2166,fun(U_2166,U_2166),plus_plus(U_2166),U_2167),U_2167)),zero_zero(U_2166)))
        | ~ sP136(U_2166,U_2168,U_2167) )
    & ! [U_2166,U_2168,U_2167] :
        ( sP136(U_2166,U_2168,U_2167)
        | ~ linord219039673up_add(U_2166) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP136])],[f_571_3]) ).

cnf(f_571_5,plain,
    ( sP136(U_2166,U_2168,U_2167)
    | ~ linord219039673up_add(U_2166) ),
    inference(clausify,[status(thm)],[f_571_4]) ).

cnf(f_571_6,plain,
    ( hBOOL(hAPP(U_2166,bool,hAPP(U_2166,fun(U_2166,bool),ord_less(U_2166),U_2167),zero_zero(U_2166)))
    | ~ hBOOL(hAPP(U_2166,bool,hAPP(U_2166,fun(U_2166,bool),ord_less(U_2166),hAPP(U_2166,U_2166,hAPP(U_2166,fun(U_2166,U_2166),plus_plus(U_2166),U_2167),U_2167)),zero_zero(U_2166)))
    | ~ sP136(U_2166,U_2168,U_2167) ),
    inference(clausify,[status(thm)],[f_571_4]) ).

cnf(f_571_7,plain,
    ( hBOOL(hAPP(U_2166,bool,hAPP(U_2166,fun(U_2166,bool),ord_less(U_2166),hAPP(U_2166,U_2166,hAPP(U_2166,fun(U_2166,U_2166),plus_plus(U_2166),U_2168),U_2168)),zero_zero(U_2166)))
    | ~ hBOOL(hAPP(U_2166,bool,hAPP(U_2166,fun(U_2166,bool),ord_less(U_2166),U_2168),zero_zero(U_2166)))
    | ~ sP136(U_2166,U_2168,U_2167) ),
    inference(clausify,[status(thm)],[f_571_4]) ).

fof(f_572_1,plain,
    ! [X_a] :
      ( ! [B,A_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(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)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) )
      | ~ ordere216010020id_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_501_add__pos__pos]) ).

fof(f_572_2,plain,
    ! [U_2171] :
      ( ! [U_2170,U_2169] :
          ( hBOOL(hAPP(U_2171,bool,hAPP(U_2171,fun(U_2171,bool),ord_less(U_2171),zero_zero(U_2171)),hAPP(U_2171,U_2171,hAPP(U_2171,fun(U_2171,U_2171),plus_plus(U_2171),U_2169),U_2170)))
          | ~ hBOOL(hAPP(U_2171,bool,hAPP(U_2171,fun(U_2171,bool),ord_less(U_2171),zero_zero(U_2171)),U_2170))
          | ~ hBOOL(hAPP(U_2171,bool,hAPP(U_2171,fun(U_2171,bool),ord_less(U_2171),zero_zero(U_2171)),U_2169)) )
      | ~ ordere216010020id_add(U_2171) ),
    inference(variable_rename,[status(thm)],[f_572_1]) ).

fof(f_572_3,plain,
    ! [U_2171,U_2170,U_2169] :
      ( hBOOL(hAPP(U_2171,bool,hAPP(U_2171,fun(U_2171,bool),ord_less(U_2171),zero_zero(U_2171)),hAPP(U_2171,U_2171,hAPP(U_2171,fun(U_2171,U_2171),plus_plus(U_2171),U_2169),U_2170)))
      | ~ hBOOL(hAPP(U_2171,bool,hAPP(U_2171,fun(U_2171,bool),ord_less(U_2171),zero_zero(U_2171)),U_2170))
      | ~ hBOOL(hAPP(U_2171,bool,hAPP(U_2171,fun(U_2171,bool),ord_less(U_2171),zero_zero(U_2171)),U_2169))
      | ~ ordere216010020id_add(U_2171) ),
    inference(definitional_conversion,[status(esa)],[f_572_2]) ).

cnf(f_572_4,plain,
    ( hBOOL(hAPP(U_2171,bool,hAPP(U_2171,fun(U_2171,bool),ord_less(U_2171),zero_zero(U_2171)),hAPP(U_2171,U_2171,hAPP(U_2171,fun(U_2171,U_2171),plus_plus(U_2171),U_2169),U_2170)))
    | ~ hBOOL(hAPP(U_2171,bool,hAPP(U_2171,fun(U_2171,bool),ord_less(U_2171),zero_zero(U_2171)),U_2170))
    | ~ hBOOL(hAPP(U_2171,bool,hAPP(U_2171,fun(U_2171,bool),ord_less(U_2171),zero_zero(U_2171)),U_2169))
    | ~ ordere216010020id_add(U_2171) ),
    inference(clausify,[status(thm)],[f_572_3]) ).

fof(f_573_1,plain,
    ! [X_a] :
      ( ! [B,A_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),B)),zero_zero(X_a)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a))) )
      | ~ ordere216010020id_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_502_add__neg__neg]) ).

fof(f_573_2,plain,
    ! [U_2174] :
      ( ! [U_2173,U_2172] :
          ( hBOOL(hAPP(U_2174,bool,hAPP(U_2174,fun(U_2174,bool),ord_less(U_2174),hAPP(U_2174,U_2174,hAPP(U_2174,fun(U_2174,U_2174),plus_plus(U_2174),U_2172),U_2173)),zero_zero(U_2174)))
          | ~ hBOOL(hAPP(U_2174,bool,hAPP(U_2174,fun(U_2174,bool),ord_less(U_2174),U_2173),zero_zero(U_2174)))
          | ~ hBOOL(hAPP(U_2174,bool,hAPP(U_2174,fun(U_2174,bool),ord_less(U_2174),U_2172),zero_zero(U_2174))) )
      | ~ ordere216010020id_add(U_2174) ),
    inference(variable_rename,[status(thm)],[f_573_1]) ).

fof(f_573_3,plain,
    ! [U_2174,U_2172,U_2173] :
      ( hBOOL(hAPP(U_2174,bool,hAPP(U_2174,fun(U_2174,bool),ord_less(U_2174),hAPP(U_2174,U_2174,hAPP(U_2174,fun(U_2174,U_2174),plus_plus(U_2174),U_2172),U_2173)),zero_zero(U_2174)))
      | ~ hBOOL(hAPP(U_2174,bool,hAPP(U_2174,fun(U_2174,bool),ord_less(U_2174),U_2173),zero_zero(U_2174)))
      | ~ hBOOL(hAPP(U_2174,bool,hAPP(U_2174,fun(U_2174,bool),ord_less(U_2174),U_2172),zero_zero(U_2174)))
      | ~ ordere216010020id_add(U_2174) ),
    inference(definitional_conversion,[status(esa)],[f_573_2]) ).

cnf(f_573_4,plain,
    ( hBOOL(hAPP(U_2174,bool,hAPP(U_2174,fun(U_2174,bool),ord_less(U_2174),hAPP(U_2174,U_2174,hAPP(U_2174,fun(U_2174,U_2174),plus_plus(U_2174),U_2172),U_2173)),zero_zero(U_2174)))
    | ~ hBOOL(hAPP(U_2174,bool,hAPP(U_2174,fun(U_2174,bool),ord_less(U_2174),U_2173),zero_zero(U_2174)))
    | ~ hBOOL(hAPP(U_2174,bool,hAPP(U_2174,fun(U_2174,bool),ord_less(U_2174),U_2172),zero_zero(U_2174)))
    | ~ ordere216010020id_add(U_2174) ),
    inference(clausify,[status(thm)],[f_573_3]) ).

fof(f_574_1,plain,
    ! [X_a] :
      ( ! [B,C,A_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),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),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_503_pos__add__strict]) ).

fof(f_574_2,plain,
    ! [U_2178] :
      ( ! [U_2177,U_2176,U_2175] :
          ( hBOOL(hAPP(U_2178,bool,hAPP(U_2178,fun(U_2178,bool),ord_less(U_2178),U_2177),hAPP(U_2178,U_2178,hAPP(U_2178,fun(U_2178,U_2178),plus_plus(U_2178),U_2175),U_2176)))
          | ~ hBOOL(hAPP(U_2178,bool,hAPP(U_2178,fun(U_2178,bool),ord_less(U_2178),U_2177),U_2176))
          | ~ hBOOL(hAPP(U_2178,bool,hAPP(U_2178,fun(U_2178,bool),ord_less(U_2178),zero_zero(U_2178)),U_2175)) )
      | ~ linordered_semidom(U_2178) ),
    inference(variable_rename,[status(thm)],[f_574_1]) ).

fof(f_574_3,plain,
    ! [U_2175,U_2176,U_2177,U_2178] :
      ( hBOOL(hAPP(U_2178,bool,hAPP(U_2178,fun(U_2178,bool),ord_less(U_2178),U_2177),hAPP(U_2178,U_2178,hAPP(U_2178,fun(U_2178,U_2178),plus_plus(U_2178),U_2175),U_2176)))
      | ~ hBOOL(hAPP(U_2178,bool,hAPP(U_2178,fun(U_2178,bool),ord_less(U_2178),U_2177),U_2176))
      | ~ hBOOL(hAPP(U_2178,bool,hAPP(U_2178,fun(U_2178,bool),ord_less(U_2178),zero_zero(U_2178)),U_2175))
      | ~ linordered_semidom(U_2178) ),
    inference(definitional_conversion,[status(esa)],[f_574_2]) ).

cnf(f_574_4,plain,
    ( hBOOL(hAPP(U_2178,bool,hAPP(U_2178,fun(U_2178,bool),ord_less(U_2178),U_2177),hAPP(U_2178,U_2178,hAPP(U_2178,fun(U_2178,U_2178),plus_plus(U_2178),U_2175),U_2176)))
    | ~ hBOOL(hAPP(U_2178,bool,hAPP(U_2178,fun(U_2178,bool),ord_less(U_2178),U_2177),U_2176))
    | ~ hBOOL(hAPP(U_2178,bool,hAPP(U_2178,fun(U_2178,bool),ord_less(U_2178),zero_zero(U_2178)),U_2175))
    | ~ linordered_semidom(U_2178) ),
    inference(clausify,[status(thm)],[f_574_3]) ).

fof(f_575_1,plain,
    ! [X_b] :
      ( ! [A_2,B_3] :
          ( ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),B_3))
            | ~ 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_3)),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_3)),zero_zero(X_b)))
            | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),B_3)) ) )
      | ~ ordered_ab_group_add(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_504_le__iff__diff__le__0]) ).

fof(f_575_2,plain,
    ! [U_2181] :
      ( ! [U_2180,U_2179] :
          ( ( hBOOL(hAPP(U_2181,bool,hAPP(U_2181,fun(U_2181,bool),ord_less_eq(U_2181),U_2180),U_2179))
            | ~ hBOOL(hAPP(U_2181,bool,hAPP(U_2181,fun(U_2181,bool),ord_less_eq(U_2181),hAPP(U_2181,U_2181,hAPP(U_2181,fun(U_2181,U_2181),minus_minus(U_2181),U_2180),U_2179)),zero_zero(U_2181))) )
          & ( hBOOL(hAPP(U_2181,bool,hAPP(U_2181,fun(U_2181,bool),ord_less_eq(U_2181),hAPP(U_2181,U_2181,hAPP(U_2181,fun(U_2181,U_2181),minus_minus(U_2181),U_2180),U_2179)),zero_zero(U_2181)))
            | ~ hBOOL(hAPP(U_2181,bool,hAPP(U_2181,fun(U_2181,bool),ord_less_eq(U_2181),U_2180),U_2179)) ) )
      | ~ ordered_ab_group_add(U_2181) ),
    inference(variable_rename,[status(thm)],[f_575_1]) ).

fof(f_575_3,plain,
    ! [U_2181] :
      ( ( ! [U_2185,U_2183] :
            ( hBOOL(hAPP(U_2181,bool,hAPP(U_2181,fun(U_2181,bool),ord_less_eq(U_2181),U_2185),U_2183))
            | ~ hBOOL(hAPP(U_2181,bool,hAPP(U_2181,fun(U_2181,bool),ord_less_eq(U_2181),hAPP(U_2181,U_2181,hAPP(U_2181,fun(U_2181,U_2181),minus_minus(U_2181),U_2185),U_2183)),zero_zero(U_2181))) )
        & ! [U_2184,U_2182] :
            ( hBOOL(hAPP(U_2181,bool,hAPP(U_2181,fun(U_2181,bool),ord_less_eq(U_2181),hAPP(U_2181,U_2181,hAPP(U_2181,fun(U_2181,U_2181),minus_minus(U_2181),U_2184),U_2182)),zero_zero(U_2181)))
            | ~ hBOOL(hAPP(U_2181,bool,hAPP(U_2181,fun(U_2181,bool),ord_less_eq(U_2181),U_2184),U_2182)) ) )
      | ~ ordered_ab_group_add(U_2181) ),
    inference(miniscope,[status(thm)],[f_575_2]) ).

fof(f_575_4,plain,
    ( ! [U_2181,U_2184,U_2182,U_2183,U_2185] :
        ( hBOOL(hAPP(U_2181,bool,hAPP(U_2181,fun(U_2181,bool),ord_less_eq(U_2181),U_2185),U_2183))
        | ~ hBOOL(hAPP(U_2181,bool,hAPP(U_2181,fun(U_2181,bool),ord_less_eq(U_2181),hAPP(U_2181,U_2181,hAPP(U_2181,fun(U_2181,U_2181),minus_minus(U_2181),U_2185),U_2183)),zero_zero(U_2181)))
        | ~ sP137(U_2181,U_2184,U_2182,U_2183,U_2185) )
    & ! [U_2181,U_2184,U_2182,U_2183,U_2185] :
        ( hBOOL(hAPP(U_2181,bool,hAPP(U_2181,fun(U_2181,bool),ord_less_eq(U_2181),hAPP(U_2181,U_2181,hAPP(U_2181,fun(U_2181,U_2181),minus_minus(U_2181),U_2184),U_2182)),zero_zero(U_2181)))
        | ~ hBOOL(hAPP(U_2181,bool,hAPP(U_2181,fun(U_2181,bool),ord_less_eq(U_2181),U_2184),U_2182))
        | ~ sP137(U_2181,U_2184,U_2182,U_2183,U_2185) )
    & ! [U_2181,U_2184,U_2182,U_2183,U_2185] :
        ( sP137(U_2181,U_2184,U_2182,U_2183,U_2185)
        | ~ ordered_ab_group_add(U_2181) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP137])],[f_575_3]) ).

cnf(f_575_5,plain,
    ( sP137(U_2181,U_2184,U_2182,U_2183,U_2185)
    | ~ ordered_ab_group_add(U_2181) ),
    inference(clausify,[status(thm)],[f_575_4]) ).

cnf(f_575_6,plain,
    ( hBOOL(hAPP(U_2181,bool,hAPP(U_2181,fun(U_2181,bool),ord_less_eq(U_2181),hAPP(U_2181,U_2181,hAPP(U_2181,fun(U_2181,U_2181),minus_minus(U_2181),U_2184),U_2182)),zero_zero(U_2181)))
    | ~ hBOOL(hAPP(U_2181,bool,hAPP(U_2181,fun(U_2181,bool),ord_less_eq(U_2181),U_2184),U_2182))
    | ~ sP137(U_2181,U_2184,U_2182,U_2183,U_2185) ),
    inference(clausify,[status(thm)],[f_575_4]) ).

cnf(f_575_7,plain,
    ( hBOOL(hAPP(U_2181,bool,hAPP(U_2181,fun(U_2181,bool),ord_less_eq(U_2181),U_2185),U_2183))
    | ~ hBOOL(hAPP(U_2181,bool,hAPP(U_2181,fun(U_2181,bool),ord_less_eq(U_2181),hAPP(U_2181,U_2181,hAPP(U_2181,fun(U_2181,U_2181),minus_minus(U_2181),U_2185),U_2183)),zero_zero(U_2181)))
    | ~ sP137(U_2181,U_2184,U_2182,U_2183,U_2185) ),
    inference(clausify,[status(thm)],[f_575_4]) ).

fof(f_576_1,plain,
    ! [X_b] :
      ( ! [A_2,B_3] :
          ( ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_3))
            | ~ 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),minus_minus(X_b),A_2),B_3)),zero_zero(X_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),minus_minus(X_b),A_2),B_3)),zero_zero(X_b)))
            | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_3)) ) )
      | ~ ordered_ab_group_add(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_505_less__iff__diff__less__0]) ).

fof(f_576_2,plain,
    ! [U_2188] :
      ( ! [U_2187,U_2186] :
          ( ( hBOOL(hAPP(U_2188,bool,hAPP(U_2188,fun(U_2188,bool),ord_less(U_2188),U_2187),U_2186))
            | ~ hBOOL(hAPP(U_2188,bool,hAPP(U_2188,fun(U_2188,bool),ord_less(U_2188),hAPP(U_2188,U_2188,hAPP(U_2188,fun(U_2188,U_2188),minus_minus(U_2188),U_2187),U_2186)),zero_zero(U_2188))) )
          & ( hBOOL(hAPP(U_2188,bool,hAPP(U_2188,fun(U_2188,bool),ord_less(U_2188),hAPP(U_2188,U_2188,hAPP(U_2188,fun(U_2188,U_2188),minus_minus(U_2188),U_2187),U_2186)),zero_zero(U_2188)))
            | ~ hBOOL(hAPP(U_2188,bool,hAPP(U_2188,fun(U_2188,bool),ord_less(U_2188),U_2187),U_2186)) ) )
      | ~ ordered_ab_group_add(U_2188) ),
    inference(variable_rename,[status(thm)],[f_576_1]) ).

fof(f_576_3,plain,
    ! [U_2188] :
      ( ( ! [U_2192,U_2190] :
            ( hBOOL(hAPP(U_2188,bool,hAPP(U_2188,fun(U_2188,bool),ord_less(U_2188),U_2192),U_2190))
            | ~ hBOOL(hAPP(U_2188,bool,hAPP(U_2188,fun(U_2188,bool),ord_less(U_2188),hAPP(U_2188,U_2188,hAPP(U_2188,fun(U_2188,U_2188),minus_minus(U_2188),U_2192),U_2190)),zero_zero(U_2188))) )
        & ! [U_2191,U_2189] :
            ( hBOOL(hAPP(U_2188,bool,hAPP(U_2188,fun(U_2188,bool),ord_less(U_2188),hAPP(U_2188,U_2188,hAPP(U_2188,fun(U_2188,U_2188),minus_minus(U_2188),U_2191),U_2189)),zero_zero(U_2188)))
            | ~ hBOOL(hAPP(U_2188,bool,hAPP(U_2188,fun(U_2188,bool),ord_less(U_2188),U_2191),U_2189)) ) )
      | ~ ordered_ab_group_add(U_2188) ),
    inference(miniscope,[status(thm)],[f_576_2]) ).

fof(f_576_4,plain,
    ( ! [U_2188,U_2191,U_2189,U_2190,U_2192] :
        ( hBOOL(hAPP(U_2188,bool,hAPP(U_2188,fun(U_2188,bool),ord_less(U_2188),U_2192),U_2190))
        | ~ hBOOL(hAPP(U_2188,bool,hAPP(U_2188,fun(U_2188,bool),ord_less(U_2188),hAPP(U_2188,U_2188,hAPP(U_2188,fun(U_2188,U_2188),minus_minus(U_2188),U_2192),U_2190)),zero_zero(U_2188)))
        | ~ sP138(U_2188,U_2191,U_2189,U_2190,U_2192) )
    & ! [U_2188,U_2191,U_2189,U_2190,U_2192] :
        ( hBOOL(hAPP(U_2188,bool,hAPP(U_2188,fun(U_2188,bool),ord_less(U_2188),hAPP(U_2188,U_2188,hAPP(U_2188,fun(U_2188,U_2188),minus_minus(U_2188),U_2191),U_2189)),zero_zero(U_2188)))
        | ~ hBOOL(hAPP(U_2188,bool,hAPP(U_2188,fun(U_2188,bool),ord_less(U_2188),U_2191),U_2189))
        | ~ sP138(U_2188,U_2191,U_2189,U_2190,U_2192) )
    & ! [U_2188,U_2191,U_2189,U_2190,U_2192] :
        ( sP138(U_2188,U_2191,U_2189,U_2190,U_2192)
        | ~ ordered_ab_group_add(U_2188) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP138])],[f_576_3]) ).

cnf(f_576_5,plain,
    ( sP138(U_2188,U_2191,U_2189,U_2190,U_2192)
    | ~ ordered_ab_group_add(U_2188) ),
    inference(clausify,[status(thm)],[f_576_4]) ).

cnf(f_576_6,plain,
    ( hBOOL(hAPP(U_2188,bool,hAPP(U_2188,fun(U_2188,bool),ord_less(U_2188),hAPP(U_2188,U_2188,hAPP(U_2188,fun(U_2188,U_2188),minus_minus(U_2188),U_2191),U_2189)),zero_zero(U_2188)))
    | ~ hBOOL(hAPP(U_2188,bool,hAPP(U_2188,fun(U_2188,bool),ord_less(U_2188),U_2191),U_2189))
    | ~ sP138(U_2188,U_2191,U_2189,U_2190,U_2192) ),
    inference(clausify,[status(thm)],[f_576_4]) ).

cnf(f_576_7,plain,
    ( hBOOL(hAPP(U_2188,bool,hAPP(U_2188,fun(U_2188,bool),ord_less(U_2188),U_2192),U_2190))
    | ~ hBOOL(hAPP(U_2188,bool,hAPP(U_2188,fun(U_2188,bool),ord_less(U_2188),hAPP(U_2188,U_2188,hAPP(U_2188,fun(U_2188,U_2188),minus_minus(U_2188),U_2192),U_2190)),zero_zero(U_2188)))
    | ~ sP138(U_2188,U_2191,U_2189,U_2190,U_2192) ),
    inference(clausify,[status(thm)],[f_576_4]) ).

fof(f_577_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_506_not__one__le__zero]) ).

fof(f_577_2,plain,
    ! [U_2193] :
      ( ~ hBOOL(hAPP(U_2193,bool,hAPP(U_2193,fun(U_2193,bool),ord_less_eq(U_2193),one_one(U_2193)),zero_zero(U_2193)))
      | ~ linordered_semidom(U_2193) ),
    inference(variable_rename,[status(thm)],[f_577_1]) ).

fof(f_577_3,plain,
    ! [U_2193] :
      ( ~ hBOOL(hAPP(U_2193,bool,hAPP(U_2193,fun(U_2193,bool),ord_less_eq(U_2193),one_one(U_2193)),zero_zero(U_2193)))
      | ~ linordered_semidom(U_2193) ),
    inference(definitional_conversion,[status(esa)],[f_577_2]) ).

cnf(f_577_4,plain,
    ( ~ hBOOL(hAPP(U_2193,bool,hAPP(U_2193,fun(U_2193,bool),ord_less_eq(U_2193),one_one(U_2193)),zero_zero(U_2193)))
    | ~ linordered_semidom(U_2193) ),
    inference(clausify,[status(thm)],[f_577_3]) ).

fof(f_578_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_507_zero__le__one]) ).

fof(f_578_2,plain,
    ! [U_2194] :
      ( hBOOL(hAPP(U_2194,bool,hAPP(U_2194,fun(U_2194,bool),ord_less_eq(U_2194),zero_zero(U_2194)),one_one(U_2194)))
      | ~ linordered_semidom(U_2194) ),
    inference(variable_rename,[status(thm)],[f_578_1]) ).

fof(f_578_3,plain,
    ! [U_2194] :
      ( hBOOL(hAPP(U_2194,bool,hAPP(U_2194,fun(U_2194,bool),ord_less_eq(U_2194),zero_zero(U_2194)),one_one(U_2194)))
      | ~ linordered_semidom(U_2194) ),
    inference(definitional_conversion,[status(esa)],[f_578_2]) ).

cnf(f_578_4,plain,
    ( hBOOL(hAPP(U_2194,bool,hAPP(U_2194,fun(U_2194,bool),ord_less_eq(U_2194),zero_zero(U_2194)),one_one(U_2194)))
    | ~ linordered_semidom(U_2194) ),
    inference(clausify,[status(thm)],[f_578_3]) ).

fof(f_579_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_508_zero__less__one]) ).

fof(f_579_2,plain,
    ! [U_2195] :
      ( hBOOL(hAPP(U_2195,bool,hAPP(U_2195,fun(U_2195,bool),ord_less(U_2195),zero_zero(U_2195)),one_one(U_2195)))
      | ~ linordered_semidom(U_2195) ),
    inference(variable_rename,[status(thm)],[f_579_1]) ).

fof(f_579_3,plain,
    ! [U_2195] :
      ( hBOOL(hAPP(U_2195,bool,hAPP(U_2195,fun(U_2195,bool),ord_less(U_2195),zero_zero(U_2195)),one_one(U_2195)))
      | ~ linordered_semidom(U_2195) ),
    inference(definitional_conversion,[status(esa)],[f_579_2]) ).

cnf(f_579_4,plain,
    ( hBOOL(hAPP(U_2195,bool,hAPP(U_2195,fun(U_2195,bool),ord_less(U_2195),zero_zero(U_2195)),one_one(U_2195)))
    | ~ linordered_semidom(U_2195) ),
    inference(clausify,[status(thm)],[f_579_3]) ).

fof(f_580_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_509_not__one__less__zero]) ).

fof(f_580_2,plain,
    ! [U_2196] :
      ( ~ hBOOL(hAPP(U_2196,bool,hAPP(U_2196,fun(U_2196,bool),ord_less(U_2196),one_one(U_2196)),zero_zero(U_2196)))
      | ~ linordered_semidom(U_2196) ),
    inference(variable_rename,[status(thm)],[f_580_1]) ).

fof(f_580_3,plain,
    ! [U_2196] :
      ( ~ hBOOL(hAPP(U_2196,bool,hAPP(U_2196,fun(U_2196,bool),ord_less(U_2196),one_one(U_2196)),zero_zero(U_2196)))
      | ~ linordered_semidom(U_2196) ),
    inference(definitional_conversion,[status(esa)],[f_580_2]) ).

cnf(f_580_4,plain,
    ( ~ hBOOL(hAPP(U_2196,bool,hAPP(U_2196,fun(U_2196,bool),ord_less(U_2196),one_one(U_2196)),zero_zero(U_2196)))
    | ~ linordered_semidom(U_2196) ),
    inference(clausify,[status(thm)],[f_580_3]) ).

fof(f_581_1,plain,
    ! [Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na))
        | ! [M_2] : Na != hAPP(nat,nat,suc,M_2) )
      & ( ? [M_2] : Na = hAPP(nat,nat,suc,M_2)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_510_gr0__conv__Suc]) ).

fof(f_581_2,plain,
    ! [U_2199] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2199))
        | ! [U_2198] : U_2199 != hAPP(nat,nat,suc,U_2198) )
      & ( ? [U_2197] : U_2199 = hAPP(nat,nat,suc,U_2197)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2199)) ) ),
    inference(variable_rename,[status(thm)],[f_581_1]) ).

fof(f_581_3,plain,
    ( ! [U_2201] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2201))
        | ! [U_2198] : U_2201 != hAPP(nat,nat,suc,U_2198) )
    & ! [U_2200] :
        ( ? [U_2197] : U_2200 = hAPP(nat,nat,suc,U_2197)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2200)) ) ),
    inference(miniscope,[status(thm)],[f_581_2]) ).

fof(f_581_4,plain,
    ( ! [U_2201] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2201))
        | ! [U_2198] : U_2201 != hAPP(nat,nat,suc,U_2198) )
    & ! [U_2200] :
        ( U_2200 = hAPP(nat,nat,suc,sK82(U_2200))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2200)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK82]),skolemize(U_2197,sK82(U_2200))],[f_581_3]) ).

fof(f_581_5,plain,
    ( ! [U_2198,U_2201] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2201))
        | U_2201 != hAPP(nat,nat,suc,U_2198) )
    & ! [U_2200] :
        ( U_2200 = hAPP(nat,nat,suc,sK82(U_2200))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2200)) ) ),
    inference(definitional_conversion,[status(esa)],[f_581_4]) ).

cnf(f_581_6,plain,
    ( U_2200 = hAPP(nat,nat,suc,sK82(U_2200))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2200)) ),
    inference(clausify,[status(thm)],[f_581_5]) ).

cnf(f_581_7,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2201))
    | U_2201 != hAPP(nat,nat,suc,U_2198) ),
    inference(clausify,[status(thm)],[f_581_5]) ).

fof(f_582_1,plain,
    ! [Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,zero_zero(nat))))
        | Na != zero_zero(nat) )
      & ( Na = zero_zero(nat)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,zero_zero(nat)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_511_less__Suc0]) ).

fof(f_582_2,plain,
    ! [U_2202] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2202),hAPP(nat,nat,suc,zero_zero(nat))))
        | U_2202 != zero_zero(nat) )
      & ( U_2202 = zero_zero(nat)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2202),hAPP(nat,nat,suc,zero_zero(nat)))) ) ),
    inference(variable_rename,[status(thm)],[f_582_1]) ).

fof(f_582_3,plain,
    ( ! [U_2204] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2204),hAPP(nat,nat,suc,zero_zero(nat))))
        | U_2204 != zero_zero(nat) )
    & ! [U_2203] :
        ( U_2203 = zero_zero(nat)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2203),hAPP(nat,nat,suc,zero_zero(nat)))) ) ),
    inference(miniscope,[status(thm)],[f_582_2]) ).

fof(f_582_4,plain,
    ( ! [U_2204] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2204),hAPP(nat,nat,suc,zero_zero(nat))))
        | U_2204 != zero_zero(nat) )
    & ! [U_2203] :
        ( U_2203 = zero_zero(nat)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2203),hAPP(nat,nat,suc,zero_zero(nat)))) ) ),
    inference(definitional_conversion,[status(esa)],[f_582_3]) ).

cnf(f_582_5,plain,
    ( U_2203 = zero_zero(nat)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2203),hAPP(nat,nat,suc,zero_zero(nat)))) ),
    inference(clausify,[status(thm)],[f_582_4]) ).

cnf(f_582_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2204),hAPP(nat,nat,suc,zero_zero(nat))))
    | U_2204 != zero_zero(nat) ),
    inference(clausify,[status(thm)],[f_582_4]) ).

fof(f_583_1,plain,
    ! [M,Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,Na)))
        | ( ! [J_2] :
              ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_2),Na))
              | M != hAPP(nat,nat,suc,J_2) )
          & M != zero_zero(nat) ) )
      & ( ? [J_2] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_2),Na))
            & M = hAPP(nat,nat,suc,J_2) )
        | M = zero_zero(nat)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_512_less__Suc__eq__0__disj]) ).

fof(f_583_2,plain,
    ! [U_2208,U_2207] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2208),hAPP(nat,nat,suc,U_2207)))
        | ( ! [U_2206] :
              ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2206),U_2207))
              | U_2208 != hAPP(nat,nat,suc,U_2206) )
          & U_2208 != zero_zero(nat) ) )
      & ( ? [U_2205] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2205),U_2207))
            & U_2208 = hAPP(nat,nat,suc,U_2205) )
        | U_2208 = zero_zero(nat)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2208),hAPP(nat,nat,suc,U_2207))) ) ),
    inference(variable_rename,[status(thm)],[f_583_1]) ).

fof(f_583_3,plain,
    ( ! [U_2212,U_2210] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2212),hAPP(nat,nat,suc,U_2210)))
        | ( ! [U_2206] :
              ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2206),U_2210))
              | U_2212 != hAPP(nat,nat,suc,U_2206) )
          & U_2212 != zero_zero(nat) ) )
    & ! [U_2211,U_2209] :
        ( ? [U_2205] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2205),U_2209))
            & U_2211 = hAPP(nat,nat,suc,U_2205) )
        | U_2211 = zero_zero(nat)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2211),hAPP(nat,nat,suc,U_2209))) ) ),
    inference(miniscope,[status(thm)],[f_583_2]) ).

fof(f_583_4,plain,
    ( ! [U_2212,U_2210] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2212),hAPP(nat,nat,suc,U_2210)))
        | ( ! [U_2206] :
              ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2206),U_2210))
              | U_2212 != hAPP(nat,nat,suc,U_2206) )
          & U_2212 != zero_zero(nat) ) )
    & ! [U_2211,U_2209] :
        ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK83(U_2211,U_2209)),U_2209))
          & U_2211 = hAPP(nat,nat,suc,sK83(U_2211,U_2209)) )
        | U_2211 = zero_zero(nat)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2211),hAPP(nat,nat,suc,U_2209))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK83]),skolemize(U_2205,sK83(U_2211,U_2209))],[f_583_3]) ).

fof(f_583_5,plain,
    ( ! [U_2212,U_2206,U_2210] :
        ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2206),U_2210))
        | U_2212 != hAPP(nat,nat,suc,U_2206)
        | ~ sP140(U_2212,U_2206,U_2210) )
    & ! [U_2212,U_2206,U_2210] :
        ( U_2212 != zero_zero(nat)
        | ~ sP140(U_2212,U_2206,U_2210) )
    & ! [U_2209,U_2211] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK83(U_2211,U_2209)),U_2209))
        | ~ sP139(U_2209,U_2211) )
    & ! [U_2209,U_2211] :
        ( U_2211 = hAPP(nat,nat,suc,sK83(U_2211,U_2209))
        | ~ sP139(U_2209,U_2211) )
    & ! [U_2212,U_2206,U_2210] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2212),hAPP(nat,nat,suc,U_2210)))
        | sP140(U_2212,U_2206,U_2210) )
    & ! [U_2209,U_2211] :
        ( sP139(U_2209,U_2211)
        | U_2211 = zero_zero(nat)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2211),hAPP(nat,nat,suc,U_2209))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP139,sP140])],[f_583_4]) ).

cnf(f_583_6,plain,
    ( sP139(U_2209,U_2211)
    | U_2211 = zero_zero(nat)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2211),hAPP(nat,nat,suc,U_2209))) ),
    inference(clausify,[status(thm)],[f_583_5]) ).

cnf(f_583_7,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2212),hAPP(nat,nat,suc,U_2210)))
    | sP140(U_2212,U_2206,U_2210) ),
    inference(clausify,[status(thm)],[f_583_5]) ).

cnf(f_583_8,plain,
    ( U_2211 = hAPP(nat,nat,suc,sK83(U_2211,U_2209))
    | ~ sP139(U_2209,U_2211) ),
    inference(clausify,[status(thm)],[f_583_5]) ).

cnf(f_583_9,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK83(U_2211,U_2209)),U_2209))
    | ~ sP139(U_2209,U_2211) ),
    inference(clausify,[status(thm)],[f_583_5]) ).

cnf(f_583_10,plain,
    ( U_2212 != zero_zero(nat)
    | ~ sP140(U_2212,U_2206,U_2210) ),
    inference(clausify,[status(thm)],[f_583_5]) ).

cnf(f_583_11,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2206),U_2210))
    | U_2212 != hAPP(nat,nat,suc,U_2206)
    | ~ sP140(U_2212,U_2206,U_2210) ),
    inference(clausify,[status(thm)],[f_583_5]) ).

fof(f_584_1,plain,
    ! [M,Na] :
      ( ( hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),Na)
        | ( ( Na != hAPP(nat,nat,suc,zero_zero(nat))
            | M != zero_zero(nat) )
          & ( Na != zero_zero(nat)
            | M != hAPP(nat,nat,suc,zero_zero(nat)) ) ) )
      & ( ( Na = hAPP(nat,nat,suc,zero_zero(nat))
          & M = zero_zero(nat) )
        | ( Na = zero_zero(nat)
          & M = hAPP(nat,nat,suc,zero_zero(nat)) )
        | hAPP(nat,nat,suc,zero_zero(nat)) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),Na) ) ),
    inference(fof_nnf,[status(thm)],[fact_513_one__is__add]) ).

fof(f_584_2,plain,
    ! [U_2214,U_2213] :
      ( ( hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2214),U_2213)
        | ( ( U_2213 != hAPP(nat,nat,suc,zero_zero(nat))
            | U_2214 != zero_zero(nat) )
          & ( U_2213 != zero_zero(nat)
            | U_2214 != hAPP(nat,nat,suc,zero_zero(nat)) ) ) )
      & ( ( U_2213 = hAPP(nat,nat,suc,zero_zero(nat))
          & U_2214 = zero_zero(nat) )
        | ( U_2213 = zero_zero(nat)
          & U_2214 = 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_2214),U_2213) ) ),
    inference(variable_rename,[status(thm)],[f_584_1]) ).

fof(f_584_3,plain,
    ( ! [U_2218,U_2216] :
        ( hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2218),U_2216)
        | ( ( U_2216 != hAPP(nat,nat,suc,zero_zero(nat))
            | U_2218 != zero_zero(nat) )
          & ( U_2216 != zero_zero(nat)
            | U_2218 != hAPP(nat,nat,suc,zero_zero(nat)) ) ) )
    & ! [U_2217,U_2215] :
        ( ( U_2215 = hAPP(nat,nat,suc,zero_zero(nat))
          & U_2217 = zero_zero(nat) )
        | ( U_2215 = zero_zero(nat)
          & U_2217 = 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_2217),U_2215) ) ),
    inference(miniscope,[status(thm)],[f_584_2]) ).

fof(f_584_4,plain,
    ( ! [U_2216,U_2218] :
        ( U_2216 != hAPP(nat,nat,suc,zero_zero(nat))
        | U_2218 != zero_zero(nat)
        | ~ sP143(U_2216,U_2218) )
    & ! [U_2216,U_2218] :
        ( U_2216 != zero_zero(nat)
        | U_2218 != hAPP(nat,nat,suc,zero_zero(nat))
        | ~ sP143(U_2216,U_2218) )
    & ! [U_2215,U_2217] :
        ( U_2215 = hAPP(nat,nat,suc,zero_zero(nat))
        | ~ sP142(U_2215,U_2217) )
    & ! [U_2215,U_2217] :
        ( U_2217 = zero_zero(nat)
        | ~ sP142(U_2215,U_2217) )
    & ! [U_2215,U_2217] :
        ( U_2215 = zero_zero(nat)
        | ~ sP141(U_2215,U_2217) )
    & ! [U_2215,U_2217] :
        ( U_2217 = hAPP(nat,nat,suc,zero_zero(nat))
        | ~ sP141(U_2215,U_2217) )
    & ! [U_2216,U_2218] :
        ( hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2218),U_2216)
        | sP143(U_2216,U_2218) )
    & ! [U_2215,U_2217] :
        ( sP142(U_2215,U_2217)
        | sP141(U_2215,U_2217)
        | hAPP(nat,nat,suc,zero_zero(nat)) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2217),U_2215) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP141,sP142,sP143])],[f_584_3]) ).

cnf(f_584_5,plain,
    ( sP142(U_2215,U_2217)
    | sP141(U_2215,U_2217)
    | hAPP(nat,nat,suc,zero_zero(nat)) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2217),U_2215) ),
    inference(clausify,[status(thm)],[f_584_4]) ).

cnf(f_584_6,plain,
    ( hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2218),U_2216)
    | sP143(U_2216,U_2218) ),
    inference(clausify,[status(thm)],[f_584_4]) ).

cnf(f_584_7,plain,
    ( U_2217 = hAPP(nat,nat,suc,zero_zero(nat))
    | ~ sP141(U_2215,U_2217) ),
    inference(clausify,[status(thm)],[f_584_4]) ).

cnf(f_584_8,plain,
    ( U_2215 = zero_zero(nat)
    | ~ sP141(U_2215,U_2217) ),
    inference(clausify,[status(thm)],[f_584_4]) ).

cnf(f_584_9,plain,
    ( U_2217 = zero_zero(nat)
    | ~ sP142(U_2215,U_2217) ),
    inference(clausify,[status(thm)],[f_584_4]) ).

cnf(f_584_10,plain,
    ( U_2215 = hAPP(nat,nat,suc,zero_zero(nat))
    | ~ sP142(U_2215,U_2217) ),
    inference(clausify,[status(thm)],[f_584_4]) ).

cnf(f_584_11,plain,
    ( U_2216 != zero_zero(nat)
    | U_2218 != hAPP(nat,nat,suc,zero_zero(nat))
    | ~ sP143(U_2216,U_2218) ),
    inference(clausify,[status(thm)],[f_584_4]) ).

cnf(f_584_12,plain,
    ( U_2216 != hAPP(nat,nat,suc,zero_zero(nat))
    | U_2218 != zero_zero(nat)
    | ~ sP143(U_2216,U_2218) ),
    inference(clausify,[status(thm)],[f_584_4]) ).

fof(f_585_1,plain,
    ! [M,Na] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),Na) = hAPP(nat,nat,suc,zero_zero(nat))
        | ( ( Na != hAPP(nat,nat,suc,zero_zero(nat))
            | M != zero_zero(nat) )
          & ( Na != zero_zero(nat)
            | M != hAPP(nat,nat,suc,zero_zero(nat)) ) ) )
      & ( ( Na = hAPP(nat,nat,suc,zero_zero(nat))
          & M = zero_zero(nat) )
        | ( Na = zero_zero(nat)
          & M = hAPP(nat,nat,suc,zero_zero(nat)) )
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),Na) != hAPP(nat,nat,suc,zero_zero(nat)) ) ),
    inference(fof_nnf,[status(thm)],[fact_514_add__is__1]) ).

fof(f_585_2,plain,
    ! [U_2220,U_2219] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2220),U_2219) = hAPP(nat,nat,suc,zero_zero(nat))
        | ( ( U_2219 != hAPP(nat,nat,suc,zero_zero(nat))
            | U_2220 != zero_zero(nat) )
          & ( U_2219 != zero_zero(nat)
            | U_2220 != hAPP(nat,nat,suc,zero_zero(nat)) ) ) )
      & ( ( U_2219 = hAPP(nat,nat,suc,zero_zero(nat))
          & U_2220 = zero_zero(nat) )
        | ( U_2219 = zero_zero(nat)
          & U_2220 = hAPP(nat,nat,suc,zero_zero(nat)) )
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2220),U_2219) != hAPP(nat,nat,suc,zero_zero(nat)) ) ),
    inference(variable_rename,[status(thm)],[f_585_1]) ).

fof(f_585_3,plain,
    ( ! [U_2224,U_2222] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2224),U_2222) = hAPP(nat,nat,suc,zero_zero(nat))
        | ( ( U_2222 != hAPP(nat,nat,suc,zero_zero(nat))
            | U_2224 != zero_zero(nat) )
          & ( U_2222 != zero_zero(nat)
            | U_2224 != hAPP(nat,nat,suc,zero_zero(nat)) ) ) )
    & ! [U_2223,U_2221] :
        ( ( U_2221 = hAPP(nat,nat,suc,zero_zero(nat))
          & U_2223 = zero_zero(nat) )
        | ( U_2221 = zero_zero(nat)
          & U_2223 = hAPP(nat,nat,suc,zero_zero(nat)) )
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2223),U_2221) != hAPP(nat,nat,suc,zero_zero(nat)) ) ),
    inference(miniscope,[status(thm)],[f_585_2]) ).

fof(f_585_4,plain,
    ( ! [U_2222,U_2224] :
        ( U_2222 != hAPP(nat,nat,suc,zero_zero(nat))
        | U_2224 != zero_zero(nat)
        | ~ sP146(U_2222,U_2224) )
    & ! [U_2222,U_2224] :
        ( U_2222 != zero_zero(nat)
        | U_2224 != hAPP(nat,nat,suc,zero_zero(nat))
        | ~ sP146(U_2222,U_2224) )
    & ! [U_2223,U_2221] :
        ( U_2221 = hAPP(nat,nat,suc,zero_zero(nat))
        | ~ sP145(U_2223,U_2221) )
    & ! [U_2223,U_2221] :
        ( U_2223 = zero_zero(nat)
        | ~ sP145(U_2223,U_2221) )
    & ! [U_2223,U_2221] :
        ( U_2221 = zero_zero(nat)
        | ~ sP144(U_2223,U_2221) )
    & ! [U_2223,U_2221] :
        ( U_2223 = hAPP(nat,nat,suc,zero_zero(nat))
        | ~ sP144(U_2223,U_2221) )
    & ! [U_2222,U_2224] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2224),U_2222) = hAPP(nat,nat,suc,zero_zero(nat))
        | sP146(U_2222,U_2224) )
    & ! [U_2223,U_2221] :
        ( sP145(U_2223,U_2221)
        | sP144(U_2223,U_2221)
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2223),U_2221) != hAPP(nat,nat,suc,zero_zero(nat)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP144,sP145,sP146])],[f_585_3]) ).

cnf(f_585_5,plain,
    ( sP145(U_2223,U_2221)
    | sP144(U_2223,U_2221)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2223),U_2221) != hAPP(nat,nat,suc,zero_zero(nat)) ),
    inference(clausify,[status(thm)],[f_585_4]) ).

cnf(f_585_6,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2224),U_2222) = hAPP(nat,nat,suc,zero_zero(nat))
    | sP146(U_2222,U_2224) ),
    inference(clausify,[status(thm)],[f_585_4]) ).

cnf(f_585_7,plain,
    ( U_2223 = hAPP(nat,nat,suc,zero_zero(nat))
    | ~ sP144(U_2223,U_2221) ),
    inference(clausify,[status(thm)],[f_585_4]) ).

cnf(f_585_8,plain,
    ( U_2221 = zero_zero(nat)
    | ~ sP144(U_2223,U_2221) ),
    inference(clausify,[status(thm)],[f_585_4]) ).

cnf(f_585_9,plain,
    ( U_2223 = zero_zero(nat)
    | ~ sP145(U_2223,U_2221) ),
    inference(clausify,[status(thm)],[f_585_4]) ).

cnf(f_585_10,plain,
    ( U_2221 = hAPP(nat,nat,suc,zero_zero(nat))
    | ~ sP145(U_2223,U_2221) ),
    inference(clausify,[status(thm)],[f_585_4]) ).

cnf(f_585_11,plain,
    ( U_2222 != zero_zero(nat)
    | U_2224 != hAPP(nat,nat,suc,zero_zero(nat))
    | ~ sP146(U_2222,U_2224) ),
    inference(clausify,[status(thm)],[f_585_4]) ).

cnf(f_585_12,plain,
    ( U_2222 != hAPP(nat,nat,suc,zero_zero(nat))
    | U_2224 != zero_zero(nat)
    | ~ sP146(U_2222,U_2224) ),
    inference(clausify,[status(thm)],[f_585_4]) ).

fof(f_586_1,plain,
    ! [M,Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),Na)))
        | ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na))
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M)) ) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_515_add__gr__0]) ).

fof(f_586_2,plain,
    ! [U_2226,U_2225] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2226),U_2225)))
        | ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2225))
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2226)) ) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2225))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2226))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2226),U_2225))) ) ),
    inference(variable_rename,[status(thm)],[f_586_1]) ).

fof(f_586_3,plain,
    ( ! [U_2230,U_2228] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2230),U_2228)))
        | ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2228))
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2230)) ) )
    & ! [U_2229,U_2227] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2227))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2229))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2229),U_2227))) ) ),
    inference(miniscope,[status(thm)],[f_586_2]) ).

fof(f_586_4,plain,
    ( ! [U_2228,U_2230] :
        ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2228))
        | ~ sP147(U_2228,U_2230) )
    & ! [U_2228,U_2230] :
        ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2230))
        | ~ sP147(U_2228,U_2230) )
    & ! [U_2228,U_2230] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2230),U_2228)))
        | sP147(U_2228,U_2230) )
    & ! [U_2227,U_2229] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2227))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2229))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2229),U_2227))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP147])],[f_586_3]) ).

cnf(f_586_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2227))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2229))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2229),U_2227))) ),
    inference(clausify,[status(thm)],[f_586_4]) ).

cnf(f_586_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2230),U_2228)))
    | sP147(U_2228,U_2230) ),
    inference(clausify,[status(thm)],[f_586_4]) ).

cnf(f_586_7,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2230))
    | ~ sP147(U_2228,U_2230) ),
    inference(clausify,[status(thm)],[f_586_4]) ).

cnf(f_586_8,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2228))
    | ~ sP147(U_2228,U_2230) ),
    inference(clausify,[status(thm)],[f_586_4]) ).

fof(f_587_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_516_card_Oempty]) ).

fof(f_587_2,plain,
    ! [U_2231] : hAPP(fun(U_2231,bool),nat,finite_card(U_2231),bot_bot(fun(U_2231,bool))) = zero_zero(nat),
    inference(variable_rename,[status(thm)],[f_587_1]) ).

fof(f_587_3,plain,
    ! [U_2231] : hAPP(fun(U_2231,bool),nat,finite_card(U_2231),bot_bot(fun(U_2231,bool))) = zero_zero(nat),
    inference(definitional_conversion,[status(esa)],[f_587_2]) ).

cnf(f_587_4,plain,
    hAPP(fun(U_2231,bool),nat,finite_card(U_2231),bot_bot(fun(U_2231,bool))) = zero_zero(nat),
    inference(clausify,[status(thm)],[f_587_3]) ).

fof(f_588_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_517_card__infinite]) ).

fof(f_588_2,plain,
    ! [U_2233,U_2232] :
      ( hAPP(fun(U_2233,bool),nat,finite_card(U_2233),U_2232) = zero_zero(nat)
      | hBOOL(hAPP(fun(U_2233,bool),bool,finite_finite(U_2233),U_2232)) ),
    inference(variable_rename,[status(thm)],[f_588_1]) ).

fof(f_588_3,plain,
    ! [U_2233,U_2232] :
      ( hAPP(fun(U_2233,bool),nat,finite_card(U_2233),U_2232) = zero_zero(nat)
      | hBOOL(hAPP(fun(U_2233,bool),bool,finite_finite(U_2233),U_2232)) ),
    inference(definitional_conversion,[status(esa)],[f_588_2]) ).

cnf(f_588_4,plain,
    ( hAPP(fun(U_2233,bool),nat,finite_card(U_2233),U_2232) = zero_zero(nat)
    | hBOOL(hAPP(fun(U_2233,bool),bool,finite_finite(U_2233),U_2232)) ),
    inference(clausify,[status(thm)],[f_588_3]) ).

fof(f_589_1,plain,
    ! [Na,M] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Na),M)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Na),M))) ) ),
    inference(fof_nnf,[status(thm)],[fact_518_zero__less__diff]) ).

fof(f_589_2,plain,
    ! [U_2235,U_2234] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2235),U_2234)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2234),U_2235)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2234),U_2235))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2235),U_2234))) ) ),
    inference(variable_rename,[status(thm)],[f_589_1]) ).

fof(f_589_3,plain,
    ( ! [U_2239,U_2237] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2239),U_2237)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2237),U_2239)) )
    & ! [U_2238,U_2236] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2236),U_2238))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2238),U_2236))) ) ),
    inference(miniscope,[status(thm)],[f_589_2]) ).

fof(f_589_4,plain,
    ( ! [U_2237,U_2239] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2239),U_2237)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2237),U_2239)) )
    & ! [U_2238,U_2236] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2236),U_2238))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2238),U_2236))) ) ),
    inference(definitional_conversion,[status(esa)],[f_589_3]) ).

cnf(f_589_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2236),U_2238))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2238),U_2236))) ),
    inference(clausify,[status(thm)],[f_589_4]) ).

cnf(f_589_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2239),U_2237)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2237),U_2239)) ),
    inference(clausify,[status(thm)],[f_589_4]) ).

fof(f_590_1,plain,
    ! [M_1,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_1),N)),M_1))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M_1))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) ),
    inference(fof_nnf,[status(thm)],[fact_519_diff__less]) ).

fof(f_590_2,plain,
    ! [U_2241,U_2240] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2241),U_2240)),U_2241))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2241))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2240)) ),
    inference(variable_rename,[status(thm)],[f_590_1]) ).

fof(f_590_3,plain,
    ! [U_2240,U_2241] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2241),U_2240)),U_2241))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2241))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2240)) ),
    inference(definitional_conversion,[status(esa)],[f_590_2]) ).

cnf(f_590_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_2241),U_2240)),U_2241))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2241))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2240)) ),
    inference(clausify,[status(thm)],[f_590_3]) ).

fof(f_591_1,plain,
    ! [N,M_1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M_1)) = zero_zero(nat),
    inference(fof_nnf,[status(thm)],[fact_520_diff__add__0]) ).

fof(f_591_2,plain,
    ! [U_2243,U_2242] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2243),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2243),U_2242)) = zero_zero(nat),
    inference(variable_rename,[status(thm)],[f_591_1]) ).

fof(f_591_3,plain,
    ! [U_2242,U_2243] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2243),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2243),U_2242)) = zero_zero(nat),
    inference(definitional_conversion,[status(esa)],[f_591_2]) ).

cnf(f_591_4,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2243),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2243),U_2242)) = zero_zero(nat),
    inference(clausify,[status(thm)],[f_591_3]) ).

fof(f_592_1,plain,
    ! [M,Na] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),Na) = zero_zero(nat)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na))
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),Na) != zero_zero(nat) ) ),
    inference(fof_nnf,[status(thm)],[fact_521_diff__is__0__eq]) ).

fof(f_592_2,plain,
    ! [U_2245,U_2244] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2245),U_2244) = zero_zero(nat)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2245),U_2244)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2245),U_2244))
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2245),U_2244) != zero_zero(nat) ) ),
    inference(variable_rename,[status(thm)],[f_592_1]) ).

fof(f_592_3,plain,
    ( ! [U_2249,U_2247] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2249),U_2247) = zero_zero(nat)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2249),U_2247)) )
    & ! [U_2248,U_2246] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2248),U_2246))
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2248),U_2246) != zero_zero(nat) ) ),
    inference(miniscope,[status(thm)],[f_592_2]) ).

fof(f_592_4,plain,
    ( ! [U_2249,U_2247] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2249),U_2247) = zero_zero(nat)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2249),U_2247)) )
    & ! [U_2248,U_2246] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2248),U_2246))
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2248),U_2246) != zero_zero(nat) ) ),
    inference(definitional_conversion,[status(esa)],[f_592_3]) ).

cnf(f_592_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2248),U_2246))
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2248),U_2246) != zero_zero(nat) ),
    inference(clausify,[status(thm)],[f_592_4]) ).

cnf(f_592_6,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2249),U_2247) = zero_zero(nat)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2249),U_2247)) ),
    inference(clausify,[status(thm)],[f_592_4]) ).

fof(f_593_1,plain,
    ! [M_1,N] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N) = zero_zero(nat)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)) ),
    inference(fof_nnf,[status(thm)],[fact_522_diff__is__0__eq_H]) ).

fof(f_593_2,plain,
    ! [U_2251,U_2250] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2251),U_2250) = zero_zero(nat)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2251),U_2250)) ),
    inference(variable_rename,[status(thm)],[f_593_1]) ).

fof(f_593_3,plain,
    ! [U_2250,U_2251] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2251),U_2250) = zero_zero(nat)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2251),U_2250)) ),
    inference(definitional_conversion,[status(esa)],[f_593_2]) ).

cnf(f_593_4,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2251),U_2250) = zero_zero(nat)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2251),U_2250)) ),
    inference(clausify,[status(thm)],[f_593_3]) ).

fof(f_594_1,plain,
    one_one(nat) = hAPP(nat,nat,suc,zero_zero(nat)),
    inference(fof_nnf,[status(thm)],[fact_523_One__nat__def]) ).

fof(f_594_2,plain,
    one_one(nat) = hAPP(nat,nat,suc,zero_zero(nat)),
    inference(definitional_conversion,[status(esa)],[f_594_1]) ).

cnf(f_594_3,plain,
    one_one(nat) = hAPP(nat,nat,suc,zero_zero(nat)),
    inference(clausify,[status(thm)],[f_594_2]) ).

fof(f_595_1,plain,
    ! [M,Na] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,suc,Na)) = hAPP(nat,nat,hAPP(fun(nat,nat),fun(nat,nat),hAPP(nat,fun(fun(nat,nat),fun(nat,nat)),nat_case(nat),zero_zero(nat)),combi(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),Na)),
    inference(fof_nnf,[status(thm)],[fact_524_diff__Suc]) ).

fof(f_595_2,plain,
    ! [U_2253,U_2252] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2253),hAPP(nat,nat,suc,U_2252)) = hAPP(nat,nat,hAPP(fun(nat,nat),fun(nat,nat),hAPP(nat,fun(fun(nat,nat),fun(nat,nat)),nat_case(nat),zero_zero(nat)),combi(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2253),U_2252)),
    inference(variable_rename,[status(thm)],[f_595_1]) ).

fof(f_595_3,plain,
    ! [U_2253,U_2252] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2253),hAPP(nat,nat,suc,U_2252)) = hAPP(nat,nat,hAPP(fun(nat,nat),fun(nat,nat),hAPP(nat,fun(fun(nat,nat),fun(nat,nat)),nat_case(nat),zero_zero(nat)),combi(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2253),U_2252)),
    inference(definitional_conversion,[status(esa)],[f_595_2]) ).

cnf(f_595_4,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2253),hAPP(nat,nat,suc,U_2252)) = hAPP(nat,nat,hAPP(fun(nat,nat),fun(nat,nat),hAPP(nat,fun(fun(nat,nat),fun(nat,nat)),nat_case(nat),zero_zero(nat)),combi(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2253),U_2252)),
    inference(clausify,[status(thm)],[f_595_3]) ).

fof(f_596_1,plain,
    ! [X_a] :
      ( ! [B,A_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(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)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) )
      | ~ ordere216010020id_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_525_add__pos__nonneg]) ).

fof(f_596_2,plain,
    ! [U_2256] :
      ( ! [U_2255,U_2254] :
          ( hBOOL(hAPP(U_2256,bool,hAPP(U_2256,fun(U_2256,bool),ord_less(U_2256),zero_zero(U_2256)),hAPP(U_2256,U_2256,hAPP(U_2256,fun(U_2256,U_2256),plus_plus(U_2256),U_2254),U_2255)))
          | ~ hBOOL(hAPP(U_2256,bool,hAPP(U_2256,fun(U_2256,bool),ord_less_eq(U_2256),zero_zero(U_2256)),U_2255))
          | ~ hBOOL(hAPP(U_2256,bool,hAPP(U_2256,fun(U_2256,bool),ord_less(U_2256),zero_zero(U_2256)),U_2254)) )
      | ~ ordere216010020id_add(U_2256) ),
    inference(variable_rename,[status(thm)],[f_596_1]) ).

fof(f_596_3,plain,
    ! [U_2254,U_2255,U_2256] :
      ( hBOOL(hAPP(U_2256,bool,hAPP(U_2256,fun(U_2256,bool),ord_less(U_2256),zero_zero(U_2256)),hAPP(U_2256,U_2256,hAPP(U_2256,fun(U_2256,U_2256),plus_plus(U_2256),U_2254),U_2255)))
      | ~ hBOOL(hAPP(U_2256,bool,hAPP(U_2256,fun(U_2256,bool),ord_less_eq(U_2256),zero_zero(U_2256)),U_2255))
      | ~ hBOOL(hAPP(U_2256,bool,hAPP(U_2256,fun(U_2256,bool),ord_less(U_2256),zero_zero(U_2256)),U_2254))
      | ~ ordere216010020id_add(U_2256) ),
    inference(definitional_conversion,[status(esa)],[f_596_2]) ).

cnf(f_596_4,plain,
    ( hBOOL(hAPP(U_2256,bool,hAPP(U_2256,fun(U_2256,bool),ord_less(U_2256),zero_zero(U_2256)),hAPP(U_2256,U_2256,hAPP(U_2256,fun(U_2256,U_2256),plus_plus(U_2256),U_2254),U_2255)))
    | ~ hBOOL(hAPP(U_2256,bool,hAPP(U_2256,fun(U_2256,bool),ord_less_eq(U_2256),zero_zero(U_2256)),U_2255))
    | ~ hBOOL(hAPP(U_2256,bool,hAPP(U_2256,fun(U_2256,bool),ord_less(U_2256),zero_zero(U_2256)),U_2254))
    | ~ ordere216010020id_add(U_2256) ),
    inference(clausify,[status(thm)],[f_596_3]) ).

fof(f_597_1,plain,
    ! [X_a] :
      ( ! [B,A_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(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)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B))
          | ~ 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_526_add__nonneg__pos]) ).

fof(f_597_2,plain,
    ! [U_2259] :
      ( ! [U_2258,U_2257] :
          ( hBOOL(hAPP(U_2259,bool,hAPP(U_2259,fun(U_2259,bool),ord_less(U_2259),zero_zero(U_2259)),hAPP(U_2259,U_2259,hAPP(U_2259,fun(U_2259,U_2259),plus_plus(U_2259),U_2257),U_2258)))
          | ~ hBOOL(hAPP(U_2259,bool,hAPP(U_2259,fun(U_2259,bool),ord_less(U_2259),zero_zero(U_2259)),U_2258))
          | ~ hBOOL(hAPP(U_2259,bool,hAPP(U_2259,fun(U_2259,bool),ord_less_eq(U_2259),zero_zero(U_2259)),U_2257)) )
      | ~ ordere216010020id_add(U_2259) ),
    inference(variable_rename,[status(thm)],[f_597_1]) ).

fof(f_597_3,plain,
    ! [U_2259,U_2257,U_2258] :
      ( hBOOL(hAPP(U_2259,bool,hAPP(U_2259,fun(U_2259,bool),ord_less(U_2259),zero_zero(U_2259)),hAPP(U_2259,U_2259,hAPP(U_2259,fun(U_2259,U_2259),plus_plus(U_2259),U_2257),U_2258)))
      | ~ hBOOL(hAPP(U_2259,bool,hAPP(U_2259,fun(U_2259,bool),ord_less(U_2259),zero_zero(U_2259)),U_2258))
      | ~ hBOOL(hAPP(U_2259,bool,hAPP(U_2259,fun(U_2259,bool),ord_less_eq(U_2259),zero_zero(U_2259)),U_2257))
      | ~ ordere216010020id_add(U_2259) ),
    inference(definitional_conversion,[status(esa)],[f_597_2]) ).

cnf(f_597_4,plain,
    ( hBOOL(hAPP(U_2259,bool,hAPP(U_2259,fun(U_2259,bool),ord_less(U_2259),zero_zero(U_2259)),hAPP(U_2259,U_2259,hAPP(U_2259,fun(U_2259,U_2259),plus_plus(U_2259),U_2257),U_2258)))
    | ~ hBOOL(hAPP(U_2259,bool,hAPP(U_2259,fun(U_2259,bool),ord_less(U_2259),zero_zero(U_2259)),U_2258))
    | ~ hBOOL(hAPP(U_2259,bool,hAPP(U_2259,fun(U_2259,bool),ord_less_eq(U_2259),zero_zero(U_2259)),U_2257))
    | ~ ordere216010020id_add(U_2259) ),
    inference(clausify,[status(thm)],[f_597_3]) ).

fof(f_598_1,plain,
    ! [X_a] :
      ( ! [B,C,A_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),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),C))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) )
      | ~ ordere216010020id_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_527_add__strict__increasing]) ).

fof(f_598_2,plain,
    ! [U_2263] :
      ( ! [U_2262,U_2261,U_2260] :
          ( hBOOL(hAPP(U_2263,bool,hAPP(U_2263,fun(U_2263,bool),ord_less(U_2263),U_2262),hAPP(U_2263,U_2263,hAPP(U_2263,fun(U_2263,U_2263),plus_plus(U_2263),U_2260),U_2261)))
          | ~ hBOOL(hAPP(U_2263,bool,hAPP(U_2263,fun(U_2263,bool),ord_less_eq(U_2263),U_2262),U_2261))
          | ~ hBOOL(hAPP(U_2263,bool,hAPP(U_2263,fun(U_2263,bool),ord_less(U_2263),zero_zero(U_2263)),U_2260)) )
      | ~ ordere216010020id_add(U_2263) ),
    inference(variable_rename,[status(thm)],[f_598_1]) ).

fof(f_598_3,plain,
    ! [U_2263,U_2260,U_2261,U_2262] :
      ( hBOOL(hAPP(U_2263,bool,hAPP(U_2263,fun(U_2263,bool),ord_less(U_2263),U_2262),hAPP(U_2263,U_2263,hAPP(U_2263,fun(U_2263,U_2263),plus_plus(U_2263),U_2260),U_2261)))
      | ~ hBOOL(hAPP(U_2263,bool,hAPP(U_2263,fun(U_2263,bool),ord_less_eq(U_2263),U_2262),U_2261))
      | ~ hBOOL(hAPP(U_2263,bool,hAPP(U_2263,fun(U_2263,bool),ord_less(U_2263),zero_zero(U_2263)),U_2260))
      | ~ ordere216010020id_add(U_2263) ),
    inference(definitional_conversion,[status(esa)],[f_598_2]) ).

cnf(f_598_4,plain,
    ( hBOOL(hAPP(U_2263,bool,hAPP(U_2263,fun(U_2263,bool),ord_less(U_2263),U_2262),hAPP(U_2263,U_2263,hAPP(U_2263,fun(U_2263,U_2263),plus_plus(U_2263),U_2260),U_2261)))
    | ~ hBOOL(hAPP(U_2263,bool,hAPP(U_2263,fun(U_2263,bool),ord_less_eq(U_2263),U_2262),U_2261))
    | ~ hBOOL(hAPP(U_2263,bool,hAPP(U_2263,fun(U_2263,bool),ord_less(U_2263),zero_zero(U_2263)),U_2260))
    | ~ ordere216010020id_add(U_2263) ),
    inference(clausify,[status(thm)],[f_598_3]) ).

fof(f_599_1,plain,
    ! [X_a] :
      ( ! [B,C,A_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),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),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_528_add__strict__increasing2]) ).

fof(f_599_2,plain,
    ! [U_2267] :
      ( ! [U_2266,U_2265,U_2264] :
          ( hBOOL(hAPP(U_2267,bool,hAPP(U_2267,fun(U_2267,bool),ord_less(U_2267),U_2266),hAPP(U_2267,U_2267,hAPP(U_2267,fun(U_2267,U_2267),plus_plus(U_2267),U_2264),U_2265)))
          | ~ hBOOL(hAPP(U_2267,bool,hAPP(U_2267,fun(U_2267,bool),ord_less(U_2267),U_2266),U_2265))
          | ~ hBOOL(hAPP(U_2267,bool,hAPP(U_2267,fun(U_2267,bool),ord_less_eq(U_2267),zero_zero(U_2267)),U_2264)) )
      | ~ ordere216010020id_add(U_2267) ),
    inference(variable_rename,[status(thm)],[f_599_1]) ).

fof(f_599_3,plain,
    ! [U_2264,U_2265,U_2267,U_2266] :
      ( hBOOL(hAPP(U_2267,bool,hAPP(U_2267,fun(U_2267,bool),ord_less(U_2267),U_2266),hAPP(U_2267,U_2267,hAPP(U_2267,fun(U_2267,U_2267),plus_plus(U_2267),U_2264),U_2265)))
      | ~ hBOOL(hAPP(U_2267,bool,hAPP(U_2267,fun(U_2267,bool),ord_less(U_2267),U_2266),U_2265))
      | ~ hBOOL(hAPP(U_2267,bool,hAPP(U_2267,fun(U_2267,bool),ord_less_eq(U_2267),zero_zero(U_2267)),U_2264))
      | ~ ordere216010020id_add(U_2267) ),
    inference(definitional_conversion,[status(esa)],[f_599_2]) ).

cnf(f_599_4,plain,
    ( hBOOL(hAPP(U_2267,bool,hAPP(U_2267,fun(U_2267,bool),ord_less(U_2267),U_2266),hAPP(U_2267,U_2267,hAPP(U_2267,fun(U_2267,U_2267),plus_plus(U_2267),U_2264),U_2265)))
    | ~ hBOOL(hAPP(U_2267,bool,hAPP(U_2267,fun(U_2267,bool),ord_less(U_2267),U_2266),U_2265))
    | ~ hBOOL(hAPP(U_2267,bool,hAPP(U_2267,fun(U_2267,bool),ord_less_eq(U_2267),zero_zero(U_2267)),U_2264))
    | ~ ordere216010020id_add(U_2267) ),
    inference(clausify,[status(thm)],[f_599_3]) ).

fof(f_600_1,plain,
    ! [X_a] :
      ( ! [B,A_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),B)),zero_zero(X_a)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),zero_zero(X_a)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a))) )
      | ~ ordere216010020id_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_529_add__neg__nonpos]) ).

fof(f_600_2,plain,
    ! [U_2270] :
      ( ! [U_2269,U_2268] :
          ( hBOOL(hAPP(U_2270,bool,hAPP(U_2270,fun(U_2270,bool),ord_less(U_2270),hAPP(U_2270,U_2270,hAPP(U_2270,fun(U_2270,U_2270),plus_plus(U_2270),U_2268),U_2269)),zero_zero(U_2270)))
          | ~ hBOOL(hAPP(U_2270,bool,hAPP(U_2270,fun(U_2270,bool),ord_less_eq(U_2270),U_2269),zero_zero(U_2270)))
          | ~ hBOOL(hAPP(U_2270,bool,hAPP(U_2270,fun(U_2270,bool),ord_less(U_2270),U_2268),zero_zero(U_2270))) )
      | ~ ordere216010020id_add(U_2270) ),
    inference(variable_rename,[status(thm)],[f_600_1]) ).

fof(f_600_3,plain,
    ! [U_2270,U_2269,U_2268] :
      ( hBOOL(hAPP(U_2270,bool,hAPP(U_2270,fun(U_2270,bool),ord_less(U_2270),hAPP(U_2270,U_2270,hAPP(U_2270,fun(U_2270,U_2270),plus_plus(U_2270),U_2268),U_2269)),zero_zero(U_2270)))
      | ~ hBOOL(hAPP(U_2270,bool,hAPP(U_2270,fun(U_2270,bool),ord_less_eq(U_2270),U_2269),zero_zero(U_2270)))
      | ~ hBOOL(hAPP(U_2270,bool,hAPP(U_2270,fun(U_2270,bool),ord_less(U_2270),U_2268),zero_zero(U_2270)))
      | ~ ordere216010020id_add(U_2270) ),
    inference(definitional_conversion,[status(esa)],[f_600_2]) ).

cnf(f_600_4,plain,
    ( hBOOL(hAPP(U_2270,bool,hAPP(U_2270,fun(U_2270,bool),ord_less(U_2270),hAPP(U_2270,U_2270,hAPP(U_2270,fun(U_2270,U_2270),plus_plus(U_2270),U_2268),U_2269)),zero_zero(U_2270)))
    | ~ hBOOL(hAPP(U_2270,bool,hAPP(U_2270,fun(U_2270,bool),ord_less_eq(U_2270),U_2269),zero_zero(U_2270)))
    | ~ hBOOL(hAPP(U_2270,bool,hAPP(U_2270,fun(U_2270,bool),ord_less(U_2270),U_2268),zero_zero(U_2270)))
    | ~ ordere216010020id_add(U_2270) ),
    inference(clausify,[status(thm)],[f_600_3]) ).

fof(f_601_1,plain,
    ! [X_a] :
      ( ! [B,A_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),B)),zero_zero(X_a)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),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_530_add__nonpos__neg]) ).

fof(f_601_2,plain,
    ! [U_2273] :
      ( ! [U_2272,U_2271] :
          ( hBOOL(hAPP(U_2273,bool,hAPP(U_2273,fun(U_2273,bool),ord_less(U_2273),hAPP(U_2273,U_2273,hAPP(U_2273,fun(U_2273,U_2273),plus_plus(U_2273),U_2271),U_2272)),zero_zero(U_2273)))
          | ~ hBOOL(hAPP(U_2273,bool,hAPP(U_2273,fun(U_2273,bool),ord_less(U_2273),U_2272),zero_zero(U_2273)))
          | ~ hBOOL(hAPP(U_2273,bool,hAPP(U_2273,fun(U_2273,bool),ord_less_eq(U_2273),U_2271),zero_zero(U_2273))) )
      | ~ ordere216010020id_add(U_2273) ),
    inference(variable_rename,[status(thm)],[f_601_1]) ).

fof(f_601_3,plain,
    ! [U_2272,U_2273,U_2271] :
      ( hBOOL(hAPP(U_2273,bool,hAPP(U_2273,fun(U_2273,bool),ord_less(U_2273),hAPP(U_2273,U_2273,hAPP(U_2273,fun(U_2273,U_2273),plus_plus(U_2273),U_2271),U_2272)),zero_zero(U_2273)))
      | ~ hBOOL(hAPP(U_2273,bool,hAPP(U_2273,fun(U_2273,bool),ord_less(U_2273),U_2272),zero_zero(U_2273)))
      | ~ hBOOL(hAPP(U_2273,bool,hAPP(U_2273,fun(U_2273,bool),ord_less_eq(U_2273),U_2271),zero_zero(U_2273)))
      | ~ ordere216010020id_add(U_2273) ),
    inference(definitional_conversion,[status(esa)],[f_601_2]) ).

cnf(f_601_4,plain,
    ( hBOOL(hAPP(U_2273,bool,hAPP(U_2273,fun(U_2273,bool),ord_less(U_2273),hAPP(U_2273,U_2273,hAPP(U_2273,fun(U_2273,U_2273),plus_plus(U_2273),U_2271),U_2272)),zero_zero(U_2273)))
    | ~ hBOOL(hAPP(U_2273,bool,hAPP(U_2273,fun(U_2273,bool),ord_less(U_2273),U_2272),zero_zero(U_2273)))
    | ~ hBOOL(hAPP(U_2273,bool,hAPP(U_2273,fun(U_2273,bool),ord_less_eq(U_2273),U_2271),zero_zero(U_2273)))
    | ~ ordere216010020id_add(U_2273) ),
    inference(clausify,[status(thm)],[f_601_3]) ).

fof(f_602_1,plain,
    ! [X_a] :
      ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),one_one(X_a))))
      | ~ linordered_semidom(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_531_zero__less__two]) ).

fof(f_602_2,plain,
    ! [U_2274] :
      ( hBOOL(hAPP(U_2274,bool,hAPP(U_2274,fun(U_2274,bool),ord_less(U_2274),zero_zero(U_2274)),hAPP(U_2274,U_2274,hAPP(U_2274,fun(U_2274,U_2274),plus_plus(U_2274),one_one(U_2274)),one_one(U_2274))))
      | ~ linordered_semidom(U_2274) ),
    inference(variable_rename,[status(thm)],[f_602_1]) ).

fof(f_602_3,plain,
    ! [U_2274] :
      ( hBOOL(hAPP(U_2274,bool,hAPP(U_2274,fun(U_2274,bool),ord_less(U_2274),zero_zero(U_2274)),hAPP(U_2274,U_2274,hAPP(U_2274,fun(U_2274,U_2274),plus_plus(U_2274),one_one(U_2274)),one_one(U_2274))))
      | ~ linordered_semidom(U_2274) ),
    inference(definitional_conversion,[status(esa)],[f_602_2]) ).

cnf(f_602_4,plain,
    ( hBOOL(hAPP(U_2274,bool,hAPP(U_2274,fun(U_2274,bool),ord_less(U_2274),zero_zero(U_2274)),hAPP(U_2274,U_2274,hAPP(U_2274,fun(U_2274,U_2274),plus_plus(U_2274),one_one(U_2274)),one_one(U_2274))))
    | ~ linordered_semidom(U_2274) ),
    inference(clausify,[status(thm)],[f_602_3]) ).

fof(f_603_1,plain,
    ! [X_b,X_2] :
      ( ( hBOOL(hAPP(X_b,bool,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),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),bot_bot(fun(X_b,bool))))
        | ~ hBOOL(hAPP(X_b,bool,bot_bot(fun(X_b,bool)),X_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_532_bot__empty__eq]) ).

fof(f_603_2,plain,
    ! [U_2276,U_2275] :
      ( ( hBOOL(hAPP(U_2276,bool,bot_bot(fun(U_2276,bool)),U_2275))
        | ~ hBOOL(hAPP(fun(U_2276,bool),bool,hAPP(U_2276,fun(fun(U_2276,bool),bool),member(U_2276),U_2275),bot_bot(fun(U_2276,bool)))) )
      & ( hBOOL(hAPP(fun(U_2276,bool),bool,hAPP(U_2276,fun(fun(U_2276,bool),bool),member(U_2276),U_2275),bot_bot(fun(U_2276,bool))))
        | ~ hBOOL(hAPP(U_2276,bool,bot_bot(fun(U_2276,bool)),U_2275)) ) ),
    inference(variable_rename,[status(thm)],[f_603_1]) ).

fof(f_603_3,plain,
    ( ! [U_2280,U_2278] :
        ( hBOOL(hAPP(U_2280,bool,bot_bot(fun(U_2280,bool)),U_2278))
        | ~ hBOOL(hAPP(fun(U_2280,bool),bool,hAPP(U_2280,fun(fun(U_2280,bool),bool),member(U_2280),U_2278),bot_bot(fun(U_2280,bool)))) )
    & ! [U_2279,U_2277] :
        ( hBOOL(hAPP(fun(U_2279,bool),bool,hAPP(U_2279,fun(fun(U_2279,bool),bool),member(U_2279),U_2277),bot_bot(fun(U_2279,bool))))
        | ~ hBOOL(hAPP(U_2279,bool,bot_bot(fun(U_2279,bool)),U_2277)) ) ),
    inference(miniscope,[status(thm)],[f_603_2]) ).

fof(f_603_4,plain,
    ( ! [U_2278,U_2280] :
        ( hBOOL(hAPP(U_2280,bool,bot_bot(fun(U_2280,bool)),U_2278))
        | ~ hBOOL(hAPP(fun(U_2280,bool),bool,hAPP(U_2280,fun(fun(U_2280,bool),bool),member(U_2280),U_2278),bot_bot(fun(U_2280,bool)))) )
    & ! [U_2279,U_2277] :
        ( hBOOL(hAPP(fun(U_2279,bool),bool,hAPP(U_2279,fun(fun(U_2279,bool),bool),member(U_2279),U_2277),bot_bot(fun(U_2279,bool))))
        | ~ hBOOL(hAPP(U_2279,bool,bot_bot(fun(U_2279,bool)),U_2277)) ) ),
    inference(definitional_conversion,[status(esa)],[f_603_3]) ).

cnf(f_603_5,plain,
    ( hBOOL(hAPP(fun(U_2279,bool),bool,hAPP(U_2279,fun(fun(U_2279,bool),bool),member(U_2279),U_2277),bot_bot(fun(U_2279,bool))))
    | ~ hBOOL(hAPP(U_2279,bool,bot_bot(fun(U_2279,bool)),U_2277)) ),
    inference(clausify,[status(thm)],[f_603_4]) ).

cnf(f_603_6,plain,
    ( hBOOL(hAPP(U_2280,bool,bot_bot(fun(U_2280,bool)),U_2278))
    | ~ hBOOL(hAPP(fun(U_2280,bool),bool,hAPP(U_2280,fun(fun(U_2280,bool),bool),member(U_2280),U_2278),bot_bot(fun(U_2280,bool)))) ),
    inference(clausify,[status(thm)],[f_603_4]) ).

fof(f_604_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))
          & 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))
        | ti(fun(X_b,bool),A_3) = bot_bot(fun(X_b,bool))
        | hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3) != zero_zero(nat) ) ),
    inference(fof_nnf,[status(thm)],[fact_533_card__eq__0__iff]) ).

fof(f_604_2,plain,
    ! [U_2282,U_2281] :
      ( ( hAPP(fun(U_2282,bool),nat,finite_card(U_2282),U_2281) = zero_zero(nat)
        | ( hBOOL(hAPP(fun(U_2282,bool),bool,finite_finite(U_2282),U_2281))
          & ti(fun(U_2282,bool),U_2281) != bot_bot(fun(U_2282,bool)) ) )
      & ( ~ hBOOL(hAPP(fun(U_2282,bool),bool,finite_finite(U_2282),U_2281))
        | ti(fun(U_2282,bool),U_2281) = bot_bot(fun(U_2282,bool))
        | hAPP(fun(U_2282,bool),nat,finite_card(U_2282),U_2281) != zero_zero(nat) ) ),
    inference(variable_rename,[status(thm)],[f_604_1]) ).

fof(f_604_3,plain,
    ( ! [U_2286,U_2284] :
        ( hAPP(fun(U_2286,bool),nat,finite_card(U_2286),U_2284) = zero_zero(nat)
        | ( hBOOL(hAPP(fun(U_2286,bool),bool,finite_finite(U_2286),U_2284))
          & ti(fun(U_2286,bool),U_2284) != bot_bot(fun(U_2286,bool)) ) )
    & ! [U_2285,U_2283] :
        ( ~ hBOOL(hAPP(fun(U_2285,bool),bool,finite_finite(U_2285),U_2283))
        | ti(fun(U_2285,bool),U_2283) = bot_bot(fun(U_2285,bool))
        | hAPP(fun(U_2285,bool),nat,finite_card(U_2285),U_2283) != zero_zero(nat) ) ),
    inference(miniscope,[status(thm)],[f_604_2]) ).

fof(f_604_4,plain,
    ( ! [U_2284,U_2286] :
        ( hBOOL(hAPP(fun(U_2286,bool),bool,finite_finite(U_2286),U_2284))
        | ~ sP148(U_2284,U_2286) )
    & ! [U_2284,U_2286] :
        ( ti(fun(U_2286,bool),U_2284) != bot_bot(fun(U_2286,bool))
        | ~ sP148(U_2284,U_2286) )
    & ! [U_2284,U_2286] :
        ( hAPP(fun(U_2286,bool),nat,finite_card(U_2286),U_2284) = zero_zero(nat)
        | sP148(U_2284,U_2286) )
    & ! [U_2283,U_2285] :
        ( ~ hBOOL(hAPP(fun(U_2285,bool),bool,finite_finite(U_2285),U_2283))
        | ti(fun(U_2285,bool),U_2283) = bot_bot(fun(U_2285,bool))
        | hAPP(fun(U_2285,bool),nat,finite_card(U_2285),U_2283) != zero_zero(nat) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP148])],[f_604_3]) ).

cnf(f_604_5,plain,
    ( ~ hBOOL(hAPP(fun(U_2285,bool),bool,finite_finite(U_2285),U_2283))
    | ti(fun(U_2285,bool),U_2283) = bot_bot(fun(U_2285,bool))
    | hAPP(fun(U_2285,bool),nat,finite_card(U_2285),U_2283) != zero_zero(nat) ),
    inference(clausify,[status(thm)],[f_604_4]) ).

cnf(f_604_6,plain,
    ( hAPP(fun(U_2286,bool),nat,finite_card(U_2286),U_2284) = zero_zero(nat)
    | sP148(U_2284,U_2286) ),
    inference(clausify,[status(thm)],[f_604_4]) ).

cnf(f_604_7,plain,
    ( ti(fun(U_2286,bool),U_2284) != bot_bot(fun(U_2286,bool))
    | ~ sP148(U_2284,U_2286) ),
    inference(clausify,[status(thm)],[f_604_4]) ).

cnf(f_604_8,plain,
    ( hBOOL(hAPP(fun(U_2286,bool),bool,finite_finite(U_2286),U_2284))
    | ~ sP148(U_2284,U_2286) ),
    inference(clausify,[status(thm)],[f_604_4]) ).

fof(f_605_1,plain,
    ! [X_b,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(nat),zero_zero(nat)),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))) ),
    inference(fof_nnf,[status(thm)],[fact_534_card__ge__0__finite]) ).

fof(f_605_2,plain,
    ! [U_2288,U_2287] :
      ( hBOOL(hAPP(fun(U_2288,bool),bool,finite_finite(U_2288),U_2287))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(U_2288,bool),nat,finite_card(U_2288),U_2287))) ),
    inference(variable_rename,[status(thm)],[f_605_1]) ).

fof(f_605_3,plain,
    ! [U_2288,U_2287] :
      ( hBOOL(hAPP(fun(U_2288,bool),bool,finite_finite(U_2288),U_2287))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(U_2288,bool),nat,finite_card(U_2288),U_2287))) ),
    inference(definitional_conversion,[status(esa)],[f_605_2]) ).

cnf(f_605_4,plain,
    ( hBOOL(hAPP(fun(U_2288,bool),bool,finite_finite(U_2288),U_2287))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(U_2288,bool),nat,finite_card(U_2288),U_2287))) ),
    inference(clausify,[status(thm)],[f_605_3]) ).

fof(f_606_1,plain,
    ! [N] :
      ( hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,suc,zero_zero(nat)))) = N
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) ),
    inference(fof_nnf,[status(thm)],[fact_535_Suc__pred]) ).

fof(f_606_2,plain,
    ! [U_2289] :
      ( hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2289),hAPP(nat,nat,suc,zero_zero(nat)))) = U_2289
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2289)) ),
    inference(variable_rename,[status(thm)],[f_606_1]) ).

fof(f_606_3,plain,
    ! [U_2289] :
      ( hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2289),hAPP(nat,nat,suc,zero_zero(nat)))) = U_2289
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2289)) ),
    inference(definitional_conversion,[status(esa)],[f_606_2]) ).

cnf(f_606_4,plain,
    ( hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2289),hAPP(nat,nat,suc,zero_zero(nat)))) = U_2289
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2289)) ),
    inference(clausify,[status(thm)],[f_606_3]) ).

fof(f_607_1,plain,
    ! [I_2,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,suc,I_2))),N))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) ),
    inference(fof_nnf,[status(thm)],[fact_536_diff__Suc__less]) ).

fof(f_607_2,plain,
    ! [U_2291,U_2290] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2290),hAPP(nat,nat,suc,U_2291))),U_2290))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2290)) ),
    inference(variable_rename,[status(thm)],[f_607_1]) ).

fof(f_607_3,plain,
    ! [U_2290,U_2291] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2290),hAPP(nat,nat,suc,U_2291))),U_2290))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2290)) ),
    inference(definitional_conversion,[status(esa)],[f_607_2]) ).

cnf(f_607_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_2290),hAPP(nat,nat,suc,U_2291))),U_2290))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2290)) ),
    inference(clausify,[status(thm)],[f_607_3]) ).

fof(f_608_1,plain,
    ! [X_b,Q_3,Pa,X_1] :
      ( hBOOL(hAPP(X_b,bool,Q_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)),Pa),Q_3))
      | ~ hBOOL(hAPP(X_b,bool,Pa,X_1)) ),
    inference(fof_nnf,[status(thm)],[fact_537_rev__predicate1D]) ).

fof(f_608_2,plain,
    ! [U_2295,U_2294,U_2293,U_2292] :
      ( hBOOL(hAPP(U_2295,bool,U_2294,U_2292))
      | ~ hBOOL(hAPP(fun(U_2295,bool),bool,hAPP(fun(U_2295,bool),fun(fun(U_2295,bool),bool),ord_less_eq(fun(U_2295,bool)),U_2293),U_2294))
      | ~ hBOOL(hAPP(U_2295,bool,U_2293,U_2292)) ),
    inference(variable_rename,[status(thm)],[f_608_1]) ).

fof(f_608_3,plain,
    ! [U_2292,U_2293,U_2295,U_2294] :
      ( hBOOL(hAPP(U_2295,bool,U_2294,U_2292))
      | ~ hBOOL(hAPP(fun(U_2295,bool),bool,hAPP(fun(U_2295,bool),fun(fun(U_2295,bool),bool),ord_less_eq(fun(U_2295,bool)),U_2293),U_2294))
      | ~ hBOOL(hAPP(U_2295,bool,U_2293,U_2292)) ),
    inference(definitional_conversion,[status(esa)],[f_608_2]) ).

cnf(f_608_4,plain,
    ( hBOOL(hAPP(U_2295,bool,U_2294,U_2292))
    | ~ hBOOL(hAPP(fun(U_2295,bool),bool,hAPP(fun(U_2295,bool),fun(fun(U_2295,bool),bool),ord_less_eq(fun(U_2295,bool)),U_2293),U_2294))
    | ~ hBOOL(hAPP(U_2295,bool,U_2293,U_2292)) ),
    inference(clausify,[status(thm)],[f_608_3]) ).

fof(f_609_1,plain,
    ! [X_b,X_1,Pa,Q_3] :
      ( hBOOL(hAPP(X_b,bool,Q_3,X_1))
      | ~ hBOOL(hAPP(X_b,bool,Pa,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)),Pa),Q_3)) ),
    inference(fof_nnf,[status(thm)],[fact_538_predicate1D]) ).

fof(f_609_2,plain,
    ! [U_2299,U_2298,U_2297,U_2296] :
      ( hBOOL(hAPP(U_2299,bool,U_2296,U_2298))
      | ~ hBOOL(hAPP(U_2299,bool,U_2297,U_2298))
      | ~ hBOOL(hAPP(fun(U_2299,bool),bool,hAPP(fun(U_2299,bool),fun(fun(U_2299,bool),bool),ord_less_eq(fun(U_2299,bool)),U_2297),U_2296)) ),
    inference(variable_rename,[status(thm)],[f_609_1]) ).

fof(f_609_3,plain,
    ! [U_2299,U_2297,U_2296,U_2298] :
      ( hBOOL(hAPP(U_2299,bool,U_2296,U_2298))
      | ~ hBOOL(hAPP(U_2299,bool,U_2297,U_2298))
      | ~ hBOOL(hAPP(fun(U_2299,bool),bool,hAPP(fun(U_2299,bool),fun(fun(U_2299,bool),bool),ord_less_eq(fun(U_2299,bool)),U_2297),U_2296)) ),
    inference(definitional_conversion,[status(esa)],[f_609_2]) ).

cnf(f_609_4,plain,
    ( hBOOL(hAPP(U_2299,bool,U_2296,U_2298))
    | ~ hBOOL(hAPP(U_2299,bool,U_2297,U_2298))
    | ~ hBOOL(hAPP(fun(U_2299,bool),bool,hAPP(fun(U_2299,bool),fun(fun(U_2299,bool),bool),ord_less_eq(fun(U_2299,bool)),U_2297),U_2296)) ),
    inference(clausify,[status(thm)],[f_609_3]) ).

fof(f_610_1,plain,
    ! [Pa,A_2,B_3] :
      ( ( hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A_2),B_3)))
        | ? [D_2] :
            ( ~ hBOOL(hAPP(nat,bool,Pa,D_2))
            & A_2 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B_3),D_2) )
        | ( ~ hBOOL(hAPP(nat,bool,Pa,zero_zero(nat)))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_2),B_3)) ) )
      & ( ( ! [D_2] :
              ( hBOOL(hAPP(nat,bool,Pa,D_2))
              | A_2 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B_3),D_2) )
          & ( hBOOL(hAPP(nat,bool,Pa,zero_zero(nat)))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_2),B_3)) ) )
        | ~ hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A_2),B_3))) ) ),
    inference(fof_nnf,[status(thm)],[fact_539_nat__diff__split]) ).

fof(f_610_2,plain,
    ! [U_2304,U_2303,U_2302] :
      ( ( hBOOL(hAPP(nat,bool,U_2304,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2303),U_2302)))
        | ? [U_2301] :
            ( ~ hBOOL(hAPP(nat,bool,U_2304,U_2301))
            & U_2303 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2302),U_2301) )
        | ( ~ hBOOL(hAPP(nat,bool,U_2304,zero_zero(nat)))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2303),U_2302)) ) )
      & ( ( ! [U_2300] :
              ( hBOOL(hAPP(nat,bool,U_2304,U_2300))
              | U_2303 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2302),U_2300) )
          & ( hBOOL(hAPP(nat,bool,U_2304,zero_zero(nat)))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2303),U_2302)) ) )
        | ~ hBOOL(hAPP(nat,bool,U_2304,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2303),U_2302))) ) ),
    inference(variable_rename,[status(thm)],[f_610_1]) ).

fof(f_610_3,plain,
    ( ! [U_2310,U_2308,U_2306] :
        ( hBOOL(hAPP(nat,bool,U_2310,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2308),U_2306)))
        | ? [U_2301] :
            ( ~ hBOOL(hAPP(nat,bool,U_2310,U_2301))
            & U_2308 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2306),U_2301) )
        | ( ~ hBOOL(hAPP(nat,bool,U_2310,zero_zero(nat)))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2308),U_2306)) ) )
    & ! [U_2309,U_2307,U_2305] :
        ( ( ! [U_2300] :
              ( hBOOL(hAPP(nat,bool,U_2309,U_2300))
              | U_2307 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2305),U_2300) )
          & ( hBOOL(hAPP(nat,bool,U_2309,zero_zero(nat)))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2307),U_2305)) ) )
        | ~ hBOOL(hAPP(nat,bool,U_2309,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2307),U_2305))) ) ),
    inference(miniscope,[status(thm)],[f_610_2]) ).

fof(f_610_4,plain,
    ( ! [U_2310,U_2308,U_2306] :
        ( hBOOL(hAPP(nat,bool,U_2310,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2308),U_2306)))
        | ( ~ hBOOL(hAPP(nat,bool,U_2310,sK84(U_2310,U_2308,U_2306)))
          & U_2308 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2306),sK84(U_2310,U_2308,U_2306)) )
        | ( ~ hBOOL(hAPP(nat,bool,U_2310,zero_zero(nat)))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2308),U_2306)) ) )
    & ! [U_2309,U_2307,U_2305] :
        ( ( ! [U_2300] :
              ( hBOOL(hAPP(nat,bool,U_2309,U_2300))
              | U_2307 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2305),U_2300) )
          & ( hBOOL(hAPP(nat,bool,U_2309,zero_zero(nat)))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2307),U_2305)) ) )
        | ~ hBOOL(hAPP(nat,bool,U_2309,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2307),U_2305))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK84]),skolemize(U_2301,sK84(U_2310,U_2308,U_2306))],[f_610_3]) ).

fof(f_610_5,plain,
    ( ! [U_2308,U_2306,U_2310] :
        ( ~ hBOOL(hAPP(nat,bool,U_2310,sK84(U_2310,U_2308,U_2306)))
        | ~ sP151(U_2308,U_2306,U_2310) )
    & ! [U_2308,U_2306,U_2310] :
        ( U_2308 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2306),sK84(U_2310,U_2308,U_2306))
        | ~ sP151(U_2308,U_2306,U_2310) )
    & ! [U_2308,U_2306,U_2310] :
        ( ~ hBOOL(hAPP(nat,bool,U_2310,zero_zero(nat)))
        | ~ sP150(U_2308,U_2306,U_2310) )
    & ! [U_2308,U_2306,U_2310] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2308),U_2306))
        | ~ sP150(U_2308,U_2306,U_2310) )
    & ! [U_2300,U_2309,U_2305,U_2307] :
        ( hBOOL(hAPP(nat,bool,U_2309,U_2300))
        | U_2307 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2305),U_2300)
        | ~ sP149(U_2300,U_2309,U_2305,U_2307) )
    & ! [U_2300,U_2309,U_2305,U_2307] :
        ( hBOOL(hAPP(nat,bool,U_2309,zero_zero(nat)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2307),U_2305))
        | ~ sP149(U_2300,U_2309,U_2305,U_2307) )
    & ! [U_2308,U_2306,U_2310] :
        ( hBOOL(hAPP(nat,bool,U_2310,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2308),U_2306)))
        | sP151(U_2308,U_2306,U_2310)
        | sP150(U_2308,U_2306,U_2310) )
    & ! [U_2300,U_2309,U_2305,U_2307] :
        ( sP149(U_2300,U_2309,U_2305,U_2307)
        | ~ hBOOL(hAPP(nat,bool,U_2309,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2307),U_2305))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP149,sP150,sP151])],[f_610_4]) ).

cnf(f_610_6,plain,
    ( sP149(U_2300,U_2309,U_2305,U_2307)
    | ~ hBOOL(hAPP(nat,bool,U_2309,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2307),U_2305))) ),
    inference(clausify,[status(thm)],[f_610_5]) ).

cnf(f_610_7,plain,
    ( hBOOL(hAPP(nat,bool,U_2310,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2308),U_2306)))
    | sP151(U_2308,U_2306,U_2310)
    | sP150(U_2308,U_2306,U_2310) ),
    inference(clausify,[status(thm)],[f_610_5]) ).

cnf(f_610_8,plain,
    ( hBOOL(hAPP(nat,bool,U_2309,zero_zero(nat)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2307),U_2305))
    | ~ sP149(U_2300,U_2309,U_2305,U_2307) ),
    inference(clausify,[status(thm)],[f_610_5]) ).

cnf(f_610_9,plain,
    ( hBOOL(hAPP(nat,bool,U_2309,U_2300))
    | U_2307 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2305),U_2300)
    | ~ sP149(U_2300,U_2309,U_2305,U_2307) ),
    inference(clausify,[status(thm)],[f_610_5]) ).

cnf(f_610_10,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2308),U_2306))
    | ~ sP150(U_2308,U_2306,U_2310) ),
    inference(clausify,[status(thm)],[f_610_5]) ).

cnf(f_610_11,plain,
    ( ~ hBOOL(hAPP(nat,bool,U_2310,zero_zero(nat)))
    | ~ sP150(U_2308,U_2306,U_2310) ),
    inference(clausify,[status(thm)],[f_610_5]) ).

cnf(f_610_12,plain,
    ( U_2308 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2306),sK84(U_2310,U_2308,U_2306))
    | ~ sP151(U_2308,U_2306,U_2310) ),
    inference(clausify,[status(thm)],[f_610_5]) ).

cnf(f_610_13,plain,
    ( ~ hBOOL(hAPP(nat,bool,U_2310,sK84(U_2310,U_2308,U_2306)))
    | ~ sP151(U_2308,U_2306,U_2310) ),
    inference(clausify,[status(thm)],[f_610_5]) ).

fof(f_611_1,plain,
    ! [Pa,A_2,B_3] :
      ( ( hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A_2),B_3)))
        | ? [D_2] :
            ( ~ hBOOL(hAPP(nat,bool,Pa,D_2))
            & A_2 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B_3),D_2) )
        | ( ~ hBOOL(hAPP(nat,bool,Pa,zero_zero(nat)))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_2),B_3)) ) )
      & ( ( ! [D_2] :
              ( hBOOL(hAPP(nat,bool,Pa,D_2))
              | A_2 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B_3),D_2) )
          & ( hBOOL(hAPP(nat,bool,Pa,zero_zero(nat)))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_2),B_3)) ) )
        | ~ hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A_2),B_3))) ) ),
    inference(fof_nnf,[status(thm)],[fact_540_nat__diff__split__asm]) ).

fof(f_611_2,plain,
    ! [U_2315,U_2314,U_2313] :
      ( ( hBOOL(hAPP(nat,bool,U_2315,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2314),U_2313)))
        | ? [U_2312] :
            ( ~ hBOOL(hAPP(nat,bool,U_2315,U_2312))
            & U_2314 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2313),U_2312) )
        | ( ~ hBOOL(hAPP(nat,bool,U_2315,zero_zero(nat)))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2314),U_2313)) ) )
      & ( ( ! [U_2311] :
              ( hBOOL(hAPP(nat,bool,U_2315,U_2311))
              | U_2314 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2313),U_2311) )
          & ( hBOOL(hAPP(nat,bool,U_2315,zero_zero(nat)))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2314),U_2313)) ) )
        | ~ hBOOL(hAPP(nat,bool,U_2315,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2314),U_2313))) ) ),
    inference(variable_rename,[status(thm)],[f_611_1]) ).

fof(f_611_3,plain,
    ( ! [U_2321,U_2319,U_2317] :
        ( hBOOL(hAPP(nat,bool,U_2321,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2319),U_2317)))
        | ? [U_2312] :
            ( ~ hBOOL(hAPP(nat,bool,U_2321,U_2312))
            & U_2319 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2317),U_2312) )
        | ( ~ hBOOL(hAPP(nat,bool,U_2321,zero_zero(nat)))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2319),U_2317)) ) )
    & ! [U_2320,U_2318,U_2316] :
        ( ( ! [U_2311] :
              ( hBOOL(hAPP(nat,bool,U_2320,U_2311))
              | U_2318 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2316),U_2311) )
          & ( hBOOL(hAPP(nat,bool,U_2320,zero_zero(nat)))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2318),U_2316)) ) )
        | ~ hBOOL(hAPP(nat,bool,U_2320,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2318),U_2316))) ) ),
    inference(miniscope,[status(thm)],[f_611_2]) ).

fof(f_611_4,plain,
    ( ! [U_2321,U_2319,U_2317] :
        ( hBOOL(hAPP(nat,bool,U_2321,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2319),U_2317)))
        | ( ~ hBOOL(hAPP(nat,bool,U_2321,sK85(U_2321,U_2319,U_2317)))
          & U_2319 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2317),sK85(U_2321,U_2319,U_2317)) )
        | ( ~ hBOOL(hAPP(nat,bool,U_2321,zero_zero(nat)))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2319),U_2317)) ) )
    & ! [U_2320,U_2318,U_2316] :
        ( ( ! [U_2311] :
              ( hBOOL(hAPP(nat,bool,U_2320,U_2311))
              | U_2318 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2316),U_2311) )
          & ( hBOOL(hAPP(nat,bool,U_2320,zero_zero(nat)))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2318),U_2316)) ) )
        | ~ hBOOL(hAPP(nat,bool,U_2320,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2318),U_2316))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK85]),skolemize(U_2312,sK85(U_2321,U_2319,U_2317))],[f_611_3]) ).

fof(f_611_5,plain,
    ( ! [U_2319,U_2317,U_2321] :
        ( ~ hBOOL(hAPP(nat,bool,U_2321,sK85(U_2321,U_2319,U_2317)))
        | ~ sP154(U_2319,U_2317,U_2321) )
    & ! [U_2319,U_2317,U_2321] :
        ( U_2319 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2317),sK85(U_2321,U_2319,U_2317))
        | ~ sP154(U_2319,U_2317,U_2321) )
    & ! [U_2319,U_2317,U_2321] :
        ( ~ hBOOL(hAPP(nat,bool,U_2321,zero_zero(nat)))
        | ~ sP153(U_2319,U_2317,U_2321) )
    & ! [U_2319,U_2317,U_2321] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2319),U_2317))
        | ~ sP153(U_2319,U_2317,U_2321) )
    & ! [U_2311,U_2318,U_2316,U_2320] :
        ( hBOOL(hAPP(nat,bool,U_2320,U_2311))
        | U_2318 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2316),U_2311)
        | ~ sP152(U_2311,U_2318,U_2316,U_2320) )
    & ! [U_2311,U_2318,U_2316,U_2320] :
        ( hBOOL(hAPP(nat,bool,U_2320,zero_zero(nat)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2318),U_2316))
        | ~ sP152(U_2311,U_2318,U_2316,U_2320) )
    & ! [U_2319,U_2317,U_2321] :
        ( hBOOL(hAPP(nat,bool,U_2321,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2319),U_2317)))
        | sP154(U_2319,U_2317,U_2321)
        | sP153(U_2319,U_2317,U_2321) )
    & ! [U_2311,U_2318,U_2316,U_2320] :
        ( sP152(U_2311,U_2318,U_2316,U_2320)
        | ~ hBOOL(hAPP(nat,bool,U_2320,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2318),U_2316))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP152,sP153,sP154])],[f_611_4]) ).

cnf(f_611_6,plain,
    ( sP152(U_2311,U_2318,U_2316,U_2320)
    | ~ hBOOL(hAPP(nat,bool,U_2320,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2318),U_2316))) ),
    inference(clausify,[status(thm)],[f_611_5]) ).

cnf(f_611_7,plain,
    ( hBOOL(hAPP(nat,bool,U_2321,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2319),U_2317)))
    | sP154(U_2319,U_2317,U_2321)
    | sP153(U_2319,U_2317,U_2321) ),
    inference(clausify,[status(thm)],[f_611_5]) ).

cnf(f_611_8,plain,
    ( hBOOL(hAPP(nat,bool,U_2320,zero_zero(nat)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2318),U_2316))
    | ~ sP152(U_2311,U_2318,U_2316,U_2320) ),
    inference(clausify,[status(thm)],[f_611_5]) ).

cnf(f_611_9,plain,
    ( hBOOL(hAPP(nat,bool,U_2320,U_2311))
    | U_2318 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2316),U_2311)
    | ~ sP152(U_2311,U_2318,U_2316,U_2320) ),
    inference(clausify,[status(thm)],[f_611_5]) ).

cnf(f_611_10,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2319),U_2317))
    | ~ sP153(U_2319,U_2317,U_2321) ),
    inference(clausify,[status(thm)],[f_611_5]) ).

cnf(f_611_11,plain,
    ( ~ hBOOL(hAPP(nat,bool,U_2321,zero_zero(nat)))
    | ~ sP153(U_2319,U_2317,U_2321) ),
    inference(clausify,[status(thm)],[f_611_5]) ).

cnf(f_611_12,plain,
    ( U_2319 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2317),sK85(U_2321,U_2319,U_2317))
    | ~ sP154(U_2319,U_2317,U_2321) ),
    inference(clausify,[status(thm)],[f_611_5]) ).

cnf(f_611_13,plain,
    ( ~ hBOOL(hAPP(nat,bool,U_2321,sK85(U_2321,U_2319,U_2317)))
    | ~ sP154(U_2319,U_2317,U_2321) ),
    inference(clausify,[status(thm)],[f_611_5]) ).

fof(f_612_1,plain,
    ! [I_1,M_3] :
      ( hAPP(nat,nat,suc,hAPP(fun(nat,bool),nat,finite_card(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),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),M_3))),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))))) = hAPP(fun(nat,bool),nat,finite_card(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),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),M_3))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,I_1)))))
      | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),M_3)) ),
    inference(fof_nnf,[status(thm)],[fact_541_card__less__Suc]) ).

fof(f_612_2,plain,
    ! [U_2323,U_2322] :
      ( hAPP(nat,nat,suc,hAPP(fun(nat,bool),nat,finite_card(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),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),U_2322))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_2323))))) = hAPP(fun(nat,bool),nat,finite_card(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),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),U_2322))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,U_2323)))))
      | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),U_2322)) ),
    inference(variable_rename,[status(thm)],[f_612_1]) ).

fof(f_612_3,plain,
    ! [U_2323,U_2322] :
      ( hAPP(nat,nat,suc,hAPP(fun(nat,bool),nat,finite_card(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),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),U_2322))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_2323))))) = hAPP(fun(nat,bool),nat,finite_card(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),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),U_2322))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,U_2323)))))
      | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),U_2322)) ),
    inference(definitional_conversion,[status(esa)],[f_612_2]) ).

cnf(f_612_4,plain,
    ( hAPP(nat,nat,suc,hAPP(fun(nat,bool),nat,finite_card(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),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),U_2322))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_2323))))) = hAPP(fun(nat,bool),nat,finite_card(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),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),U_2322))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,U_2323)))))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),U_2322)) ),
    inference(clausify,[status(thm)],[f_612_3]) ).

fof(f_613_1,plain,
    ! [I_1,M_3] :
      ( hAPP(fun(nat,bool),nat,finite_card(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),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),M_3))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,I_1))))) != zero_zero(nat)
      | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),M_3)) ),
    inference(fof_nnf,[status(thm)],[fact_542_card__less]) ).

fof(f_613_2,plain,
    ! [U_2325,U_2324] :
      ( hAPP(fun(nat,bool),nat,finite_card(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),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),U_2324))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,U_2325))))) != zero_zero(nat)
      | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),U_2324)) ),
    inference(variable_rename,[status(thm)],[f_613_1]) ).

fof(f_613_3,plain,
    ! [U_2324,U_2325] :
      ( hAPP(fun(nat,bool),nat,finite_card(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),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),U_2324))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,U_2325))))) != zero_zero(nat)
      | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),U_2324)) ),
    inference(definitional_conversion,[status(esa)],[f_613_2]) ).

cnf(f_613_4,plain,
    ( hAPP(fun(nat,bool),nat,finite_card(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),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),U_2324))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,U_2325))))) != zero_zero(nat)
    | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),U_2324)) ),
    inference(clausify,[status(thm)],[f_613_3]) ).

fof(f_614_1,plain,
    ! [I_1,M_3] :
      ( hAPP(fun(nat,bool),nat,finite_card(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),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),M_3))),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)))) = hAPP(fun(nat,bool),nat,finite_card(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),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),M_3))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,I_1)))))
      | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),M_3)) ),
    inference(fof_nnf,[status(thm)],[fact_543_card__less__Suc2]) ).

fof(f_614_2,plain,
    ! [U_2327,U_2326] :
      ( hAPP(fun(nat,bool),nat,finite_card(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),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),U_2326))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_2327)))) = hAPP(fun(nat,bool),nat,finite_card(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),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),U_2326))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,U_2327)))))
      | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),U_2326)) ),
    inference(variable_rename,[status(thm)],[f_614_1]) ).

fof(f_614_3,plain,
    ! [U_2326,U_2327] :
      ( hAPP(fun(nat,bool),nat,finite_card(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),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),U_2326))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_2327)))) = hAPP(fun(nat,bool),nat,finite_card(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),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),U_2326))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,U_2327)))))
      | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),U_2326)) ),
    inference(definitional_conversion,[status(esa)],[f_614_2]) ).

cnf(f_614_4,plain,
    ( hAPP(fun(nat,bool),nat,finite_card(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),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),U_2326))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_2327)))) = hAPP(fun(nat,bool),nat,finite_card(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),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),U_2326))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,U_2327)))))
    | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),U_2326)) ),
    inference(clausify,[status(thm)],[f_614_3]) ).

fof(f_615_1,plain,
    ! [X_b,A_3] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),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))
        | 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))
          & ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) )
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))) ) ),
    inference(fof_nnf,[status(thm)],[fact_544_card__gt__0__iff]) ).

fof(f_615_2,plain,
    ! [U_2329,U_2328] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(U_2329,bool),nat,finite_card(U_2329),U_2328)))
        | ~ hBOOL(hAPP(fun(U_2329,bool),bool,finite_finite(U_2329),U_2328))
        | ti(fun(U_2329,bool),U_2328) = bot_bot(fun(U_2329,bool)) )
      & ( ( hBOOL(hAPP(fun(U_2329,bool),bool,finite_finite(U_2329),U_2328))
          & ti(fun(U_2329,bool),U_2328) != bot_bot(fun(U_2329,bool)) )
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(U_2329,bool),nat,finite_card(U_2329),U_2328))) ) ),
    inference(variable_rename,[status(thm)],[f_615_1]) ).

fof(f_615_3,plain,
    ( ! [U_2333,U_2331] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(U_2333,bool),nat,finite_card(U_2333),U_2331)))
        | ~ hBOOL(hAPP(fun(U_2333,bool),bool,finite_finite(U_2333),U_2331))
        | ti(fun(U_2333,bool),U_2331) = bot_bot(fun(U_2333,bool)) )
    & ! [U_2332,U_2330] :
        ( ( hBOOL(hAPP(fun(U_2332,bool),bool,finite_finite(U_2332),U_2330))
          & ti(fun(U_2332,bool),U_2330) != bot_bot(fun(U_2332,bool)) )
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(U_2332,bool),nat,finite_card(U_2332),U_2330))) ) ),
    inference(miniscope,[status(thm)],[f_615_2]) ).

fof(f_615_4,plain,
    ( ! [U_2330,U_2332] :
        ( hBOOL(hAPP(fun(U_2332,bool),bool,finite_finite(U_2332),U_2330))
        | ~ sP155(U_2330,U_2332) )
    & ! [U_2330,U_2332] :
        ( ti(fun(U_2332,bool),U_2330) != bot_bot(fun(U_2332,bool))
        | ~ sP155(U_2330,U_2332) )
    & ! [U_2333,U_2331] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(U_2333,bool),nat,finite_card(U_2333),U_2331)))
        | ~ hBOOL(hAPP(fun(U_2333,bool),bool,finite_finite(U_2333),U_2331))
        | ti(fun(U_2333,bool),U_2331) = bot_bot(fun(U_2333,bool)) )
    & ! [U_2330,U_2332] :
        ( sP155(U_2330,U_2332)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(U_2332,bool),nat,finite_card(U_2332),U_2330))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP155])],[f_615_3]) ).

cnf(f_615_5,plain,
    ( sP155(U_2330,U_2332)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(U_2332,bool),nat,finite_card(U_2332),U_2330))) ),
    inference(clausify,[status(thm)],[f_615_4]) ).

cnf(f_615_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(U_2333,bool),nat,finite_card(U_2333),U_2331)))
    | ~ hBOOL(hAPP(fun(U_2333,bool),bool,finite_finite(U_2333),U_2331))
    | ti(fun(U_2333,bool),U_2331) = bot_bot(fun(U_2333,bool)) ),
    inference(clausify,[status(thm)],[f_615_4]) ).

cnf(f_615_7,plain,
    ( ti(fun(U_2332,bool),U_2330) != bot_bot(fun(U_2332,bool))
    | ~ sP155(U_2330,U_2332) ),
    inference(clausify,[status(thm)],[f_615_4]) ).

cnf(f_615_8,plain,
    ( hBOOL(hAPP(fun(U_2332,bool),bool,finite_finite(U_2332),U_2330))
    | ~ sP155(U_2330,U_2332) ),
    inference(clausify,[status(thm)],[f_615_4]) ).

fof(f_616_1,plain,
    ! [N] :
      ( hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat))) = N
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) ),
    inference(fof_nnf,[status(thm)],[fact_545_Suc__diff__1]) ).

fof(f_616_2,plain,
    ! [U_2334] :
      ( hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2334),one_one(nat))) = U_2334
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2334)) ),
    inference(variable_rename,[status(thm)],[f_616_1]) ).

fof(f_616_3,plain,
    ! [U_2334] :
      ( hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2334),one_one(nat))) = U_2334
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2334)) ),
    inference(definitional_conversion,[status(esa)],[f_616_2]) ).

cnf(f_616_4,plain,
    ( hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2334),one_one(nat))) = U_2334
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2334)) ),
    inference(clausify,[status(thm)],[f_616_3]) ).

fof(f_617_1,plain,
    ! [N] :
      ( N = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) ),
    inference(fof_nnf,[status(thm)],[fact_546_Suc__pred_H]) ).

fof(f_617_2,plain,
    ! [U_2335] :
      ( U_2335 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2335),one_one(nat)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2335)) ),
    inference(variable_rename,[status(thm)],[f_617_1]) ).

fof(f_617_3,plain,
    ! [U_2335] :
      ( U_2335 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2335),one_one(nat)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2335)) ),
    inference(definitional_conversion,[status(esa)],[f_617_2]) ).

cnf(f_617_4,plain,
    ( U_2335 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2335),one_one(nat)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2335)) ),
    inference(clausify,[status(thm)],[f_617_3]) ).

fof(f_618_1,plain,
    ! [N,M_1] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),one_one(nat))),N))
        | M_1 = zero_zero(nat) )
      & ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N) = N
        | M_1 != zero_zero(nat) ) ),
    inference(fof_nnf,[status(thm)],[fact_547_add__eq__if]) ).

fof(f_618_2,plain,
    ! [U_2337,U_2336] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2336),U_2337) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2336),one_one(nat))),U_2337))
        | U_2336 = zero_zero(nat) )
      & ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2336),U_2337) = U_2337
        | U_2336 != zero_zero(nat) ) ),
    inference(variable_rename,[status(thm)],[f_618_1]) ).

fof(f_618_3,plain,
    ( ! [U_2341,U_2339] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2339),U_2341) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2339),one_one(nat))),U_2341))
        | U_2339 = zero_zero(nat) )
    & ! [U_2340,U_2338] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2338),U_2340) = U_2340
        | U_2338 != zero_zero(nat) ) ),
    inference(miniscope,[status(thm)],[f_618_2]) ).

fof(f_618_4,plain,
    ( ! [U_2341,U_2339] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2339),U_2341) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2339),one_one(nat))),U_2341))
        | U_2339 = zero_zero(nat) )
    & ! [U_2338,U_2340] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2338),U_2340) = U_2340
        | U_2338 != zero_zero(nat) ) ),
    inference(definitional_conversion,[status(esa)],[f_618_3]) ).

cnf(f_618_5,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2338),U_2340) = U_2340
    | U_2338 != zero_zero(nat) ),
    inference(clausify,[status(thm)],[f_618_4]) ).

cnf(f_618_6,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2339),U_2341) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2339),one_one(nat))),U_2341))
    | U_2339 = zero_zero(nat) ),
    inference(clausify,[status(thm)],[f_618_4]) ).

fof(f_619_1,plain,
    ! [Na,Pa] :
      ( ? [K_2] :
          ( hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_2),one_one(nat))))
          & ! [I] :
              ( ~ hBOOL(hAPP(nat,bool,Pa,I))
              | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),K_2)) )
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_2),Na)) )
      | ~ hBOOL(hAPP(nat,bool,Pa,Na))
      | hBOOL(hAPP(nat,bool,Pa,zero_zero(nat))) ),
    inference(fof_nnf,[status(thm)],[fact_548_ex__least__nat__less]) ).

fof(f_619_2,plain,
    ! [U_2345,U_2344] :
      ( ? [U_2343] :
          ( hBOOL(hAPP(nat,bool,U_2344,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2343),one_one(nat))))
          & ! [U_2342] :
              ( ~ hBOOL(hAPP(nat,bool,U_2344,U_2342))
              | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2342),U_2343)) )
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2343),U_2345)) )
      | ~ hBOOL(hAPP(nat,bool,U_2344,U_2345))
      | hBOOL(hAPP(nat,bool,U_2344,zero_zero(nat))) ),
    inference(variable_rename,[status(thm)],[f_619_1]) ).

fof(f_619_3,plain,
    ! [U_2345,U_2344] :
      ( ( hBOOL(hAPP(nat,bool,U_2344,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),sK86(U_2345,U_2344)),one_one(nat))))
        & ! [U_2342] :
            ( ~ hBOOL(hAPP(nat,bool,U_2344,U_2342))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2342),sK86(U_2345,U_2344))) )
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK86(U_2345,U_2344)),U_2345)) )
      | ~ hBOOL(hAPP(nat,bool,U_2344,U_2345))
      | hBOOL(hAPP(nat,bool,U_2344,zero_zero(nat))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK86]),skolemize(U_2343,sK86(U_2345,U_2344))],[f_619_2]) ).

fof(f_619_4,plain,
    ( ! [U_2342,U_2344,U_2345] :
        ( hBOOL(hAPP(nat,bool,U_2344,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),sK86(U_2345,U_2344)),one_one(nat))))
        | ~ sP156(U_2342,U_2344,U_2345) )
    & ! [U_2342,U_2344,U_2345] :
        ( ~ hBOOL(hAPP(nat,bool,U_2344,U_2342))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2342),sK86(U_2345,U_2344)))
        | ~ sP156(U_2342,U_2344,U_2345) )
    & ! [U_2342,U_2344,U_2345] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK86(U_2345,U_2344)),U_2345))
        | ~ sP156(U_2342,U_2344,U_2345) )
    & ! [U_2342,U_2344,U_2345] :
        ( sP156(U_2342,U_2344,U_2345)
        | ~ hBOOL(hAPP(nat,bool,U_2344,U_2345))
        | hBOOL(hAPP(nat,bool,U_2344,zero_zero(nat))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP156])],[f_619_3]) ).

cnf(f_619_5,plain,
    ( sP156(U_2342,U_2344,U_2345)
    | ~ hBOOL(hAPP(nat,bool,U_2344,U_2345))
    | hBOOL(hAPP(nat,bool,U_2344,zero_zero(nat))) ),
    inference(clausify,[status(thm)],[f_619_4]) ).

cnf(f_619_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK86(U_2345,U_2344)),U_2345))
    | ~ sP156(U_2342,U_2344,U_2345) ),
    inference(clausify,[status(thm)],[f_619_4]) ).

cnf(f_619_7,plain,
    ( ~ hBOOL(hAPP(nat,bool,U_2344,U_2342))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2342),sK86(U_2345,U_2344)))
    | ~ sP156(U_2342,U_2344,U_2345) ),
    inference(clausify,[status(thm)],[f_619_4]) ).

cnf(f_619_8,plain,
    ( hBOOL(hAPP(nat,bool,U_2344,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),sK86(U_2345,U_2344)),one_one(nat))))
    | ~ sP156(U_2342,U_2344,U_2345) ),
    inference(clausify,[status(thm)],[f_619_4]) ).

fof(f_620_1,plain,
    ! [X_b,A_3,K] :
      ( ( hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3) = hAPP(nat,nat,suc,K)
        | ! [B_5,B_4] :
            ( ( ti(fun(X_b,bool),B_4) != bot_bot(fun(X_b,bool))
              & K = zero_zero(nat) )
            | hAPP(fun(X_b,bool),nat,finite_card(X_b),B_4) != K
            | hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_5),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),B_5),B_4) ) )
      & ( ? [B_5,B_4] :
            ( ( ti(fun(X_b,bool),B_4) = bot_bot(fun(X_b,bool))
              | K != zero_zero(nat) )
            & hAPP(fun(X_b,bool),nat,finite_card(X_b),B_4) = K
            & ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_5),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),B_5),B_4) )
        | hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3) != hAPP(nat,nat,suc,K) ) ),
    inference(fof_nnf,[status(thm)],[fact_549_card__Suc__eq]) ).

fof(f_620_2,plain,
    ! [U_2352,U_2351,U_2350] :
      ( ( hAPP(fun(U_2352,bool),nat,finite_card(U_2352),U_2351) = hAPP(nat,nat,suc,U_2350)
        | ! [U_2349,U_2348] :
            ( ( ti(fun(U_2352,bool),U_2348) != bot_bot(fun(U_2352,bool))
              & U_2350 = zero_zero(nat) )
            | hAPP(fun(U_2352,bool),nat,finite_card(U_2352),U_2348) != U_2350
            | hBOOL(hAPP(fun(U_2352,bool),bool,hAPP(U_2352,fun(fun(U_2352,bool),bool),member(U_2352),U_2349),U_2348))
            | ti(fun(U_2352,bool),U_2351) != hAPP(fun(U_2352,bool),fun(U_2352,bool),hAPP(U_2352,fun(fun(U_2352,bool),fun(U_2352,bool)),insert(U_2352),U_2349),U_2348) ) )
      & ( ? [U_2347,U_2346] :
            ( ( ti(fun(U_2352,bool),U_2346) = bot_bot(fun(U_2352,bool))
              | U_2350 != zero_zero(nat) )
            & hAPP(fun(U_2352,bool),nat,finite_card(U_2352),U_2346) = U_2350
            & ~ hBOOL(hAPP(fun(U_2352,bool),bool,hAPP(U_2352,fun(fun(U_2352,bool),bool),member(U_2352),U_2347),U_2346))
            & ti(fun(U_2352,bool),U_2351) = hAPP(fun(U_2352,bool),fun(U_2352,bool),hAPP(U_2352,fun(fun(U_2352,bool),fun(U_2352,bool)),insert(U_2352),U_2347),U_2346) )
        | hAPP(fun(U_2352,bool),nat,finite_card(U_2352),U_2351) != hAPP(nat,nat,suc,U_2350) ) ),
    inference(variable_rename,[status(thm)],[f_620_1]) ).

fof(f_620_3,plain,
    ( ! [U_2358,U_2356,U_2354] :
        ( hAPP(fun(U_2358,bool),nat,finite_card(U_2358),U_2356) = hAPP(nat,nat,suc,U_2354)
        | ! [U_2349,U_2348] :
            ( ( ti(fun(U_2358,bool),U_2348) != bot_bot(fun(U_2358,bool))
              & U_2354 = zero_zero(nat) )
            | hAPP(fun(U_2358,bool),nat,finite_card(U_2358),U_2348) != U_2354
            | hBOOL(hAPP(fun(U_2358,bool),bool,hAPP(U_2358,fun(fun(U_2358,bool),bool),member(U_2358),U_2349),U_2348))
            | ti(fun(U_2358,bool),U_2356) != hAPP(fun(U_2358,bool),fun(U_2358,bool),hAPP(U_2358,fun(fun(U_2358,bool),fun(U_2358,bool)),insert(U_2358),U_2349),U_2348) ) )
    & ! [U_2357,U_2355,U_2353] :
        ( ? [U_2347,U_2346] :
            ( ( ti(fun(U_2357,bool),U_2346) = bot_bot(fun(U_2357,bool))
              | U_2353 != zero_zero(nat) )
            & hAPP(fun(U_2357,bool),nat,finite_card(U_2357),U_2346) = U_2353
            & ~ hBOOL(hAPP(fun(U_2357,bool),bool,hAPP(U_2357,fun(fun(U_2357,bool),bool),member(U_2357),U_2347),U_2346))
            & ti(fun(U_2357,bool),U_2355) = hAPP(fun(U_2357,bool),fun(U_2357,bool),hAPP(U_2357,fun(fun(U_2357,bool),fun(U_2357,bool)),insert(U_2357),U_2347),U_2346) )
        | hAPP(fun(U_2357,bool),nat,finite_card(U_2357),U_2355) != hAPP(nat,nat,suc,U_2353) ) ),
    inference(miniscope,[status(thm)],[f_620_2]) ).

fof(f_620_4,plain,
    ( ! [U_2358,U_2356,U_2354] :
        ( hAPP(fun(U_2358,bool),nat,finite_card(U_2358),U_2356) = hAPP(nat,nat,suc,U_2354)
        | ! [U_2349,U_2348] :
            ( ( ti(fun(U_2358,bool),U_2348) != bot_bot(fun(U_2358,bool))
              & U_2354 = zero_zero(nat) )
            | hAPP(fun(U_2358,bool),nat,finite_card(U_2358),U_2348) != U_2354
            | hBOOL(hAPP(fun(U_2358,bool),bool,hAPP(U_2358,fun(fun(U_2358,bool),bool),member(U_2358),U_2349),U_2348))
            | ti(fun(U_2358,bool),U_2356) != hAPP(fun(U_2358,bool),fun(U_2358,bool),hAPP(U_2358,fun(fun(U_2358,bool),fun(U_2358,bool)),insert(U_2358),U_2349),U_2348) ) )
    & ! [U_2357,U_2355,U_2353] :
        ( ? [U_2346] :
            ( ( ti(fun(U_2357,bool),U_2346) = bot_bot(fun(U_2357,bool))
              | U_2353 != zero_zero(nat) )
            & hAPP(fun(U_2357,bool),nat,finite_card(U_2357),U_2346) = U_2353
            & ~ hBOOL(hAPP(fun(U_2357,bool),bool,hAPP(U_2357,fun(fun(U_2357,bool),bool),member(U_2357),sK87(U_2357,U_2355,U_2353)),U_2346))
            & ti(fun(U_2357,bool),U_2355) = hAPP(fun(U_2357,bool),fun(U_2357,bool),hAPP(U_2357,fun(fun(U_2357,bool),fun(U_2357,bool)),insert(U_2357),sK87(U_2357,U_2355,U_2353)),U_2346) )
        | hAPP(fun(U_2357,bool),nat,finite_card(U_2357),U_2355) != hAPP(nat,nat,suc,U_2353) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK87]),skolemize(U_2347,sK87(U_2357,U_2355,U_2353))],[f_620_3]) ).

fof(f_620_5,plain,
    ( ! [U_2358,U_2356,U_2354] :
        ( hAPP(fun(U_2358,bool),nat,finite_card(U_2358),U_2356) = hAPP(nat,nat,suc,U_2354)
        | ! [U_2349,U_2348] :
            ( ( ti(fun(U_2358,bool),U_2348) != bot_bot(fun(U_2358,bool))
              & U_2354 = zero_zero(nat) )
            | hAPP(fun(U_2358,bool),nat,finite_card(U_2358),U_2348) != U_2354
            | hBOOL(hAPP(fun(U_2358,bool),bool,hAPP(U_2358,fun(fun(U_2358,bool),bool),member(U_2358),U_2349),U_2348))
            | ti(fun(U_2358,bool),U_2356) != hAPP(fun(U_2358,bool),fun(U_2358,bool),hAPP(U_2358,fun(fun(U_2358,bool),fun(U_2358,bool)),insert(U_2358),U_2349),U_2348) ) )
    & ! [U_2357,U_2355,U_2353] :
        ( ( ( ti(fun(U_2357,bool),sK88(U_2357,U_2355,U_2353)) = bot_bot(fun(U_2357,bool))
            | U_2353 != zero_zero(nat) )
          & hAPP(fun(U_2357,bool),nat,finite_card(U_2357),sK88(U_2357,U_2355,U_2353)) = U_2353
          & ~ hBOOL(hAPP(fun(U_2357,bool),bool,hAPP(U_2357,fun(fun(U_2357,bool),bool),member(U_2357),sK87(U_2357,U_2355,U_2353)),sK88(U_2357,U_2355,U_2353)))
          & ti(fun(U_2357,bool),U_2355) = hAPP(fun(U_2357,bool),fun(U_2357,bool),hAPP(U_2357,fun(fun(U_2357,bool),fun(U_2357,bool)),insert(U_2357),sK87(U_2357,U_2355,U_2353)),sK88(U_2357,U_2355,U_2353)) )
        | hAPP(fun(U_2357,bool),nat,finite_card(U_2357),U_2355) != hAPP(nat,nat,suc,U_2353) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK88]),skolemize(U_2346,sK88(U_2357,U_2355,U_2353))],[f_620_4]) ).

fof(f_620_6,plain,
    ( ! [U_2354,U_2348,U_2358] :
        ( ti(fun(U_2358,bool),U_2348) != bot_bot(fun(U_2358,bool))
        | ~ sP158(U_2354,U_2348,U_2358) )
    & ! [U_2354,U_2348,U_2358] :
        ( U_2354 = zero_zero(nat)
        | ~ sP158(U_2354,U_2348,U_2358) )
    & ! [U_2355,U_2353,U_2357] :
        ( ti(fun(U_2357,bool),sK88(U_2357,U_2355,U_2353)) = bot_bot(fun(U_2357,bool))
        | U_2353 != zero_zero(nat)
        | ~ sP157(U_2355,U_2353,U_2357) )
    & ! [U_2355,U_2353,U_2357] :
        ( hAPP(fun(U_2357,bool),nat,finite_card(U_2357),sK88(U_2357,U_2355,U_2353)) = U_2353
        | ~ sP157(U_2355,U_2353,U_2357) )
    & ! [U_2355,U_2353,U_2357] :
        ( ~ hBOOL(hAPP(fun(U_2357,bool),bool,hAPP(U_2357,fun(fun(U_2357,bool),bool),member(U_2357),sK87(U_2357,U_2355,U_2353)),sK88(U_2357,U_2355,U_2353)))
        | ~ sP157(U_2355,U_2353,U_2357) )
    & ! [U_2355,U_2353,U_2357] :
        ( ti(fun(U_2357,bool),U_2355) = hAPP(fun(U_2357,bool),fun(U_2357,bool),hAPP(U_2357,fun(fun(U_2357,bool),fun(U_2357,bool)),insert(U_2357),sK87(U_2357,U_2355,U_2353)),sK88(U_2357,U_2355,U_2353))
        | ~ sP157(U_2355,U_2353,U_2357) )
    & ! [U_2354,U_2348,U_2349,U_2356,U_2358] :
        ( hAPP(fun(U_2358,bool),nat,finite_card(U_2358),U_2356) = hAPP(nat,nat,suc,U_2354)
        | sP158(U_2354,U_2348,U_2358)
        | hAPP(fun(U_2358,bool),nat,finite_card(U_2358),U_2348) != U_2354
        | hBOOL(hAPP(fun(U_2358,bool),bool,hAPP(U_2358,fun(fun(U_2358,bool),bool),member(U_2358),U_2349),U_2348))
        | ti(fun(U_2358,bool),U_2356) != hAPP(fun(U_2358,bool),fun(U_2358,bool),hAPP(U_2358,fun(fun(U_2358,bool),fun(U_2358,bool)),insert(U_2358),U_2349),U_2348) )
    & ! [U_2355,U_2353,U_2357] :
        ( sP157(U_2355,U_2353,U_2357)
        | hAPP(fun(U_2357,bool),nat,finite_card(U_2357),U_2355) != hAPP(nat,nat,suc,U_2353) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP157,sP158])],[f_620_5]) ).

cnf(f_620_7,plain,
    ( sP157(U_2355,U_2353,U_2357)
    | hAPP(fun(U_2357,bool),nat,finite_card(U_2357),U_2355) != hAPP(nat,nat,suc,U_2353) ),
    inference(clausify,[status(thm)],[f_620_6]) ).

cnf(f_620_8,plain,
    ( hAPP(fun(U_2358,bool),nat,finite_card(U_2358),U_2356) = hAPP(nat,nat,suc,U_2354)
    | sP158(U_2354,U_2348,U_2358)
    | hAPP(fun(U_2358,bool),nat,finite_card(U_2358),U_2348) != U_2354
    | hBOOL(hAPP(fun(U_2358,bool),bool,hAPP(U_2358,fun(fun(U_2358,bool),bool),member(U_2358),U_2349),U_2348))
    | ti(fun(U_2358,bool),U_2356) != hAPP(fun(U_2358,bool),fun(U_2358,bool),hAPP(U_2358,fun(fun(U_2358,bool),fun(U_2358,bool)),insert(U_2358),U_2349),U_2348) ),
    inference(clausify,[status(thm)],[f_620_6]) ).

cnf(f_620_9,plain,
    ( ti(fun(U_2357,bool),U_2355) = hAPP(fun(U_2357,bool),fun(U_2357,bool),hAPP(U_2357,fun(fun(U_2357,bool),fun(U_2357,bool)),insert(U_2357),sK87(U_2357,U_2355,U_2353)),sK88(U_2357,U_2355,U_2353))
    | ~ sP157(U_2355,U_2353,U_2357) ),
    inference(clausify,[status(thm)],[f_620_6]) ).

cnf(f_620_10,plain,
    ( ~ hBOOL(hAPP(fun(U_2357,bool),bool,hAPP(U_2357,fun(fun(U_2357,bool),bool),member(U_2357),sK87(U_2357,U_2355,U_2353)),sK88(U_2357,U_2355,U_2353)))
    | ~ sP157(U_2355,U_2353,U_2357) ),
    inference(clausify,[status(thm)],[f_620_6]) ).

cnf(f_620_11,plain,
    ( hAPP(fun(U_2357,bool),nat,finite_card(U_2357),sK88(U_2357,U_2355,U_2353)) = U_2353
    | ~ sP157(U_2355,U_2353,U_2357) ),
    inference(clausify,[status(thm)],[f_620_6]) ).

cnf(f_620_12,plain,
    ( ti(fun(U_2357,bool),sK88(U_2357,U_2355,U_2353)) = bot_bot(fun(U_2357,bool))
    | U_2353 != zero_zero(nat)
    | ~ sP157(U_2355,U_2353,U_2357) ),
    inference(clausify,[status(thm)],[f_620_6]) ).

cnf(f_620_13,plain,
    ( U_2354 = zero_zero(nat)
    | ~ sP158(U_2354,U_2348,U_2358) ),
    inference(clausify,[status(thm)],[f_620_6]) ).

cnf(f_620_14,plain,
    ( ti(fun(U_2358,bool),U_2348) != bot_bot(fun(U_2358,bool))
    | ~ sP158(U_2354,U_2348,U_2358) ),
    inference(clausify,[status(thm)],[f_620_6]) ).

fof(f_621_1,plain,
    ! [X_b,A_3] :
      ( hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3) = zero_zero(nat)
      | ( one_one(nat) != zero_zero(nat)
        & ? [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,finite_finite(X_b),A_3)) ),
    inference(fof_nnf,[status(thm)],[fact_550_card_Oneutral]) ).

fof(f_621_2,plain,
    ! [U_2361,U_2360] :
      ( hAPP(fun(U_2361,bool),nat,finite_card(U_2361),U_2360) = zero_zero(nat)
      | ( one_one(nat) != zero_zero(nat)
        & ? [U_2359] : hBOOL(hAPP(fun(U_2361,bool),bool,hAPP(U_2361,fun(fun(U_2361,bool),bool),member(U_2361),U_2359),U_2360)) )
      | ~ hBOOL(hAPP(fun(U_2361,bool),bool,finite_finite(U_2361),U_2360)) ),
    inference(variable_rename,[status(thm)],[f_621_1]) ).

fof(f_621_3,plain,
    ! [U_2361,U_2360] :
      ( hAPP(fun(U_2361,bool),nat,finite_card(U_2361),U_2360) = zero_zero(nat)
      | ( one_one(nat) != zero_zero(nat)
        & hBOOL(hAPP(fun(U_2361,bool),bool,hAPP(U_2361,fun(fun(U_2361,bool),bool),member(U_2361),sK89(U_2361,U_2360)),U_2360)) )
      | ~ hBOOL(hAPP(fun(U_2361,bool),bool,finite_finite(U_2361),U_2360)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK89]),skolemize(U_2359,sK89(U_2361,U_2360))],[f_621_2]) ).

fof(f_621_4,plain,
    ( ! [U_2361,U_2360] :
        ( one_one(nat) != zero_zero(nat)
        | ~ sP159(U_2361,U_2360) )
    & ! [U_2361,U_2360] :
        ( hBOOL(hAPP(fun(U_2361,bool),bool,hAPP(U_2361,fun(fun(U_2361,bool),bool),member(U_2361),sK89(U_2361,U_2360)),U_2360))
        | ~ sP159(U_2361,U_2360) )
    & ! [U_2361,U_2360] :
        ( hAPP(fun(U_2361,bool),nat,finite_card(U_2361),U_2360) = zero_zero(nat)
        | sP159(U_2361,U_2360)
        | ~ hBOOL(hAPP(fun(U_2361,bool),bool,finite_finite(U_2361),U_2360)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP159])],[f_621_3]) ).

cnf(f_621_5,plain,
    ( hAPP(fun(U_2361,bool),nat,finite_card(U_2361),U_2360) = zero_zero(nat)
    | sP159(U_2361,U_2360)
    | ~ hBOOL(hAPP(fun(U_2361,bool),bool,finite_finite(U_2361),U_2360)) ),
    inference(clausify,[status(thm)],[f_621_4]) ).

cnf(f_621_6,plain,
    ( hBOOL(hAPP(fun(U_2361,bool),bool,hAPP(U_2361,fun(fun(U_2361,bool),bool),member(U_2361),sK89(U_2361,U_2360)),U_2360))
    | ~ sP159(U_2361,U_2360) ),
    inference(clausify,[status(thm)],[f_621_4]) ).

cnf(f_621_7,plain,
    ( one_one(nat) != zero_zero(nat)
    | ~ sP159(U_2361,U_2360) ),
    inference(clausify,[status(thm)],[f_621_4]) ).

fof(f_622_1,plain,
    ! [Na,Pa] :
      ( ? [K_2] :
          ( hBOOL(hAPP(nat,bool,Pa,K_2))
          & ! [I] :
              ( ~ hBOOL(hAPP(nat,bool,Pa,I))
              | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),K_2)) )
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_2),Na)) )
      | ~ hBOOL(hAPP(nat,bool,Pa,Na))
      | hBOOL(hAPP(nat,bool,Pa,zero_zero(nat))) ),
    inference(fof_nnf,[status(thm)],[fact_551_ex__least__nat__le]) ).

fof(f_622_2,plain,
    ! [U_2365,U_2364] :
      ( ? [U_2363] :
          ( hBOOL(hAPP(nat,bool,U_2364,U_2363))
          & ! [U_2362] :
              ( ~ hBOOL(hAPP(nat,bool,U_2364,U_2362))
              | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2362),U_2363)) )
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2363),U_2365)) )
      | ~ hBOOL(hAPP(nat,bool,U_2364,U_2365))
      | hBOOL(hAPP(nat,bool,U_2364,zero_zero(nat))) ),
    inference(variable_rename,[status(thm)],[f_622_1]) ).

fof(f_622_3,plain,
    ! [U_2365,U_2364] :
      ( ( hBOOL(hAPP(nat,bool,U_2364,sK90(U_2365,U_2364)))
        & ! [U_2362] :
            ( ~ hBOOL(hAPP(nat,bool,U_2364,U_2362))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2362),sK90(U_2365,U_2364))) )
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sK90(U_2365,U_2364)),U_2365)) )
      | ~ hBOOL(hAPP(nat,bool,U_2364,U_2365))
      | hBOOL(hAPP(nat,bool,U_2364,zero_zero(nat))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK90]),skolemize(U_2363,sK90(U_2365,U_2364))],[f_622_2]) ).

fof(f_622_4,plain,
    ( ! [U_2364,U_2362,U_2365] :
        ( hBOOL(hAPP(nat,bool,U_2364,sK90(U_2365,U_2364)))
        | ~ sP160(U_2364,U_2362,U_2365) )
    & ! [U_2364,U_2362,U_2365] :
        ( ~ hBOOL(hAPP(nat,bool,U_2364,U_2362))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2362),sK90(U_2365,U_2364)))
        | ~ sP160(U_2364,U_2362,U_2365) )
    & ! [U_2364,U_2362,U_2365] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sK90(U_2365,U_2364)),U_2365))
        | ~ sP160(U_2364,U_2362,U_2365) )
    & ! [U_2364,U_2362,U_2365] :
        ( sP160(U_2364,U_2362,U_2365)
        | ~ hBOOL(hAPP(nat,bool,U_2364,U_2365))
        | hBOOL(hAPP(nat,bool,U_2364,zero_zero(nat))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP160])],[f_622_3]) ).

cnf(f_622_5,plain,
    ( sP160(U_2364,U_2362,U_2365)
    | ~ hBOOL(hAPP(nat,bool,U_2364,U_2365))
    | hBOOL(hAPP(nat,bool,U_2364,zero_zero(nat))) ),
    inference(clausify,[status(thm)],[f_622_4]) ).

cnf(f_622_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sK90(U_2365,U_2364)),U_2365))
    | ~ sP160(U_2364,U_2362,U_2365) ),
    inference(clausify,[status(thm)],[f_622_4]) ).

cnf(f_622_7,plain,
    ( ~ hBOOL(hAPP(nat,bool,U_2364,U_2362))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2362),sK90(U_2365,U_2364)))
    | ~ sP160(U_2364,U_2362,U_2365) ),
    inference(clausify,[status(thm)],[f_622_4]) ).

cnf(f_622_8,plain,
    ( hBOOL(hAPP(nat,bool,U_2364,sK90(U_2365,U_2364)))
    | ~ sP160(U_2364,U_2362,U_2365) ),
    inference(clausify,[status(thm)],[f_622_4]) ).

fof(f_623_1,plain,
    ! [I_2,J] :
      ( ? [K_2] :
          ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),K_2) = J
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_2)) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J)) ),
    inference(fof_nnf,[status(thm)],[fact_552_less__imp__add__positive]) ).

fof(f_623_2,plain,
    ! [U_2368,U_2367] :
      ( ? [U_2366] :
          ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2368),U_2366) = U_2367
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2366)) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2368),U_2367)) ),
    inference(variable_rename,[status(thm)],[f_623_1]) ).

fof(f_623_3,plain,
    ! [U_2368,U_2367] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2368),sK91(U_2368,U_2367)) = U_2367
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),sK91(U_2368,U_2367))) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2368),U_2367)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK91]),skolemize(U_2366,sK91(U_2368,U_2367))],[f_623_2]) ).

fof(f_623_4,plain,
    ( ! [U_2368,U_2367] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2368),sK91(U_2368,U_2367)) = U_2367
        | ~ sP161(U_2368,U_2367) )
    & ! [U_2368,U_2367] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),sK91(U_2368,U_2367)))
        | ~ sP161(U_2368,U_2367) )
    & ! [U_2368,U_2367] :
        ( sP161(U_2368,U_2367)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2368),U_2367)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP161])],[f_623_3]) ).

cnf(f_623_5,plain,
    ( sP161(U_2368,U_2367)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2368),U_2367)) ),
    inference(clausify,[status(thm)],[f_623_4]) ).

cnf(f_623_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),sK91(U_2368,U_2367)))
    | ~ sP161(U_2368,U_2367) ),
    inference(clausify,[status(thm)],[f_623_4]) ).

cnf(f_623_7,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2368),sK91(U_2368,U_2367)) = U_2367
    | ~ sP161(U_2368,U_2367) ),
    inference(clausify,[status(thm)],[f_623_4]) ).

fof(f_624_1,plain,
    ! [N] :
      ( ? [M_2] : N = hAPP(nat,nat,suc,M_2)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) ),
    inference(fof_nnf,[status(thm)],[fact_553_gr0__implies__Suc]) ).

fof(f_624_2,plain,
    ! [U_2370] :
      ( ? [U_2369] : U_2370 = hAPP(nat,nat,suc,U_2369)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2370)) ),
    inference(variable_rename,[status(thm)],[f_624_1]) ).

fof(f_624_3,plain,
    ! [U_2370] :
      ( U_2370 = hAPP(nat,nat,suc,sK92(U_2370))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2370)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK92]),skolemize(U_2369,sK92(U_2370))],[f_624_2]) ).

fof(f_624_4,plain,
    ! [U_2370] :
      ( U_2370 = hAPP(nat,nat,suc,sK92(U_2370))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2370)) ),
    inference(definitional_conversion,[status(esa)],[f_624_3]) ).

cnf(f_624_5,plain,
    ( U_2370 = hAPP(nat,nat,suc,sK92(U_2370))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2370)) ),
    inference(clausify,[status(thm)],[f_624_4]) ).

fof(f_625_1,plain,
    ! [X_b] :
      ( ! [A_2] :
          ( ( 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),A_2)),zero_zero(X_b)))
            | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),zero_zero(X_b))) )
          & ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),zero_zero(X_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),A_2)),zero_zero(X_b))) ) )
      | ~ linordered_idom(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_554_even__less__0__iff]) ).

fof(f_625_2,plain,
    ! [U_2372] :
      ( ! [U_2371] :
          ( ( hBOOL(hAPP(U_2372,bool,hAPP(U_2372,fun(U_2372,bool),ord_less(U_2372),hAPP(U_2372,U_2372,hAPP(U_2372,fun(U_2372,U_2372),plus_plus(U_2372),U_2371),U_2371)),zero_zero(U_2372)))
            | ~ hBOOL(hAPP(U_2372,bool,hAPP(U_2372,fun(U_2372,bool),ord_less(U_2372),U_2371),zero_zero(U_2372))) )
          & ( hBOOL(hAPP(U_2372,bool,hAPP(U_2372,fun(U_2372,bool),ord_less(U_2372),U_2371),zero_zero(U_2372)))
            | ~ hBOOL(hAPP(U_2372,bool,hAPP(U_2372,fun(U_2372,bool),ord_less(U_2372),hAPP(U_2372,U_2372,hAPP(U_2372,fun(U_2372,U_2372),plus_plus(U_2372),U_2371),U_2371)),zero_zero(U_2372))) ) )
      | ~ linordered_idom(U_2372) ),
    inference(variable_rename,[status(thm)],[f_625_1]) ).

fof(f_625_3,plain,
    ! [U_2372] :
      ( ( ! [U_2374] :
            ( hBOOL(hAPP(U_2372,bool,hAPP(U_2372,fun(U_2372,bool),ord_less(U_2372),hAPP(U_2372,U_2372,hAPP(U_2372,fun(U_2372,U_2372),plus_plus(U_2372),U_2374),U_2374)),zero_zero(U_2372)))
            | ~ hBOOL(hAPP(U_2372,bool,hAPP(U_2372,fun(U_2372,bool),ord_less(U_2372),U_2374),zero_zero(U_2372))) )
        & ! [U_2373] :
            ( hBOOL(hAPP(U_2372,bool,hAPP(U_2372,fun(U_2372,bool),ord_less(U_2372),U_2373),zero_zero(U_2372)))
            | ~ hBOOL(hAPP(U_2372,bool,hAPP(U_2372,fun(U_2372,bool),ord_less(U_2372),hAPP(U_2372,U_2372,hAPP(U_2372,fun(U_2372,U_2372),plus_plus(U_2372),U_2373),U_2373)),zero_zero(U_2372))) ) )
      | ~ linordered_idom(U_2372) ),
    inference(miniscope,[status(thm)],[f_625_2]) ).

fof(f_625_4,plain,
    ( ! [U_2372,U_2374,U_2373] :
        ( hBOOL(hAPP(U_2372,bool,hAPP(U_2372,fun(U_2372,bool),ord_less(U_2372),hAPP(U_2372,U_2372,hAPP(U_2372,fun(U_2372,U_2372),plus_plus(U_2372),U_2374),U_2374)),zero_zero(U_2372)))
        | ~ hBOOL(hAPP(U_2372,bool,hAPP(U_2372,fun(U_2372,bool),ord_less(U_2372),U_2374),zero_zero(U_2372)))
        | ~ sP162(U_2372,U_2374,U_2373) )
    & ! [U_2372,U_2374,U_2373] :
        ( hBOOL(hAPP(U_2372,bool,hAPP(U_2372,fun(U_2372,bool),ord_less(U_2372),U_2373),zero_zero(U_2372)))
        | ~ hBOOL(hAPP(U_2372,bool,hAPP(U_2372,fun(U_2372,bool),ord_less(U_2372),hAPP(U_2372,U_2372,hAPP(U_2372,fun(U_2372,U_2372),plus_plus(U_2372),U_2373),U_2373)),zero_zero(U_2372)))
        | ~ sP162(U_2372,U_2374,U_2373) )
    & ! [U_2372,U_2374,U_2373] :
        ( sP162(U_2372,U_2374,U_2373)
        | ~ linordered_idom(U_2372) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP162])],[f_625_3]) ).

cnf(f_625_5,plain,
    ( sP162(U_2372,U_2374,U_2373)
    | ~ linordered_idom(U_2372) ),
    inference(clausify,[status(thm)],[f_625_4]) ).

cnf(f_625_6,plain,
    ( hBOOL(hAPP(U_2372,bool,hAPP(U_2372,fun(U_2372,bool),ord_less(U_2372),U_2373),zero_zero(U_2372)))
    | ~ hBOOL(hAPP(U_2372,bool,hAPP(U_2372,fun(U_2372,bool),ord_less(U_2372),hAPP(U_2372,U_2372,hAPP(U_2372,fun(U_2372,U_2372),plus_plus(U_2372),U_2373),U_2373)),zero_zero(U_2372)))
    | ~ sP162(U_2372,U_2374,U_2373) ),
    inference(clausify,[status(thm)],[f_625_4]) ).

cnf(f_625_7,plain,
    ( hBOOL(hAPP(U_2372,bool,hAPP(U_2372,fun(U_2372,bool),ord_less(U_2372),hAPP(U_2372,U_2372,hAPP(U_2372,fun(U_2372,U_2372),plus_plus(U_2372),U_2374),U_2374)),zero_zero(U_2372)))
    | ~ hBOOL(hAPP(U_2372,bool,hAPP(U_2372,fun(U_2372,bool),ord_less(U_2372),U_2374),zero_zero(U_2372)))
    | ~ sP162(U_2372,U_2374,U_2373) ),
    inference(clausify,[status(thm)],[f_625_4]) ).

fof(f_626_1,plain,
    ! [X_b] :
      ( ! [A_2] :
          ( ( 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)
            | ti(X_b,A_2) != zero_zero(X_b) )
          & ( ti(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) != zero_zero(X_b) ) )
      | ~ linord219039673up_add(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_555_double__eq__0__iff]) ).

fof(f_626_2,plain,
    ! [U_2376] :
      ( ! [U_2375] :
          ( ( hAPP(U_2376,U_2376,hAPP(U_2376,fun(U_2376,U_2376),plus_plus(U_2376),U_2375),U_2375) = zero_zero(U_2376)
            | ti(U_2376,U_2375) != zero_zero(U_2376) )
          & ( ti(U_2376,U_2375) = zero_zero(U_2376)
            | hAPP(U_2376,U_2376,hAPP(U_2376,fun(U_2376,U_2376),plus_plus(U_2376),U_2375),U_2375) != zero_zero(U_2376) ) )
      | ~ linord219039673up_add(U_2376) ),
    inference(variable_rename,[status(thm)],[f_626_1]) ).

fof(f_626_3,plain,
    ! [U_2376] :
      ( ( ! [U_2378] :
            ( hAPP(U_2376,U_2376,hAPP(U_2376,fun(U_2376,U_2376),plus_plus(U_2376),U_2378),U_2378) = zero_zero(U_2376)
            | ti(U_2376,U_2378) != zero_zero(U_2376) )
        & ! [U_2377] :
            ( ti(U_2376,U_2377) = zero_zero(U_2376)
            | hAPP(U_2376,U_2376,hAPP(U_2376,fun(U_2376,U_2376),plus_plus(U_2376),U_2377),U_2377) != zero_zero(U_2376) ) )
      | ~ linord219039673up_add(U_2376) ),
    inference(miniscope,[status(thm)],[f_626_2]) ).

fof(f_626_4,plain,
    ( ! [U_2378,U_2377,U_2376] :
        ( hAPP(U_2376,U_2376,hAPP(U_2376,fun(U_2376,U_2376),plus_plus(U_2376),U_2378),U_2378) = zero_zero(U_2376)
        | ti(U_2376,U_2378) != zero_zero(U_2376)
        | ~ sP163(U_2378,U_2377,U_2376) )
    & ! [U_2378,U_2377,U_2376] :
        ( ti(U_2376,U_2377) = zero_zero(U_2376)
        | hAPP(U_2376,U_2376,hAPP(U_2376,fun(U_2376,U_2376),plus_plus(U_2376),U_2377),U_2377) != zero_zero(U_2376)
        | ~ sP163(U_2378,U_2377,U_2376) )
    & ! [U_2378,U_2377,U_2376] :
        ( sP163(U_2378,U_2377,U_2376)
        | ~ linord219039673up_add(U_2376) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP163])],[f_626_3]) ).

cnf(f_626_5,plain,
    ( sP163(U_2378,U_2377,U_2376)
    | ~ linord219039673up_add(U_2376) ),
    inference(clausify,[status(thm)],[f_626_4]) ).

cnf(f_626_6,plain,
    ( ti(U_2376,U_2377) = zero_zero(U_2376)
    | hAPP(U_2376,U_2376,hAPP(U_2376,fun(U_2376,U_2376),plus_plus(U_2376),U_2377),U_2377) != zero_zero(U_2376)
    | ~ sP163(U_2378,U_2377,U_2376) ),
    inference(clausify,[status(thm)],[f_626_4]) ).

cnf(f_626_7,plain,
    ( hAPP(U_2376,U_2376,hAPP(U_2376,fun(U_2376,U_2376),plus_plus(U_2376),U_2378),U_2378) = zero_zero(U_2376)
    | ti(U_2376,U_2378) != zero_zero(U_2376)
    | ~ sP163(U_2378,U_2377,U_2376) ),
    inference(clausify,[status(thm)],[f_626_4]) ).

fof(f_627_1,plain,
    ! [X_b,A_3,K] :
      ( ? [B_5,B_4] :
          ( ( ti(fun(X_b,bool),B_4) = bot_bot(fun(X_b,bool))
            | K != zero_zero(nat) )
          & hAPP(fun(X_b,bool),nat,finite_card(X_b),B_4) = K
          & ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_5),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),B_5),B_4) )
      | hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3) != hAPP(nat,nat,suc,K) ),
    inference(fof_nnf,[status(thm)],[fact_556_card__eq__SucD]) ).

fof(f_627_2,plain,
    ! [U_2383,U_2382,U_2381] :
      ( ? [U_2380,U_2379] :
          ( ( ti(fun(U_2383,bool),U_2379) = bot_bot(fun(U_2383,bool))
            | U_2381 != zero_zero(nat) )
          & hAPP(fun(U_2383,bool),nat,finite_card(U_2383),U_2379) = U_2381
          & ~ hBOOL(hAPP(fun(U_2383,bool),bool,hAPP(U_2383,fun(fun(U_2383,bool),bool),member(U_2383),U_2380),U_2379))
          & ti(fun(U_2383,bool),U_2382) = hAPP(fun(U_2383,bool),fun(U_2383,bool),hAPP(U_2383,fun(fun(U_2383,bool),fun(U_2383,bool)),insert(U_2383),U_2380),U_2379) )
      | hAPP(fun(U_2383,bool),nat,finite_card(U_2383),U_2382) != hAPP(nat,nat,suc,U_2381) ),
    inference(variable_rename,[status(thm)],[f_627_1]) ).

fof(f_627_3,plain,
    ! [U_2383,U_2382,U_2381] :
      ( ? [U_2379] :
          ( ( ti(fun(U_2383,bool),U_2379) = bot_bot(fun(U_2383,bool))
            | U_2381 != zero_zero(nat) )
          & hAPP(fun(U_2383,bool),nat,finite_card(U_2383),U_2379) = U_2381
          & ~ hBOOL(hAPP(fun(U_2383,bool),bool,hAPP(U_2383,fun(fun(U_2383,bool),bool),member(U_2383),sK93(U_2383,U_2382,U_2381)),U_2379))
          & ti(fun(U_2383,bool),U_2382) = hAPP(fun(U_2383,bool),fun(U_2383,bool),hAPP(U_2383,fun(fun(U_2383,bool),fun(U_2383,bool)),insert(U_2383),sK93(U_2383,U_2382,U_2381)),U_2379) )
      | hAPP(fun(U_2383,bool),nat,finite_card(U_2383),U_2382) != hAPP(nat,nat,suc,U_2381) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK93]),skolemize(U_2380,sK93(U_2383,U_2382,U_2381))],[f_627_2]) ).

fof(f_627_4,plain,
    ! [U_2383,U_2382,U_2381] :
      ( ( ( ti(fun(U_2383,bool),sK94(U_2383,U_2382,U_2381)) = bot_bot(fun(U_2383,bool))
          | U_2381 != zero_zero(nat) )
        & hAPP(fun(U_2383,bool),nat,finite_card(U_2383),sK94(U_2383,U_2382,U_2381)) = U_2381
        & ~ hBOOL(hAPP(fun(U_2383,bool),bool,hAPP(U_2383,fun(fun(U_2383,bool),bool),member(U_2383),sK93(U_2383,U_2382,U_2381)),sK94(U_2383,U_2382,U_2381)))
        & ti(fun(U_2383,bool),U_2382) = hAPP(fun(U_2383,bool),fun(U_2383,bool),hAPP(U_2383,fun(fun(U_2383,bool),fun(U_2383,bool)),insert(U_2383),sK93(U_2383,U_2382,U_2381)),sK94(U_2383,U_2382,U_2381)) )
      | hAPP(fun(U_2383,bool),nat,finite_card(U_2383),U_2382) != hAPP(nat,nat,suc,U_2381) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK94]),skolemize(U_2379,sK94(U_2383,U_2382,U_2381))],[f_627_3]) ).

fof(f_627_5,plain,
    ( ! [U_2381,U_2382,U_2383] :
        ( ti(fun(U_2383,bool),sK94(U_2383,U_2382,U_2381)) = bot_bot(fun(U_2383,bool))
        | U_2381 != zero_zero(nat)
        | ~ sP164(U_2381,U_2382,U_2383) )
    & ! [U_2381,U_2382,U_2383] :
        ( hAPP(fun(U_2383,bool),nat,finite_card(U_2383),sK94(U_2383,U_2382,U_2381)) = U_2381
        | ~ sP164(U_2381,U_2382,U_2383) )
    & ! [U_2381,U_2382,U_2383] :
        ( ~ hBOOL(hAPP(fun(U_2383,bool),bool,hAPP(U_2383,fun(fun(U_2383,bool),bool),member(U_2383),sK93(U_2383,U_2382,U_2381)),sK94(U_2383,U_2382,U_2381)))
        | ~ sP164(U_2381,U_2382,U_2383) )
    & ! [U_2381,U_2382,U_2383] :
        ( ti(fun(U_2383,bool),U_2382) = hAPP(fun(U_2383,bool),fun(U_2383,bool),hAPP(U_2383,fun(fun(U_2383,bool),fun(U_2383,bool)),insert(U_2383),sK93(U_2383,U_2382,U_2381)),sK94(U_2383,U_2382,U_2381))
        | ~ sP164(U_2381,U_2382,U_2383) )
    & ! [U_2381,U_2382,U_2383] :
        ( sP164(U_2381,U_2382,U_2383)
        | hAPP(fun(U_2383,bool),nat,finite_card(U_2383),U_2382) != hAPP(nat,nat,suc,U_2381) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP164])],[f_627_4]) ).

cnf(f_627_6,plain,
    ( sP164(U_2381,U_2382,U_2383)
    | hAPP(fun(U_2383,bool),nat,finite_card(U_2383),U_2382) != hAPP(nat,nat,suc,U_2381) ),
    inference(clausify,[status(thm)],[f_627_5]) ).

cnf(f_627_7,plain,
    ( ti(fun(U_2383,bool),U_2382) = hAPP(fun(U_2383,bool),fun(U_2383,bool),hAPP(U_2383,fun(fun(U_2383,bool),fun(U_2383,bool)),insert(U_2383),sK93(U_2383,U_2382,U_2381)),sK94(U_2383,U_2382,U_2381))
    | ~ sP164(U_2381,U_2382,U_2383) ),
    inference(clausify,[status(thm)],[f_627_5]) ).

cnf(f_627_8,plain,
    ( ~ hBOOL(hAPP(fun(U_2383,bool),bool,hAPP(U_2383,fun(fun(U_2383,bool),bool),member(U_2383),sK93(U_2383,U_2382,U_2381)),sK94(U_2383,U_2382,U_2381)))
    | ~ sP164(U_2381,U_2382,U_2383) ),
    inference(clausify,[status(thm)],[f_627_5]) ).

cnf(f_627_9,plain,
    ( hAPP(fun(U_2383,bool),nat,finite_card(U_2383),sK94(U_2383,U_2382,U_2381)) = U_2381
    | ~ sP164(U_2381,U_2382,U_2383) ),
    inference(clausify,[status(thm)],[f_627_5]) ).

cnf(f_627_10,plain,
    ( ti(fun(U_2383,bool),sK94(U_2383,U_2382,U_2381)) = bot_bot(fun(U_2383,bool))
    | U_2381 != zero_zero(nat)
    | ~ sP164(U_2381,U_2382,U_2383) ),
    inference(clausify,[status(thm)],[f_627_5]) ).

fof(f_628_1,plain,
    ! [Y] :
      ( ? [Nat] : Y = hAPP(nat,nat,suc,Nat)
      | Y = zero_zero(nat) ),
    inference(fof_nnf,[status(thm)],[fact_557_nat_Oexhaust]) ).

fof(f_628_2,plain,
    ! [U_2385] :
      ( ? [U_2384] : U_2385 = hAPP(nat,nat,suc,U_2384)
      | U_2385 = zero_zero(nat) ),
    inference(variable_rename,[status(thm)],[f_628_1]) ).

fof(f_628_3,plain,
    ! [U_2385] :
      ( U_2385 = hAPP(nat,nat,suc,sK95(U_2385))
      | U_2385 = zero_zero(nat) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK95]),skolemize(U_2384,sK95(U_2385))],[f_628_2]) ).

fof(f_628_4,plain,
    ! [U_2385] :
      ( U_2385 = hAPP(nat,nat,suc,sK95(U_2385))
      | U_2385 = zero_zero(nat) ),
    inference(definitional_conversion,[status(esa)],[f_628_3]) ).

cnf(f_628_5,plain,
    ( U_2385 = hAPP(nat,nat,suc,sK95(U_2385))
    | U_2385 = zero_zero(nat) ),
    inference(clausify,[status(thm)],[f_628_4]) ).

fof(f_629_1,plain,
    ! [Pa,K] :
      ( hBOOL(hAPP(nat,bool,Pa,zero_zero(nat)))
      | ? [N_1] :
          ( ~ hBOOL(hAPP(nat,bool,Pa,N_1))
          & hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,N_1))) )
      | ~ hBOOL(hAPP(nat,bool,Pa,K)) ),
    inference(fof_nnf,[status(thm)],[fact_558_zero__induct]) ).

fof(f_629_2,plain,
    ! [U_2388,U_2387] :
      ( hBOOL(hAPP(nat,bool,U_2388,zero_zero(nat)))
      | ? [U_2386] :
          ( ~ hBOOL(hAPP(nat,bool,U_2388,U_2386))
          & hBOOL(hAPP(nat,bool,U_2388,hAPP(nat,nat,suc,U_2386))) )
      | ~ hBOOL(hAPP(nat,bool,U_2388,U_2387)) ),
    inference(variable_rename,[status(thm)],[f_629_1]) ).

fof(f_629_3,plain,
    ! [U_2388] :
      ( ! [U_2387] : ~ hBOOL(hAPP(nat,bool,U_2388,U_2387))
      | hBOOL(hAPP(nat,bool,U_2388,zero_zero(nat)))
      | ? [U_2386] :
          ( ~ hBOOL(hAPP(nat,bool,U_2388,U_2386))
          & hBOOL(hAPP(nat,bool,U_2388,hAPP(nat,nat,suc,U_2386))) ) ),
    inference(miniscope,[status(thm)],[f_629_2]) ).

fof(f_629_4,plain,
    ! [U_2388] :
      ( ! [U_2387] : ~ hBOOL(hAPP(nat,bool,U_2388,U_2387))
      | hBOOL(hAPP(nat,bool,U_2388,zero_zero(nat)))
      | ( ~ hBOOL(hAPP(nat,bool,U_2388,sK96(U_2388)))
        & hBOOL(hAPP(nat,bool,U_2388,hAPP(nat,nat,suc,sK96(U_2388)))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK96]),skolemize(U_2386,sK96(U_2388))],[f_629_3]) ).

fof(f_629_5,plain,
    ( ! [U_2388] :
        ( ~ hBOOL(hAPP(nat,bool,U_2388,sK96(U_2388)))
        | ~ sP165(U_2388) )
    & ! [U_2388] :
        ( hBOOL(hAPP(nat,bool,U_2388,hAPP(nat,nat,suc,sK96(U_2388))))
        | ~ sP165(U_2388) )
    & ! [U_2387,U_2388] :
        ( ~ hBOOL(hAPP(nat,bool,U_2388,U_2387))
        | hBOOL(hAPP(nat,bool,U_2388,zero_zero(nat)))
        | sP165(U_2388) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP165])],[f_629_4]) ).

cnf(f_629_6,plain,
    ( ~ hBOOL(hAPP(nat,bool,U_2388,U_2387))
    | hBOOL(hAPP(nat,bool,U_2388,zero_zero(nat)))
    | sP165(U_2388) ),
    inference(clausify,[status(thm)],[f_629_5]) ).

cnf(f_629_7,plain,
    ( hBOOL(hAPP(nat,bool,U_2388,hAPP(nat,nat,suc,sK96(U_2388))))
    | ~ sP165(U_2388) ),
    inference(clausify,[status(thm)],[f_629_5]) ).

cnf(f_629_8,plain,
    ( ~ hBOOL(hAPP(nat,bool,U_2388,sK96(U_2388)))
    | ~ sP165(U_2388) ),
    inference(clausify,[status(thm)],[f_629_5]) ).

fof(f_630_1,plain,
    ! [N] :
      ( ? [M_2] : N = hAPP(nat,nat,suc,M_2)
      | N = zero_zero(nat) ),
    inference(fof_nnf,[status(thm)],[fact_559_not0__implies__Suc]) ).

fof(f_630_2,plain,
    ! [U_2390] :
      ( ? [U_2389] : U_2390 = hAPP(nat,nat,suc,U_2389)
      | U_2390 = zero_zero(nat) ),
    inference(variable_rename,[status(thm)],[f_630_1]) ).

fof(f_630_3,plain,
    ! [U_2390] :
      ( U_2390 = hAPP(nat,nat,suc,sK97(U_2390))
      | U_2390 = zero_zero(nat) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK97]),skolemize(U_2389,sK97(U_2390))],[f_630_2]) ).

fof(f_630_4,plain,
    ! [U_2390] :
      ( U_2390 = hAPP(nat,nat,suc,sK97(U_2390))
      | U_2390 = zero_zero(nat) ),
    inference(definitional_conversion,[status(esa)],[f_630_3]) ).

cnf(f_630_5,plain,
    ( U_2390 = hAPP(nat,nat,suc,sK97(U_2390))
    | U_2390 = zero_zero(nat) ),
    inference(clausify,[status(thm)],[f_630_4]) ).

fof(f_631_1,plain,
    ! [Na,Pa] :
      ( hBOOL(hAPP(nat,bool,Pa,Na))
      | ? [N_1] :
          ( ~ hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,N_1)))
          & hBOOL(hAPP(nat,bool,Pa,N_1)) )
      | ~ hBOOL(hAPP(nat,bool,Pa,zero_zero(nat))) ),
    inference(fof_nnf,[status(thm)],[fact_560_nat__induct]) ).

fof(f_631_2,plain,
    ! [U_2393,U_2392] :
      ( hBOOL(hAPP(nat,bool,U_2392,U_2393))
      | ? [U_2391] :
          ( ~ hBOOL(hAPP(nat,bool,U_2392,hAPP(nat,nat,suc,U_2391)))
          & hBOOL(hAPP(nat,bool,U_2392,U_2391)) )
      | ~ hBOOL(hAPP(nat,bool,U_2392,zero_zero(nat))) ),
    inference(variable_rename,[status(thm)],[f_631_1]) ).

fof(f_631_3,plain,
    ! [U_2393,U_2392] :
      ( hBOOL(hAPP(nat,bool,U_2392,U_2393))
      | ( ~ hBOOL(hAPP(nat,bool,U_2392,hAPP(nat,nat,suc,sK98(U_2393,U_2392))))
        & hBOOL(hAPP(nat,bool,U_2392,sK98(U_2393,U_2392))) )
      | ~ hBOOL(hAPP(nat,bool,U_2392,zero_zero(nat))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK98]),skolemize(U_2391,sK98(U_2393,U_2392))],[f_631_2]) ).

fof(f_631_4,plain,
    ( ! [U_2392,U_2393] :
        ( ~ hBOOL(hAPP(nat,bool,U_2392,hAPP(nat,nat,suc,sK98(U_2393,U_2392))))
        | ~ sP166(U_2392,U_2393) )
    & ! [U_2392,U_2393] :
        ( hBOOL(hAPP(nat,bool,U_2392,sK98(U_2393,U_2392)))
        | ~ sP166(U_2392,U_2393) )
    & ! [U_2392,U_2393] :
        ( hBOOL(hAPP(nat,bool,U_2392,U_2393))
        | sP166(U_2392,U_2393)
        | ~ hBOOL(hAPP(nat,bool,U_2392,zero_zero(nat))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP166])],[f_631_3]) ).

cnf(f_631_5,plain,
    ( hBOOL(hAPP(nat,bool,U_2392,U_2393))
    | sP166(U_2392,U_2393)
    | ~ hBOOL(hAPP(nat,bool,U_2392,zero_zero(nat))) ),
    inference(clausify,[status(thm)],[f_631_4]) ).

cnf(f_631_6,plain,
    ( hBOOL(hAPP(nat,bool,U_2392,sK98(U_2393,U_2392)))
    | ~ sP166(U_2392,U_2393) ),
    inference(clausify,[status(thm)],[f_631_4]) ).

cnf(f_631_7,plain,
    ( ~ hBOOL(hAPP(nat,bool,U_2392,hAPP(nat,nat,suc,sK98(U_2393,U_2392))))
    | ~ sP166(U_2392,U_2393) ),
    inference(clausify,[status(thm)],[f_631_4]) ).

fof(f_632_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_semiring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_561_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J]) ).

fof(f_632_2,plain,
    ! [U_2395] :
      ( ! [U_2394] : hAPP(U_2395,U_2395,hAPP(U_2395,fun(U_2395,U_2395),plus_plus(U_2395),zero_zero(U_2395)),U_2394) = ti(U_2395,U_2394)
      | ~ comm_semiring_1(U_2395) ),
    inference(variable_rename,[status(thm)],[f_632_1]) ).

fof(f_632_3,plain,
    ! [U_2395,U_2394] :
      ( hAPP(U_2395,U_2395,hAPP(U_2395,fun(U_2395,U_2395),plus_plus(U_2395),zero_zero(U_2395)),U_2394) = ti(U_2395,U_2394)
      | ~ comm_semiring_1(U_2395) ),
    inference(definitional_conversion,[status(esa)],[f_632_2]) ).

cnf(f_632_4,plain,
    ( hAPP(U_2395,U_2395,hAPP(U_2395,fun(U_2395,U_2395),plus_plus(U_2395),zero_zero(U_2395)),U_2394) = ti(U_2395,U_2394)
    | ~ comm_semiring_1(U_2395) ),
    inference(clausify,[status(thm)],[f_632_3]) ).

fof(f_633_1,plain,
    ! [X_a] :
      ( ! [A_1,B,C,D] : 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)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),D)) = 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),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D))
      | ~ comm_semiring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_562_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J]) ).

fof(f_633_2,plain,
    ! [U_2400] :
      ( ! [U_2399,U_2398,U_2397,U_2396] : hAPP(U_2400,U_2400,hAPP(U_2400,fun(U_2400,U_2400),plus_plus(U_2400),hAPP(U_2400,U_2400,hAPP(U_2400,fun(U_2400,U_2400),plus_plus(U_2400),U_2399),U_2398)),hAPP(U_2400,U_2400,hAPP(U_2400,fun(U_2400,U_2400),plus_plus(U_2400),U_2397),U_2396)) = hAPP(U_2400,U_2400,hAPP(U_2400,fun(U_2400,U_2400),plus_plus(U_2400),hAPP(U_2400,U_2400,hAPP(U_2400,fun(U_2400,U_2400),plus_plus(U_2400),U_2399),U_2397)),hAPP(U_2400,U_2400,hAPP(U_2400,fun(U_2400,U_2400),plus_plus(U_2400),U_2398),U_2396))
      | ~ comm_semiring_1(U_2400) ),
    inference(variable_rename,[status(thm)],[f_633_1]) ).

fof(f_633_3,plain,
    ! [U_2400,U_2396,U_2397,U_2398,U_2399] :
      ( hAPP(U_2400,U_2400,hAPP(U_2400,fun(U_2400,U_2400),plus_plus(U_2400),hAPP(U_2400,U_2400,hAPP(U_2400,fun(U_2400,U_2400),plus_plus(U_2400),U_2399),U_2398)),hAPP(U_2400,U_2400,hAPP(U_2400,fun(U_2400,U_2400),plus_plus(U_2400),U_2397),U_2396)) = hAPP(U_2400,U_2400,hAPP(U_2400,fun(U_2400,U_2400),plus_plus(U_2400),hAPP(U_2400,U_2400,hAPP(U_2400,fun(U_2400,U_2400),plus_plus(U_2400),U_2399),U_2397)),hAPP(U_2400,U_2400,hAPP(U_2400,fun(U_2400,U_2400),plus_plus(U_2400),U_2398),U_2396))
      | ~ comm_semiring_1(U_2400) ),
    inference(definitional_conversion,[status(esa)],[f_633_2]) ).

cnf(f_633_4,plain,
    ( hAPP(U_2400,U_2400,hAPP(U_2400,fun(U_2400,U_2400),plus_plus(U_2400),hAPP(U_2400,U_2400,hAPP(U_2400,fun(U_2400,U_2400),plus_plus(U_2400),U_2399),U_2398)),hAPP(U_2400,U_2400,hAPP(U_2400,fun(U_2400,U_2400),plus_plus(U_2400),U_2397),U_2396)) = hAPP(U_2400,U_2400,hAPP(U_2400,fun(U_2400,U_2400),plus_plus(U_2400),hAPP(U_2400,U_2400,hAPP(U_2400,fun(U_2400,U_2400),plus_plus(U_2400),U_2399),U_2397)),hAPP(U_2400,U_2400,hAPP(U_2400,fun(U_2400,U_2400),plus_plus(U_2400),U_2398),U_2396))
    | ~ comm_semiring_1(U_2400) ),
    inference(clausify,[status(thm)],[f_633_3]) ).

fof(f_634_1,plain,
    ! [X_a] :
      ( ! [A_1,B,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)),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),C)),B)
      | ~ comm_semiring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_563_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J]) ).

fof(f_634_2,plain,
    ! [U_2404] :
      ( ! [U_2403,U_2402,U_2401] : hAPP(U_2404,U_2404,hAPP(U_2404,fun(U_2404,U_2404),plus_plus(U_2404),hAPP(U_2404,U_2404,hAPP(U_2404,fun(U_2404,U_2404),plus_plus(U_2404),U_2403),U_2402)),U_2401) = hAPP(U_2404,U_2404,hAPP(U_2404,fun(U_2404,U_2404),plus_plus(U_2404),hAPP(U_2404,U_2404,hAPP(U_2404,fun(U_2404,U_2404),plus_plus(U_2404),U_2403),U_2401)),U_2402)
      | ~ comm_semiring_1(U_2404) ),
    inference(variable_rename,[status(thm)],[f_634_1]) ).

fof(f_634_3,plain,
    ! [U_2401,U_2404,U_2402,U_2403] :
      ( hAPP(U_2404,U_2404,hAPP(U_2404,fun(U_2404,U_2404),plus_plus(U_2404),hAPP(U_2404,U_2404,hAPP(U_2404,fun(U_2404,U_2404),plus_plus(U_2404),U_2403),U_2402)),U_2401) = hAPP(U_2404,U_2404,hAPP(U_2404,fun(U_2404,U_2404),plus_plus(U_2404),hAPP(U_2404,U_2404,hAPP(U_2404,fun(U_2404,U_2404),plus_plus(U_2404),U_2403),U_2401)),U_2402)
      | ~ comm_semiring_1(U_2404) ),
    inference(definitional_conversion,[status(esa)],[f_634_2]) ).

cnf(f_634_4,plain,
    ( hAPP(U_2404,U_2404,hAPP(U_2404,fun(U_2404,U_2404),plus_plus(U_2404),hAPP(U_2404,U_2404,hAPP(U_2404,fun(U_2404,U_2404),plus_plus(U_2404),U_2403),U_2402)),U_2401) = hAPP(U_2404,U_2404,hAPP(U_2404,fun(U_2404,U_2404),plus_plus(U_2404),hAPP(U_2404,U_2404,hAPP(U_2404,fun(U_2404,U_2404),plus_plus(U_2404),U_2403),U_2401)),U_2402)
    | ~ comm_semiring_1(U_2404) ),
    inference(clausify,[status(thm)],[f_634_3]) ).

fof(f_635_1,plain,
    ! [X_a] :
      ( ! [A_1,B,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)),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),C))
      | ~ comm_semiring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_564_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J]) ).

fof(f_635_2,plain,
    ! [U_2408] :
      ( ! [U_2407,U_2406,U_2405] : hAPP(U_2408,U_2408,hAPP(U_2408,fun(U_2408,U_2408),plus_plus(U_2408),hAPP(U_2408,U_2408,hAPP(U_2408,fun(U_2408,U_2408),plus_plus(U_2408),U_2407),U_2406)),U_2405) = hAPP(U_2408,U_2408,hAPP(U_2408,fun(U_2408,U_2408),plus_plus(U_2408),U_2407),hAPP(U_2408,U_2408,hAPP(U_2408,fun(U_2408,U_2408),plus_plus(U_2408),U_2406),U_2405))
      | ~ comm_semiring_1(U_2408) ),
    inference(variable_rename,[status(thm)],[f_635_1]) ).

fof(f_635_3,plain,
    ! [U_2408,U_2405,U_2406,U_2407] :
      ( hAPP(U_2408,U_2408,hAPP(U_2408,fun(U_2408,U_2408),plus_plus(U_2408),hAPP(U_2408,U_2408,hAPP(U_2408,fun(U_2408,U_2408),plus_plus(U_2408),U_2407),U_2406)),U_2405) = hAPP(U_2408,U_2408,hAPP(U_2408,fun(U_2408,U_2408),plus_plus(U_2408),U_2407),hAPP(U_2408,U_2408,hAPP(U_2408,fun(U_2408,U_2408),plus_plus(U_2408),U_2406),U_2405))
      | ~ comm_semiring_1(U_2408) ),
    inference(definitional_conversion,[status(esa)],[f_635_2]) ).

cnf(f_635_4,plain,
    ( hAPP(U_2408,U_2408,hAPP(U_2408,fun(U_2408,U_2408),plus_plus(U_2408),hAPP(U_2408,U_2408,hAPP(U_2408,fun(U_2408,U_2408),plus_plus(U_2408),U_2407),U_2406)),U_2405) = hAPP(U_2408,U_2408,hAPP(U_2408,fun(U_2408,U_2408),plus_plus(U_2408),U_2407),hAPP(U_2408,U_2408,hAPP(U_2408,fun(U_2408,U_2408),plus_plus(U_2408),U_2406),U_2405))
    | ~ comm_semiring_1(U_2408) ),
    inference(clausify,[status(thm)],[f_635_3]) ).

fof(f_636_1,plain,
    ! [X_a] :
      ( ! [A_1,C,D] : 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),C),D)) = 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),C)),D)
      | ~ comm_semiring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_565_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J]) ).

fof(f_636_2,plain,
    ! [U_2412] :
      ( ! [U_2411,U_2410,U_2409] : hAPP(U_2412,U_2412,hAPP(U_2412,fun(U_2412,U_2412),plus_plus(U_2412),U_2411),hAPP(U_2412,U_2412,hAPP(U_2412,fun(U_2412,U_2412),plus_plus(U_2412),U_2410),U_2409)) = hAPP(U_2412,U_2412,hAPP(U_2412,fun(U_2412,U_2412),plus_plus(U_2412),hAPP(U_2412,U_2412,hAPP(U_2412,fun(U_2412,U_2412),plus_plus(U_2412),U_2411),U_2410)),U_2409)
      | ~ comm_semiring_1(U_2412) ),
    inference(variable_rename,[status(thm)],[f_636_1]) ).

fof(f_636_3,plain,
    ! [U_2409,U_2412,U_2411,U_2410] :
      ( hAPP(U_2412,U_2412,hAPP(U_2412,fun(U_2412,U_2412),plus_plus(U_2412),U_2411),hAPP(U_2412,U_2412,hAPP(U_2412,fun(U_2412,U_2412),plus_plus(U_2412),U_2410),U_2409)) = hAPP(U_2412,U_2412,hAPP(U_2412,fun(U_2412,U_2412),plus_plus(U_2412),hAPP(U_2412,U_2412,hAPP(U_2412,fun(U_2412,U_2412),plus_plus(U_2412),U_2411),U_2410)),U_2409)
      | ~ comm_semiring_1(U_2412) ),
    inference(definitional_conversion,[status(esa)],[f_636_2]) ).

cnf(f_636_4,plain,
    ( hAPP(U_2412,U_2412,hAPP(U_2412,fun(U_2412,U_2412),plus_plus(U_2412),U_2411),hAPP(U_2412,U_2412,hAPP(U_2412,fun(U_2412,U_2412),plus_plus(U_2412),U_2410),U_2409)) = hAPP(U_2412,U_2412,hAPP(U_2412,fun(U_2412,U_2412),plus_plus(U_2412),hAPP(U_2412,U_2412,hAPP(U_2412,fun(U_2412,U_2412),plus_plus(U_2412),U_2411),U_2410)),U_2409)
    | ~ comm_semiring_1(U_2412) ),
    inference(clausify,[status(thm)],[f_636_3]) ).

fof(f_637_1,plain,
    ! [X_a] :
      ( ! [A_1,C,D] : 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),C),D)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),D))
      | ~ comm_semiring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_566_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J]) ).

fof(f_637_2,plain,
    ! [U_2416] :
      ( ! [U_2415,U_2414,U_2413] : hAPP(U_2416,U_2416,hAPP(U_2416,fun(U_2416,U_2416),plus_plus(U_2416),U_2415),hAPP(U_2416,U_2416,hAPP(U_2416,fun(U_2416,U_2416),plus_plus(U_2416),U_2414),U_2413)) = hAPP(U_2416,U_2416,hAPP(U_2416,fun(U_2416,U_2416),plus_plus(U_2416),U_2414),hAPP(U_2416,U_2416,hAPP(U_2416,fun(U_2416,U_2416),plus_plus(U_2416),U_2415),U_2413))
      | ~ comm_semiring_1(U_2416) ),
    inference(variable_rename,[status(thm)],[f_637_1]) ).

fof(f_637_3,plain,
    ! [U_2413,U_2415,U_2416,U_2414] :
      ( hAPP(U_2416,U_2416,hAPP(U_2416,fun(U_2416,U_2416),plus_plus(U_2416),U_2415),hAPP(U_2416,U_2416,hAPP(U_2416,fun(U_2416,U_2416),plus_plus(U_2416),U_2414),U_2413)) = hAPP(U_2416,U_2416,hAPP(U_2416,fun(U_2416,U_2416),plus_plus(U_2416),U_2414),hAPP(U_2416,U_2416,hAPP(U_2416,fun(U_2416,U_2416),plus_plus(U_2416),U_2415),U_2413))
      | ~ comm_semiring_1(U_2416) ),
    inference(definitional_conversion,[status(esa)],[f_637_2]) ).

cnf(f_637_4,plain,
    ( hAPP(U_2416,U_2416,hAPP(U_2416,fun(U_2416,U_2416),plus_plus(U_2416),U_2415),hAPP(U_2416,U_2416,hAPP(U_2416,fun(U_2416,U_2416),plus_plus(U_2416),U_2414),U_2413)) = hAPP(U_2416,U_2416,hAPP(U_2416,fun(U_2416,U_2416),plus_plus(U_2416),U_2414),hAPP(U_2416,U_2416,hAPP(U_2416,fun(U_2416,U_2416),plus_plus(U_2416),U_2415),U_2413))
    | ~ comm_semiring_1(U_2416) ),
    inference(clausify,[status(thm)],[f_637_3]) ).

fof(f_638_1,plain,
    ! [X_a] :
      ( ! [A_1,C] : 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),C),A_1)
      | ~ comm_semiring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_567_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J]) ).

fof(f_638_2,plain,
    ! [U_2419] :
      ( ! [U_2418,U_2417] : hAPP(U_2419,U_2419,hAPP(U_2419,fun(U_2419,U_2419),plus_plus(U_2419),U_2418),U_2417) = hAPP(U_2419,U_2419,hAPP(U_2419,fun(U_2419,U_2419),plus_plus(U_2419),U_2417),U_2418)
      | ~ comm_semiring_1(U_2419) ),
    inference(variable_rename,[status(thm)],[f_638_1]) ).

fof(f_638_3,plain,
    ! [U_2419,U_2418,U_2417] :
      ( hAPP(U_2419,U_2419,hAPP(U_2419,fun(U_2419,U_2419),plus_plus(U_2419),U_2418),U_2417) = hAPP(U_2419,U_2419,hAPP(U_2419,fun(U_2419,U_2419),plus_plus(U_2419),U_2417),U_2418)
      | ~ comm_semiring_1(U_2419) ),
    inference(definitional_conversion,[status(esa)],[f_638_2]) ).

cnf(f_638_4,plain,
    ( hAPP(U_2419,U_2419,hAPP(U_2419,fun(U_2419,U_2419),plus_plus(U_2419),U_2418),U_2417) = hAPP(U_2419,U_2419,hAPP(U_2419,fun(U_2419,U_2419),plus_plus(U_2419),U_2417),U_2418)
    | ~ comm_semiring_1(U_2419) ),
    inference(clausify,[status(thm)],[f_638_3]) ).

fof(f_639_1,plain,
    ! [X_b] :
      ( ! [B_3,A_2] :
          ( ( ti(X_b,B_3) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),B_3),A_2)
            | ti(X_b,A_2) != zero_zero(X_b) )
          & ( ti(X_b,A_2) = zero_zero(X_b)
            | ti(X_b,B_3) != hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),B_3),A_2) ) )
      | ~ semiri456707255roduct(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_568_add__0__iff]) ).

fof(f_639_2,plain,
    ! [U_2422] :
      ( ! [U_2421,U_2420] :
          ( ( ti(U_2422,U_2421) = hAPP(U_2422,U_2422,hAPP(U_2422,fun(U_2422,U_2422),plus_plus(U_2422),U_2421),U_2420)
            | ti(U_2422,U_2420) != zero_zero(U_2422) )
          & ( ti(U_2422,U_2420) = zero_zero(U_2422)
            | ti(U_2422,U_2421) != hAPP(U_2422,U_2422,hAPP(U_2422,fun(U_2422,U_2422),plus_plus(U_2422),U_2421),U_2420) ) )
      | ~ semiri456707255roduct(U_2422) ),
    inference(variable_rename,[status(thm)],[f_639_1]) ).

fof(f_639_3,plain,
    ! [U_2422] :
      ( ( ! [U_2426,U_2424] :
            ( ti(U_2422,U_2426) = hAPP(U_2422,U_2422,hAPP(U_2422,fun(U_2422,U_2422),plus_plus(U_2422),U_2426),U_2424)
            | ti(U_2422,U_2424) != zero_zero(U_2422) )
        & ! [U_2425,U_2423] :
            ( ti(U_2422,U_2423) = zero_zero(U_2422)
            | ti(U_2422,U_2425) != hAPP(U_2422,U_2422,hAPP(U_2422,fun(U_2422,U_2422),plus_plus(U_2422),U_2425),U_2423) ) )
      | ~ semiri456707255roduct(U_2422) ),
    inference(miniscope,[status(thm)],[f_639_2]) ).

fof(f_639_4,plain,
    ( ! [U_2426,U_2422,U_2424,U_2423,U_2425] :
        ( ti(U_2422,U_2426) = hAPP(U_2422,U_2422,hAPP(U_2422,fun(U_2422,U_2422),plus_plus(U_2422),U_2426),U_2424)
        | ti(U_2422,U_2424) != zero_zero(U_2422)
        | ~ sP167(U_2426,U_2422,U_2424,U_2423,U_2425) )
    & ! [U_2426,U_2422,U_2424,U_2423,U_2425] :
        ( ti(U_2422,U_2423) = zero_zero(U_2422)
        | ti(U_2422,U_2425) != hAPP(U_2422,U_2422,hAPP(U_2422,fun(U_2422,U_2422),plus_plus(U_2422),U_2425),U_2423)
        | ~ sP167(U_2426,U_2422,U_2424,U_2423,U_2425) )
    & ! [U_2426,U_2422,U_2424,U_2423,U_2425] :
        ( sP167(U_2426,U_2422,U_2424,U_2423,U_2425)
        | ~ semiri456707255roduct(U_2422) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP167])],[f_639_3]) ).

cnf(f_639_5,plain,
    ( sP167(U_2426,U_2422,U_2424,U_2423,U_2425)
    | ~ semiri456707255roduct(U_2422) ),
    inference(clausify,[status(thm)],[f_639_4]) ).

cnf(f_639_6,plain,
    ( ti(U_2422,U_2423) = zero_zero(U_2422)
    | ti(U_2422,U_2425) != hAPP(U_2422,U_2422,hAPP(U_2422,fun(U_2422,U_2422),plus_plus(U_2422),U_2425),U_2423)
    | ~ sP167(U_2426,U_2422,U_2424,U_2423,U_2425) ),
    inference(clausify,[status(thm)],[f_639_4]) ).

cnf(f_639_7,plain,
    ( ti(U_2422,U_2426) = hAPP(U_2422,U_2422,hAPP(U_2422,fun(U_2422,U_2422),plus_plus(U_2422),U_2426),U_2424)
    | ti(U_2422,U_2424) != zero_zero(U_2422)
    | ~ sP167(U_2426,U_2422,U_2424,U_2423,U_2425) ),
    inference(clausify,[status(thm)],[f_639_4]) ).

fof(f_640_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_semiring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_569_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J]) ).

fof(f_640_2,plain,
    ! [U_2428] :
      ( ! [U_2427] : hAPP(U_2428,U_2428,hAPP(U_2428,fun(U_2428,U_2428),plus_plus(U_2428),U_2427),zero_zero(U_2428)) = ti(U_2428,U_2427)
      | ~ comm_semiring_1(U_2428) ),
    inference(variable_rename,[status(thm)],[f_640_1]) ).

fof(f_640_3,plain,
    ! [U_2428,U_2427] :
      ( hAPP(U_2428,U_2428,hAPP(U_2428,fun(U_2428,U_2428),plus_plus(U_2428),U_2427),zero_zero(U_2428)) = ti(U_2428,U_2427)
      | ~ comm_semiring_1(U_2428) ),
    inference(definitional_conversion,[status(esa)],[f_640_2]) ).

cnf(f_640_4,plain,
    ( hAPP(U_2428,U_2428,hAPP(U_2428,fun(U_2428,U_2428),plus_plus(U_2428),U_2427),zero_zero(U_2428)) = ti(U_2428,U_2427)
    | ~ comm_semiring_1(U_2428) ),
    inference(clausify,[status(thm)],[f_640_3]) ).

fof(f_641_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))
          | ? [E_2] :
              ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Y),E_2)))
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),E_2)) ) )
      | ~ linordered_field(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_570_field__le__epsilon]) ).

fof(f_641_2,plain,
    ! [U_2432] :
      ( ! [U_2431,U_2430] :
          ( hBOOL(hAPP(U_2432,bool,hAPP(U_2432,fun(U_2432,bool),ord_less_eq(U_2432),U_2431),U_2430))
          | ? [U_2429] :
              ( ~ hBOOL(hAPP(U_2432,bool,hAPP(U_2432,fun(U_2432,bool),ord_less_eq(U_2432),U_2431),hAPP(U_2432,U_2432,hAPP(U_2432,fun(U_2432,U_2432),plus_plus(U_2432),U_2430),U_2429)))
              & hBOOL(hAPP(U_2432,bool,hAPP(U_2432,fun(U_2432,bool),ord_less(U_2432),zero_zero(U_2432)),U_2429)) ) )
      | ~ linordered_field(U_2432) ),
    inference(variable_rename,[status(thm)],[f_641_1]) ).

fof(f_641_3,plain,
    ! [U_2432] :
      ( ! [U_2431,U_2430] :
          ( hBOOL(hAPP(U_2432,bool,hAPP(U_2432,fun(U_2432,bool),ord_less_eq(U_2432),U_2431),U_2430))
          | ( ~ hBOOL(hAPP(U_2432,bool,hAPP(U_2432,fun(U_2432,bool),ord_less_eq(U_2432),U_2431),hAPP(U_2432,U_2432,hAPP(U_2432,fun(U_2432,U_2432),plus_plus(U_2432),U_2430),sK99(U_2432,U_2431,U_2430))))
            & hBOOL(hAPP(U_2432,bool,hAPP(U_2432,fun(U_2432,bool),ord_less(U_2432),zero_zero(U_2432)),sK99(U_2432,U_2431,U_2430))) ) )
      | ~ linordered_field(U_2432) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK99]),skolemize(U_2429,sK99(U_2432,U_2431,U_2430))],[f_641_2]) ).

fof(f_641_4,plain,
    ( ! [U_2432,U_2431,U_2430] :
        ( ~ hBOOL(hAPP(U_2432,bool,hAPP(U_2432,fun(U_2432,bool),ord_less_eq(U_2432),U_2431),hAPP(U_2432,U_2432,hAPP(U_2432,fun(U_2432,U_2432),plus_plus(U_2432),U_2430),sK99(U_2432,U_2431,U_2430))))
        | ~ sP168(U_2432,U_2431,U_2430) )
    & ! [U_2432,U_2431,U_2430] :
        ( hBOOL(hAPP(U_2432,bool,hAPP(U_2432,fun(U_2432,bool),ord_less(U_2432),zero_zero(U_2432)),sK99(U_2432,U_2431,U_2430)))
        | ~ sP168(U_2432,U_2431,U_2430) )
    & ! [U_2432,U_2431,U_2430] :
        ( hBOOL(hAPP(U_2432,bool,hAPP(U_2432,fun(U_2432,bool),ord_less_eq(U_2432),U_2431),U_2430))
        | sP168(U_2432,U_2431,U_2430)
        | ~ linordered_field(U_2432) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP168])],[f_641_3]) ).

cnf(f_641_5,plain,
    ( hBOOL(hAPP(U_2432,bool,hAPP(U_2432,fun(U_2432,bool),ord_less_eq(U_2432),U_2431),U_2430))
    | sP168(U_2432,U_2431,U_2430)
    | ~ linordered_field(U_2432) ),
    inference(clausify,[status(thm)],[f_641_4]) ).

cnf(f_641_6,plain,
    ( hBOOL(hAPP(U_2432,bool,hAPP(U_2432,fun(U_2432,bool),ord_less(U_2432),zero_zero(U_2432)),sK99(U_2432,U_2431,U_2430)))
    | ~ sP168(U_2432,U_2431,U_2430) ),
    inference(clausify,[status(thm)],[f_641_4]) ).

cnf(f_641_7,plain,
    ( ~ hBOOL(hAPP(U_2432,bool,hAPP(U_2432,fun(U_2432,bool),ord_less_eq(U_2432),U_2431),hAPP(U_2432,U_2432,hAPP(U_2432,fun(U_2432,U_2432),plus_plus(U_2432),U_2430),sK99(U_2432,U_2431,U_2430))))
    | ~ sP168(U_2432,U_2431,U_2430) ),
    inference(clausify,[status(thm)],[f_641_4]) ).

fof(f_642_1,plain,
    ! [X_b,A_3] :
      ( hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3) = hAPP(fun(X_b,bool),nat,hAPP(nat,fun(fun(X_b,bool),nat),hAPP(fun(X_b,nat),fun(nat,fun(fun(X_b,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(X_b,nat),fun(nat,fun(fun(X_b,bool),nat))),finite_fold_image(nat,X_b),plus_plus(nat)),hAPP(nat,fun(X_b,nat),combk(nat,X_b),one_one(nat))),zero_zero(nat)),A_3)
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) ),
    inference(fof_nnf,[status(thm)],[fact_571_card_Oeq__fold__g]) ).

fof(f_642_2,plain,
    ! [U_2434,U_2433] :
      ( hAPP(fun(U_2434,bool),nat,finite_card(U_2434),U_2433) = hAPP(fun(U_2434,bool),nat,hAPP(nat,fun(fun(U_2434,bool),nat),hAPP(fun(U_2434,nat),fun(nat,fun(fun(U_2434,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(U_2434,nat),fun(nat,fun(fun(U_2434,bool),nat))),finite_fold_image(nat,U_2434),plus_plus(nat)),hAPP(nat,fun(U_2434,nat),combk(nat,U_2434),one_one(nat))),zero_zero(nat)),U_2433)
      | ~ hBOOL(hAPP(fun(U_2434,bool),bool,finite_finite(U_2434),U_2433)) ),
    inference(variable_rename,[status(thm)],[f_642_1]) ).

fof(f_642_3,plain,
    ! [U_2433,U_2434] :
      ( hAPP(fun(U_2434,bool),nat,finite_card(U_2434),U_2433) = hAPP(fun(U_2434,bool),nat,hAPP(nat,fun(fun(U_2434,bool),nat),hAPP(fun(U_2434,nat),fun(nat,fun(fun(U_2434,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(U_2434,nat),fun(nat,fun(fun(U_2434,bool),nat))),finite_fold_image(nat,U_2434),plus_plus(nat)),hAPP(nat,fun(U_2434,nat),combk(nat,U_2434),one_one(nat))),zero_zero(nat)),U_2433)
      | ~ hBOOL(hAPP(fun(U_2434,bool),bool,finite_finite(U_2434),U_2433)) ),
    inference(definitional_conversion,[status(esa)],[f_642_2]) ).

cnf(f_642_4,plain,
    ( hAPP(fun(U_2434,bool),nat,finite_card(U_2434),U_2433) = hAPP(fun(U_2434,bool),nat,hAPP(nat,fun(fun(U_2434,bool),nat),hAPP(fun(U_2434,nat),fun(nat,fun(fun(U_2434,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(U_2434,nat),fun(nat,fun(fun(U_2434,bool),nat))),finite_fold_image(nat,U_2434),plus_plus(nat)),hAPP(nat,fun(U_2434,nat),combk(nat,U_2434),one_one(nat))),zero_zero(nat)),U_2433)
    | ~ hBOOL(hAPP(fun(U_2434,bool),bool,finite_finite(U_2434),U_2433)) ),
    inference(clausify,[status(thm)],[f_642_3]) ).

fof(f_643_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)) )
      & ( hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3) = hAPP(fun(X_b,bool),nat,hAPP(nat,fun(fun(X_b,bool),nat),hAPP(fun(X_b,nat),fun(nat,fun(fun(X_b,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(X_b,nat),fun(nat,fun(fun(X_b,bool),nat))),finite_fold_image(nat,X_b),plus_plus(nat)),hAPP(nat,fun(X_b,nat),combk(nat,X_b),one_one(nat))),zero_zero(nat)),A_3)
        | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) ) ),
    inference(fof_nnf,[status(thm)],[fact_572_card__def]) ).

fof(f_643_2,plain,
    ! [U_2436,U_2435] :
      ( ( hAPP(fun(U_2436,bool),nat,finite_card(U_2436),U_2435) = zero_zero(nat)
        | hBOOL(hAPP(fun(U_2436,bool),bool,finite_finite(U_2436),U_2435)) )
      & ( hAPP(fun(U_2436,bool),nat,finite_card(U_2436),U_2435) = hAPP(fun(U_2436,bool),nat,hAPP(nat,fun(fun(U_2436,bool),nat),hAPP(fun(U_2436,nat),fun(nat,fun(fun(U_2436,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(U_2436,nat),fun(nat,fun(fun(U_2436,bool),nat))),finite_fold_image(nat,U_2436),plus_plus(nat)),hAPP(nat,fun(U_2436,nat),combk(nat,U_2436),one_one(nat))),zero_zero(nat)),U_2435)
        | ~ hBOOL(hAPP(fun(U_2436,bool),bool,finite_finite(U_2436),U_2435)) ) ),
    inference(variable_rename,[status(thm)],[f_643_1]) ).

fof(f_643_3,plain,
    ( ! [U_2440,U_2438] :
        ( hAPP(fun(U_2440,bool),nat,finite_card(U_2440),U_2438) = zero_zero(nat)
        | hBOOL(hAPP(fun(U_2440,bool),bool,finite_finite(U_2440),U_2438)) )
    & ! [U_2439,U_2437] :
        ( hAPP(fun(U_2439,bool),nat,finite_card(U_2439),U_2437) = hAPP(fun(U_2439,bool),nat,hAPP(nat,fun(fun(U_2439,bool),nat),hAPP(fun(U_2439,nat),fun(nat,fun(fun(U_2439,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(U_2439,nat),fun(nat,fun(fun(U_2439,bool),nat))),finite_fold_image(nat,U_2439),plus_plus(nat)),hAPP(nat,fun(U_2439,nat),combk(nat,U_2439),one_one(nat))),zero_zero(nat)),U_2437)
        | ~ hBOOL(hAPP(fun(U_2439,bool),bool,finite_finite(U_2439),U_2437)) ) ),
    inference(miniscope,[status(thm)],[f_643_2]) ).

fof(f_643_4,plain,
    ( ! [U_2438,U_2440] :
        ( hAPP(fun(U_2440,bool),nat,finite_card(U_2440),U_2438) = zero_zero(nat)
        | hBOOL(hAPP(fun(U_2440,bool),bool,finite_finite(U_2440),U_2438)) )
    & ! [U_2439,U_2437] :
        ( hAPP(fun(U_2439,bool),nat,finite_card(U_2439),U_2437) = hAPP(fun(U_2439,bool),nat,hAPP(nat,fun(fun(U_2439,bool),nat),hAPP(fun(U_2439,nat),fun(nat,fun(fun(U_2439,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(U_2439,nat),fun(nat,fun(fun(U_2439,bool),nat))),finite_fold_image(nat,U_2439),plus_plus(nat)),hAPP(nat,fun(U_2439,nat),combk(nat,U_2439),one_one(nat))),zero_zero(nat)),U_2437)
        | ~ hBOOL(hAPP(fun(U_2439,bool),bool,finite_finite(U_2439),U_2437)) ) ),
    inference(definitional_conversion,[status(esa)],[f_643_3]) ).

cnf(f_643_5,plain,
    ( hAPP(fun(U_2439,bool),nat,finite_card(U_2439),U_2437) = hAPP(fun(U_2439,bool),nat,hAPP(nat,fun(fun(U_2439,bool),nat),hAPP(fun(U_2439,nat),fun(nat,fun(fun(U_2439,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(U_2439,nat),fun(nat,fun(fun(U_2439,bool),nat))),finite_fold_image(nat,U_2439),plus_plus(nat)),hAPP(nat,fun(U_2439,nat),combk(nat,U_2439),one_one(nat))),zero_zero(nat)),U_2437)
    | ~ hBOOL(hAPP(fun(U_2439,bool),bool,finite_finite(U_2439),U_2437)) ),
    inference(clausify,[status(thm)],[f_643_4]) ).

cnf(f_643_6,plain,
    ( hAPP(fun(U_2440,bool),nat,finite_card(U_2440),U_2438) = zero_zero(nat)
    | hBOOL(hAPP(fun(U_2440,bool),bool,finite_finite(U_2440),U_2438)) ),
    inference(clausify,[status(thm)],[f_643_4]) ).

fof(f_644_1,plain,
    ! [X_c,X_b,F,G,Z_2] : hAPP(fun(X_c,bool),X_b,hAPP(X_b,fun(fun(X_c,bool),X_b),hAPP(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b))),finite_fold_image(X_b,X_c),F),G),Z_2),bot_bot(fun(X_c,bool))) = ti(X_b,Z_2),
    inference(fof_nnf,[status(thm)],[fact_573_fold__image__empty]) ).

fof(f_644_2,plain,
    ! [U_2445,U_2444,U_2443,U_2442,U_2441] : hAPP(fun(U_2445,bool),U_2444,hAPP(U_2444,fun(fun(U_2445,bool),U_2444),hAPP(fun(U_2445,U_2444),fun(U_2444,fun(fun(U_2445,bool),U_2444)),hAPP(fun(U_2444,fun(U_2444,U_2444)),fun(fun(U_2445,U_2444),fun(U_2444,fun(fun(U_2445,bool),U_2444))),finite_fold_image(U_2444,U_2445),U_2443),U_2442),U_2441),bot_bot(fun(U_2445,bool))) = ti(U_2444,U_2441),
    inference(variable_rename,[status(thm)],[f_644_1]) ).

fof(f_644_3,plain,
    ! [U_2441,U_2444,U_2442,U_2443,U_2445] : hAPP(fun(U_2445,bool),U_2444,hAPP(U_2444,fun(fun(U_2445,bool),U_2444),hAPP(fun(U_2445,U_2444),fun(U_2444,fun(fun(U_2445,bool),U_2444)),hAPP(fun(U_2444,fun(U_2444,U_2444)),fun(fun(U_2445,U_2444),fun(U_2444,fun(fun(U_2445,bool),U_2444))),finite_fold_image(U_2444,U_2445),U_2443),U_2442),U_2441),bot_bot(fun(U_2445,bool))) = ti(U_2444,U_2441),
    inference(definitional_conversion,[status(esa)],[f_644_2]) ).

cnf(f_644_4,plain,
    hAPP(fun(U_2445,bool),U_2444,hAPP(U_2444,fun(fun(U_2445,bool),U_2444),hAPP(fun(U_2445,U_2444),fun(U_2444,fun(fun(U_2445,bool),U_2444)),hAPP(fun(U_2444,fun(U_2444,U_2444)),fun(fun(U_2445,U_2444),fun(U_2444,fun(fun(U_2445,bool),U_2444))),finite_fold_image(U_2444,U_2445),U_2443),U_2442),U_2441),bot_bot(fun(U_2445,bool))) = ti(U_2444,U_2441),
    inference(clausify,[status(thm)],[f_644_3]) ).

fof(f_645_1,plain,
    ! [X_c,X_b,A_3,F,Z_2,G,F_1] :
      ( hAPP(fun(X_c,bool),X_b,F_1,A_3) = hAPP(fun(X_c,bool),X_b,hAPP(X_b,fun(fun(X_c,bool),X_b),hAPP(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b))),finite_fold_image(X_b,X_c),F),G),Z_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_2),G),F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_574_folding__image__simple_Oeq__fold__g]) ).

fof(f_645_2,plain,
    ! [U_2452,U_2451,U_2450,U_2449,U_2448,U_2447,U_2446] :
      ( hAPP(fun(U_2452,bool),U_2451,U_2446,U_2450) = hAPP(fun(U_2452,bool),U_2451,hAPP(U_2451,fun(fun(U_2452,bool),U_2451),hAPP(fun(U_2452,U_2451),fun(U_2451,fun(fun(U_2452,bool),U_2451)),hAPP(fun(U_2451,fun(U_2451,U_2451)),fun(fun(U_2452,U_2451),fun(U_2451,fun(fun(U_2452,bool),U_2451))),finite_fold_image(U_2451,U_2452),U_2449),U_2447),U_2448),U_2450)
      | ~ hBOOL(hAPP(fun(U_2452,bool),bool,finite_finite(U_2452),U_2450))
      | ~ hBOOL(hAPP(fun(fun(U_2452,bool),U_2451),bool,hAPP(fun(U_2452,U_2451),fun(fun(fun(U_2452,bool),U_2451),bool),hAPP(U_2451,fun(fun(U_2452,U_2451),fun(fun(fun(U_2452,bool),U_2451),bool)),hAPP(fun(U_2451,fun(U_2451,U_2451)),fun(U_2451,fun(fun(U_2452,U_2451),fun(fun(fun(U_2452,bool),U_2451),bool))),finite1357897459simple(U_2451,U_2452),U_2449),U_2448),U_2447),U_2446)) ),
    inference(variable_rename,[status(thm)],[f_645_1]) ).

fof(f_645_3,plain,
    ! [U_2447,U_2446,U_2451,U_2448,U_2449,U_2450,U_2452] :
      ( hAPP(fun(U_2452,bool),U_2451,U_2446,U_2450) = hAPP(fun(U_2452,bool),U_2451,hAPP(U_2451,fun(fun(U_2452,bool),U_2451),hAPP(fun(U_2452,U_2451),fun(U_2451,fun(fun(U_2452,bool),U_2451)),hAPP(fun(U_2451,fun(U_2451,U_2451)),fun(fun(U_2452,U_2451),fun(U_2451,fun(fun(U_2452,bool),U_2451))),finite_fold_image(U_2451,U_2452),U_2449),U_2447),U_2448),U_2450)
      | ~ hBOOL(hAPP(fun(U_2452,bool),bool,finite_finite(U_2452),U_2450))
      | ~ hBOOL(hAPP(fun(fun(U_2452,bool),U_2451),bool,hAPP(fun(U_2452,U_2451),fun(fun(fun(U_2452,bool),U_2451),bool),hAPP(U_2451,fun(fun(U_2452,U_2451),fun(fun(fun(U_2452,bool),U_2451),bool)),hAPP(fun(U_2451,fun(U_2451,U_2451)),fun(U_2451,fun(fun(U_2452,U_2451),fun(fun(fun(U_2452,bool),U_2451),bool))),finite1357897459simple(U_2451,U_2452),U_2449),U_2448),U_2447),U_2446)) ),
    inference(definitional_conversion,[status(esa)],[f_645_2]) ).

cnf(f_645_4,plain,
    ( hAPP(fun(U_2452,bool),U_2451,U_2446,U_2450) = hAPP(fun(U_2452,bool),U_2451,hAPP(U_2451,fun(fun(U_2452,bool),U_2451),hAPP(fun(U_2452,U_2451),fun(U_2451,fun(fun(U_2452,bool),U_2451)),hAPP(fun(U_2451,fun(U_2451,U_2451)),fun(fun(U_2452,U_2451),fun(U_2451,fun(fun(U_2452,bool),U_2451))),finite_fold_image(U_2451,U_2452),U_2449),U_2447),U_2448),U_2450)
    | ~ hBOOL(hAPP(fun(U_2452,bool),bool,finite_finite(U_2452),U_2450))
    | ~ hBOOL(hAPP(fun(fun(U_2452,bool),U_2451),bool,hAPP(fun(U_2452,U_2451),fun(fun(fun(U_2452,bool),U_2451),bool),hAPP(U_2451,fun(fun(U_2452,U_2451),fun(fun(fun(U_2452,bool),U_2451),bool)),hAPP(fun(U_2451,fun(U_2451,U_2451)),fun(U_2451,fun(fun(U_2452,U_2451),fun(fun(fun(U_2452,bool),U_2451),bool))),finite1357897459simple(U_2451,U_2452),U_2449),U_2448),U_2447),U_2446)) ),
    inference(clausify,[status(thm)],[f_645_3]) ).

fof(f_646_1,plain,
    ! [X_b] :
      ( ! [A_2] :
          ( ( ( 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),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),one_one(X_b)),A_2)),A_2)),zero_zero(X_b)))
              | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),zero_zero(X_b))) )
            & ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),zero_zero(X_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),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),one_one(X_b)),A_2)),A_2)),zero_zero(X_b))) ) )
          | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),ring_1_Ints(X_b))) )
      | ~ linordered_idom(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_575_Ints__odd__less__0]) ).

fof(f_646_2,plain,
    ! [U_2454] :
      ( ! [U_2453] :
          ( ( ( hBOOL(hAPP(U_2454,bool,hAPP(U_2454,fun(U_2454,bool),ord_less(U_2454),hAPP(U_2454,U_2454,hAPP(U_2454,fun(U_2454,U_2454),plus_plus(U_2454),hAPP(U_2454,U_2454,hAPP(U_2454,fun(U_2454,U_2454),plus_plus(U_2454),one_one(U_2454)),U_2453)),U_2453)),zero_zero(U_2454)))
              | ~ hBOOL(hAPP(U_2454,bool,hAPP(U_2454,fun(U_2454,bool),ord_less(U_2454),U_2453),zero_zero(U_2454))) )
            & ( hBOOL(hAPP(U_2454,bool,hAPP(U_2454,fun(U_2454,bool),ord_less(U_2454),U_2453),zero_zero(U_2454)))
              | ~ hBOOL(hAPP(U_2454,bool,hAPP(U_2454,fun(U_2454,bool),ord_less(U_2454),hAPP(U_2454,U_2454,hAPP(U_2454,fun(U_2454,U_2454),plus_plus(U_2454),hAPP(U_2454,U_2454,hAPP(U_2454,fun(U_2454,U_2454),plus_plus(U_2454),one_one(U_2454)),U_2453)),U_2453)),zero_zero(U_2454))) ) )
          | ~ hBOOL(hAPP(fun(U_2454,bool),bool,hAPP(U_2454,fun(fun(U_2454,bool),bool),member(U_2454),U_2453),ring_1_Ints(U_2454))) )
      | ~ linordered_idom(U_2454) ),
    inference(variable_rename,[status(thm)],[f_646_1]) ).

fof(f_646_3,plain,
    ( ! [U_2453,U_2454] :
        ( hBOOL(hAPP(U_2454,bool,hAPP(U_2454,fun(U_2454,bool),ord_less(U_2454),hAPP(U_2454,U_2454,hAPP(U_2454,fun(U_2454,U_2454),plus_plus(U_2454),hAPP(U_2454,U_2454,hAPP(U_2454,fun(U_2454,U_2454),plus_plus(U_2454),one_one(U_2454)),U_2453)),U_2453)),zero_zero(U_2454)))
        | ~ hBOOL(hAPP(U_2454,bool,hAPP(U_2454,fun(U_2454,bool),ord_less(U_2454),U_2453),zero_zero(U_2454)))
        | ~ sP169(U_2453,U_2454) )
    & ! [U_2453,U_2454] :
        ( hBOOL(hAPP(U_2454,bool,hAPP(U_2454,fun(U_2454,bool),ord_less(U_2454),U_2453),zero_zero(U_2454)))
        | ~ hBOOL(hAPP(U_2454,bool,hAPP(U_2454,fun(U_2454,bool),ord_less(U_2454),hAPP(U_2454,U_2454,hAPP(U_2454,fun(U_2454,U_2454),plus_plus(U_2454),hAPP(U_2454,U_2454,hAPP(U_2454,fun(U_2454,U_2454),plus_plus(U_2454),one_one(U_2454)),U_2453)),U_2453)),zero_zero(U_2454)))
        | ~ sP169(U_2453,U_2454) )
    & ! [U_2453,U_2454] :
        ( sP169(U_2453,U_2454)
        | ~ hBOOL(hAPP(fun(U_2454,bool),bool,hAPP(U_2454,fun(fun(U_2454,bool),bool),member(U_2454),U_2453),ring_1_Ints(U_2454)))
        | ~ linordered_idom(U_2454) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP169])],[f_646_2]) ).

cnf(f_646_4,plain,
    ( sP169(U_2453,U_2454)
    | ~ hBOOL(hAPP(fun(U_2454,bool),bool,hAPP(U_2454,fun(fun(U_2454,bool),bool),member(U_2454),U_2453),ring_1_Ints(U_2454)))
    | ~ linordered_idom(U_2454) ),
    inference(clausify,[status(thm)],[f_646_3]) ).

cnf(f_646_5,plain,
    ( hBOOL(hAPP(U_2454,bool,hAPP(U_2454,fun(U_2454,bool),ord_less(U_2454),U_2453),zero_zero(U_2454)))
    | ~ hBOOL(hAPP(U_2454,bool,hAPP(U_2454,fun(U_2454,bool),ord_less(U_2454),hAPP(U_2454,U_2454,hAPP(U_2454,fun(U_2454,U_2454),plus_plus(U_2454),hAPP(U_2454,U_2454,hAPP(U_2454,fun(U_2454,U_2454),plus_plus(U_2454),one_one(U_2454)),U_2453)),U_2453)),zero_zero(U_2454)))
    | ~ sP169(U_2453,U_2454) ),
    inference(clausify,[status(thm)],[f_646_3]) ).

cnf(f_646_6,plain,
    ( hBOOL(hAPP(U_2454,bool,hAPP(U_2454,fun(U_2454,bool),ord_less(U_2454),hAPP(U_2454,U_2454,hAPP(U_2454,fun(U_2454,U_2454),plus_plus(U_2454),hAPP(U_2454,U_2454,hAPP(U_2454,fun(U_2454,U_2454),plus_plus(U_2454),one_one(U_2454)),U_2453)),U_2453)),zero_zero(U_2454)))
    | ~ hBOOL(hAPP(U_2454,bool,hAPP(U_2454,fun(U_2454,bool),ord_less(U_2454),U_2453),zero_zero(U_2454)))
    | ~ sP169(U_2453,U_2454) ),
    inference(clausify,[status(thm)],[f_646_3]) ).

fof(f_647_1,plain,
    ! [V] :
      ( hAPP(int,nat,number_number_of(nat),V) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,number_number_of(nat),V)),one_one(nat)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),V))) ),
    inference(fof_nnf,[status(thm)],[fact_576_expand__Suc]) ).

fof(f_647_2,plain,
    ! [U_2455] :
      ( hAPP(int,nat,number_number_of(nat),U_2455) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,number_number_of(nat),U_2455)),one_one(nat)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),U_2455))) ),
    inference(variable_rename,[status(thm)],[f_647_1]) ).

fof(f_647_3,plain,
    ! [U_2455] :
      ( hAPP(int,nat,number_number_of(nat),U_2455) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,number_number_of(nat),U_2455)),one_one(nat)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),U_2455))) ),
    inference(definitional_conversion,[status(esa)],[f_647_2]) ).

cnf(f_647_4,plain,
    ( hAPP(int,nat,number_number_of(nat),U_2455) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,number_number_of(nat),U_2455)),one_one(nat)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),U_2455))) ),
    inference(clausify,[status(thm)],[f_647_3]) ).

fof(f_648_1,plain,
    ! [X_a] :
      ( ! [V,U_1,Y,X,A_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),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),U_1),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),V),Y))),A_1))
          | hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),U_1),V) != one_one(X_a)
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),V))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),U_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),A_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),A_1)) )
      | ~ linord626643107strict(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_577_convex__bound__lt]) ).

fof(f_648_2,plain,
    ! [U_2461] :
      ( ! [U_2460,U_2459,U_2458,U_2457,U_2456] :
          ( hBOOL(hAPP(U_2461,bool,hAPP(U_2461,fun(U_2461,bool),ord_less(U_2461),hAPP(U_2461,U_2461,hAPP(U_2461,fun(U_2461,U_2461),plus_plus(U_2461),hAPP(U_2461,U_2461,hAPP(U_2461,fun(U_2461,U_2461),times_times(U_2461),U_2459),U_2457)),hAPP(U_2461,U_2461,hAPP(U_2461,fun(U_2461,U_2461),times_times(U_2461),U_2460),U_2458))),U_2456))
          | hAPP(U_2461,U_2461,hAPP(U_2461,fun(U_2461,U_2461),plus_plus(U_2461),U_2459),U_2460) != one_one(U_2461)
          | ~ hBOOL(hAPP(U_2461,bool,hAPP(U_2461,fun(U_2461,bool),ord_less_eq(U_2461),zero_zero(U_2461)),U_2460))
          | ~ hBOOL(hAPP(U_2461,bool,hAPP(U_2461,fun(U_2461,bool),ord_less_eq(U_2461),zero_zero(U_2461)),U_2459))
          | ~ hBOOL(hAPP(U_2461,bool,hAPP(U_2461,fun(U_2461,bool),ord_less(U_2461),U_2458),U_2456))
          | ~ hBOOL(hAPP(U_2461,bool,hAPP(U_2461,fun(U_2461,bool),ord_less(U_2461),U_2457),U_2456)) )
      | ~ linord626643107strict(U_2461) ),
    inference(variable_rename,[status(thm)],[f_648_1]) ).

fof(f_648_3,plain,
    ! [U_2456,U_2457,U_2459,U_2460,U_2461,U_2458] :
      ( hBOOL(hAPP(U_2461,bool,hAPP(U_2461,fun(U_2461,bool),ord_less(U_2461),hAPP(U_2461,U_2461,hAPP(U_2461,fun(U_2461,U_2461),plus_plus(U_2461),hAPP(U_2461,U_2461,hAPP(U_2461,fun(U_2461,U_2461),times_times(U_2461),U_2459),U_2457)),hAPP(U_2461,U_2461,hAPP(U_2461,fun(U_2461,U_2461),times_times(U_2461),U_2460),U_2458))),U_2456))
      | hAPP(U_2461,U_2461,hAPP(U_2461,fun(U_2461,U_2461),plus_plus(U_2461),U_2459),U_2460) != one_one(U_2461)
      | ~ hBOOL(hAPP(U_2461,bool,hAPP(U_2461,fun(U_2461,bool),ord_less_eq(U_2461),zero_zero(U_2461)),U_2460))
      | ~ hBOOL(hAPP(U_2461,bool,hAPP(U_2461,fun(U_2461,bool),ord_less_eq(U_2461),zero_zero(U_2461)),U_2459))
      | ~ hBOOL(hAPP(U_2461,bool,hAPP(U_2461,fun(U_2461,bool),ord_less(U_2461),U_2458),U_2456))
      | ~ hBOOL(hAPP(U_2461,bool,hAPP(U_2461,fun(U_2461,bool),ord_less(U_2461),U_2457),U_2456))
      | ~ linord626643107strict(U_2461) ),
    inference(definitional_conversion,[status(esa)],[f_648_2]) ).

cnf(f_648_4,plain,
    ( hBOOL(hAPP(U_2461,bool,hAPP(U_2461,fun(U_2461,bool),ord_less(U_2461),hAPP(U_2461,U_2461,hAPP(U_2461,fun(U_2461,U_2461),plus_plus(U_2461),hAPP(U_2461,U_2461,hAPP(U_2461,fun(U_2461,U_2461),times_times(U_2461),U_2459),U_2457)),hAPP(U_2461,U_2461,hAPP(U_2461,fun(U_2461,U_2461),times_times(U_2461),U_2460),U_2458))),U_2456))
    | hAPP(U_2461,U_2461,hAPP(U_2461,fun(U_2461,U_2461),plus_plus(U_2461),U_2459),U_2460) != one_one(U_2461)
    | ~ hBOOL(hAPP(U_2461,bool,hAPP(U_2461,fun(U_2461,bool),ord_less_eq(U_2461),zero_zero(U_2461)),U_2460))
    | ~ hBOOL(hAPP(U_2461,bool,hAPP(U_2461,fun(U_2461,bool),ord_less_eq(U_2461),zero_zero(U_2461)),U_2459))
    | ~ hBOOL(hAPP(U_2461,bool,hAPP(U_2461,fun(U_2461,bool),ord_less(U_2461),U_2458),U_2456))
    | ~ hBOOL(hAPP(U_2461,bool,hAPP(U_2461,fun(U_2461,bool),ord_less(U_2461),U_2457),U_2456))
    | ~ linord626643107strict(U_2461) ),
    inference(clausify,[status(thm)],[f_648_3]) ).

fof(f_649_1,plain,
    ! [X_b] :
      ( ! [B_3,A_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),minus_minus(X_b),A_2),B_3)),ring_1_Ints(X_b)))
          | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_3),ring_1_Ints(X_b)))
          | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),ring_1_Ints(X_b))) )
      | ~ ring_1(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_578_Ints__diff]) ).

fof(f_649_2,plain,
    ! [U_2464] :
      ( ! [U_2463,U_2462] :
          ( hBOOL(hAPP(fun(U_2464,bool),bool,hAPP(U_2464,fun(fun(U_2464,bool),bool),member(U_2464),hAPP(U_2464,U_2464,hAPP(U_2464,fun(U_2464,U_2464),minus_minus(U_2464),U_2462),U_2463)),ring_1_Ints(U_2464)))
          | ~ hBOOL(hAPP(fun(U_2464,bool),bool,hAPP(U_2464,fun(fun(U_2464,bool),bool),member(U_2464),U_2463),ring_1_Ints(U_2464)))
          | ~ hBOOL(hAPP(fun(U_2464,bool),bool,hAPP(U_2464,fun(fun(U_2464,bool),bool),member(U_2464),U_2462),ring_1_Ints(U_2464))) )
      | ~ ring_1(U_2464) ),
    inference(variable_rename,[status(thm)],[f_649_1]) ).

fof(f_649_3,plain,
    ! [U_2464,U_2463,U_2462] :
      ( hBOOL(hAPP(fun(U_2464,bool),bool,hAPP(U_2464,fun(fun(U_2464,bool),bool),member(U_2464),hAPP(U_2464,U_2464,hAPP(U_2464,fun(U_2464,U_2464),minus_minus(U_2464),U_2462),U_2463)),ring_1_Ints(U_2464)))
      | ~ hBOOL(hAPP(fun(U_2464,bool),bool,hAPP(U_2464,fun(fun(U_2464,bool),bool),member(U_2464),U_2463),ring_1_Ints(U_2464)))
      | ~ hBOOL(hAPP(fun(U_2464,bool),bool,hAPP(U_2464,fun(fun(U_2464,bool),bool),member(U_2464),U_2462),ring_1_Ints(U_2464)))
      | ~ ring_1(U_2464) ),
    inference(definitional_conversion,[status(esa)],[f_649_2]) ).

cnf(f_649_4,plain,
    ( hBOOL(hAPP(fun(U_2464,bool),bool,hAPP(U_2464,fun(fun(U_2464,bool),bool),member(U_2464),hAPP(U_2464,U_2464,hAPP(U_2464,fun(U_2464,U_2464),minus_minus(U_2464),U_2462),U_2463)),ring_1_Ints(U_2464)))
    | ~ hBOOL(hAPP(fun(U_2464,bool),bool,hAPP(U_2464,fun(fun(U_2464,bool),bool),member(U_2464),U_2463),ring_1_Ints(U_2464)))
    | ~ hBOOL(hAPP(fun(U_2464,bool),bool,hAPP(U_2464,fun(fun(U_2464,bool),bool),member(U_2464),U_2462),ring_1_Ints(U_2464)))
    | ~ ring_1(U_2464) ),
    inference(clausify,[status(thm)],[f_649_3]) ).

fof(f_650_1,plain,
    ! [X_a] :
      ( ! [A_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),zero_zero(X_a)),A_1) = zero_zero(X_a)
      | ~ mult_zero(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_579_mult__zero__left]) ).

fof(f_650_2,plain,
    ! [U_2466] :
      ( ! [U_2465] : hAPP(U_2466,U_2466,hAPP(U_2466,fun(U_2466,U_2466),times_times(U_2466),zero_zero(U_2466)),U_2465) = zero_zero(U_2466)
      | ~ mult_zero(U_2466) ),
    inference(variable_rename,[status(thm)],[f_650_1]) ).

fof(f_650_3,plain,
    ! [U_2466,U_2465] :
      ( hAPP(U_2466,U_2466,hAPP(U_2466,fun(U_2466,U_2466),times_times(U_2466),zero_zero(U_2466)),U_2465) = zero_zero(U_2466)
      | ~ mult_zero(U_2466) ),
    inference(definitional_conversion,[status(esa)],[f_650_2]) ).

cnf(f_650_4,plain,
    ( hAPP(U_2466,U_2466,hAPP(U_2466,fun(U_2466,U_2466),times_times(U_2466),zero_zero(U_2466)),U_2465) = zero_zero(U_2466)
    | ~ mult_zero(U_2466) ),
    inference(clausify,[status(thm)],[f_650_3]) ).

fof(f_651_1,plain,
    ! [X_a] :
      ( ! [A_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),zero_zero(X_a)) = zero_zero(X_a)
      | ~ mult_zero(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_580_mult__zero__right]) ).

fof(f_651_2,plain,
    ! [U_2468] :
      ( ! [U_2467] : hAPP(U_2468,U_2468,hAPP(U_2468,fun(U_2468,U_2468),times_times(U_2468),U_2467),zero_zero(U_2468)) = zero_zero(U_2468)
      | ~ mult_zero(U_2468) ),
    inference(variable_rename,[status(thm)],[f_651_1]) ).

fof(f_651_3,plain,
    ! [U_2467,U_2468] :
      ( hAPP(U_2468,U_2468,hAPP(U_2468,fun(U_2468,U_2468),times_times(U_2468),U_2467),zero_zero(U_2468)) = zero_zero(U_2468)
      | ~ mult_zero(U_2468) ),
    inference(definitional_conversion,[status(esa)],[f_651_2]) ).

cnf(f_651_4,plain,
    ( hAPP(U_2468,U_2468,hAPP(U_2468,fun(U_2468,U_2468),times_times(U_2468),U_2467),zero_zero(U_2468)) = zero_zero(U_2468)
    | ~ mult_zero(U_2468) ),
    inference(clausify,[status(thm)],[f_651_3]) ).

fof(f_652_1,plain,
    ! [X_b] :
      ( ! [A_2,B_3] :
          ( ( hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),B_3) = zero_zero(X_b)
            | ( ti(X_b,B_3) != zero_zero(X_b)
              & ti(X_b,A_2) != zero_zero(X_b) ) )
          & ( ti(X_b,B_3) = zero_zero(X_b)
            | ti(X_b,A_2) = zero_zero(X_b)
            | hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),B_3) != zero_zero(X_b) ) )
      | ~ ring_n68954251visors(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_581_mult__eq__0__iff]) ).

fof(f_652_2,plain,
    ! [U_2471] :
      ( ! [U_2470,U_2469] :
          ( ( hAPP(U_2471,U_2471,hAPP(U_2471,fun(U_2471,U_2471),times_times(U_2471),U_2470),U_2469) = zero_zero(U_2471)
            | ( ti(U_2471,U_2469) != zero_zero(U_2471)
              & ti(U_2471,U_2470) != zero_zero(U_2471) ) )
          & ( ti(U_2471,U_2469) = zero_zero(U_2471)
            | ti(U_2471,U_2470) = zero_zero(U_2471)
            | hAPP(U_2471,U_2471,hAPP(U_2471,fun(U_2471,U_2471),times_times(U_2471),U_2470),U_2469) != zero_zero(U_2471) ) )
      | ~ ring_n68954251visors(U_2471) ),
    inference(variable_rename,[status(thm)],[f_652_1]) ).

fof(f_652_3,plain,
    ! [U_2471] :
      ( ( ! [U_2475,U_2473] :
            ( hAPP(U_2471,U_2471,hAPP(U_2471,fun(U_2471,U_2471),times_times(U_2471),U_2475),U_2473) = zero_zero(U_2471)
            | ( ti(U_2471,U_2473) != zero_zero(U_2471)
              & ti(U_2471,U_2475) != zero_zero(U_2471) ) )
        & ! [U_2474,U_2472] :
            ( ti(U_2471,U_2472) = zero_zero(U_2471)
            | ti(U_2471,U_2474) = zero_zero(U_2471)
            | hAPP(U_2471,U_2471,hAPP(U_2471,fun(U_2471,U_2471),times_times(U_2471),U_2474),U_2472) != zero_zero(U_2471) ) )
      | ~ ring_n68954251visors(U_2471) ),
    inference(miniscope,[status(thm)],[f_652_2]) ).

fof(f_652_4,plain,
    ( ! [U_2475,U_2471,U_2473] :
        ( ti(U_2471,U_2473) != zero_zero(U_2471)
        | ~ sP170(U_2475,U_2471,U_2473) )
    & ! [U_2475,U_2471,U_2473] :
        ( ti(U_2471,U_2475) != zero_zero(U_2471)
        | ~ sP170(U_2475,U_2471,U_2473) )
    & ! [U_2475,U_2471,U_2473,U_2472,U_2474] :
        ( hAPP(U_2471,U_2471,hAPP(U_2471,fun(U_2471,U_2471),times_times(U_2471),U_2475),U_2473) = zero_zero(U_2471)
        | sP170(U_2475,U_2471,U_2473)
        | ~ sP171(U_2475,U_2471,U_2473,U_2472,U_2474) )
    & ! [U_2475,U_2471,U_2473,U_2472,U_2474] :
        ( ti(U_2471,U_2472) = zero_zero(U_2471)
        | ti(U_2471,U_2474) = zero_zero(U_2471)
        | hAPP(U_2471,U_2471,hAPP(U_2471,fun(U_2471,U_2471),times_times(U_2471),U_2474),U_2472) != zero_zero(U_2471)
        | ~ sP171(U_2475,U_2471,U_2473,U_2472,U_2474) )
    & ! [U_2475,U_2471,U_2473,U_2472,U_2474] :
        ( sP171(U_2475,U_2471,U_2473,U_2472,U_2474)
        | ~ ring_n68954251visors(U_2471) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP170,sP171])],[f_652_3]) ).

cnf(f_652_5,plain,
    ( sP171(U_2475,U_2471,U_2473,U_2472,U_2474)
    | ~ ring_n68954251visors(U_2471) ),
    inference(clausify,[status(thm)],[f_652_4]) ).

cnf(f_652_6,plain,
    ( ti(U_2471,U_2472) = zero_zero(U_2471)
    | ti(U_2471,U_2474) = zero_zero(U_2471)
    | hAPP(U_2471,U_2471,hAPP(U_2471,fun(U_2471,U_2471),times_times(U_2471),U_2474),U_2472) != zero_zero(U_2471)
    | ~ sP171(U_2475,U_2471,U_2473,U_2472,U_2474) ),
    inference(clausify,[status(thm)],[f_652_4]) ).

cnf(f_652_7,plain,
    ( hAPP(U_2471,U_2471,hAPP(U_2471,fun(U_2471,U_2471),times_times(U_2471),U_2475),U_2473) = zero_zero(U_2471)
    | sP170(U_2475,U_2471,U_2473)
    | ~ sP171(U_2475,U_2471,U_2473,U_2472,U_2474) ),
    inference(clausify,[status(thm)],[f_652_4]) ).

cnf(f_652_8,plain,
    ( ti(U_2471,U_2475) != zero_zero(U_2471)
    | ~ sP170(U_2475,U_2471,U_2473) ),
    inference(clausify,[status(thm)],[f_652_4]) ).

cnf(f_652_9,plain,
    ( ti(U_2471,U_2473) != zero_zero(U_2471)
    | ~ sP170(U_2475,U_2471,U_2473) ),
    inference(clausify,[status(thm)],[f_652_4]) ).

fof(f_653_1,plain,
    ! [X_a] :
      ( ! [B,A_1] :
          ( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B) != zero_zero(X_a)
          | ti(X_a,B) = zero_zero(X_a)
          | ti(X_a,A_1) = zero_zero(X_a) )
      | ~ no_zero_divisors(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_582_no__zero__divisors]) ).

fof(f_653_2,plain,
    ! [U_2478] :
      ( ! [U_2477,U_2476] :
          ( hAPP(U_2478,U_2478,hAPP(U_2478,fun(U_2478,U_2478),times_times(U_2478),U_2476),U_2477) != zero_zero(U_2478)
          | ti(U_2478,U_2477) = zero_zero(U_2478)
          | ti(U_2478,U_2476) = zero_zero(U_2478) )
      | ~ no_zero_divisors(U_2478) ),
    inference(variable_rename,[status(thm)],[f_653_1]) ).

fof(f_653_3,plain,
    ! [U_2478,U_2476,U_2477] :
      ( hAPP(U_2478,U_2478,hAPP(U_2478,fun(U_2478,U_2478),times_times(U_2478),U_2476),U_2477) != zero_zero(U_2478)
      | ti(U_2478,U_2477) = zero_zero(U_2478)
      | ti(U_2478,U_2476) = zero_zero(U_2478)
      | ~ no_zero_divisors(U_2478) ),
    inference(definitional_conversion,[status(esa)],[f_653_2]) ).

cnf(f_653_4,plain,
    ( hAPP(U_2478,U_2478,hAPP(U_2478,fun(U_2478,U_2478),times_times(U_2478),U_2476),U_2477) != zero_zero(U_2478)
    | ti(U_2478,U_2477) = zero_zero(U_2478)
    | ti(U_2478,U_2476) = zero_zero(U_2478)
    | ~ no_zero_divisors(U_2478) ),
    inference(clausify,[status(thm)],[f_653_3]) ).

fof(f_654_1,plain,
    ! [X_a] :
      ( ! [A_1,B] :
          ( ti(X_a,B) = zero_zero(X_a)
          | ti(X_a,A_1) = zero_zero(X_a)
          | hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B) != zero_zero(X_a) )
      | ~ no_zero_divisors(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_583_divisors__zero]) ).

fof(f_654_2,plain,
    ! [U_2481] :
      ( ! [U_2480,U_2479] :
          ( ti(U_2481,U_2479) = zero_zero(U_2481)
          | ti(U_2481,U_2480) = zero_zero(U_2481)
          | hAPP(U_2481,U_2481,hAPP(U_2481,fun(U_2481,U_2481),times_times(U_2481),U_2480),U_2479) != zero_zero(U_2481) )
      | ~ no_zero_divisors(U_2481) ),
    inference(variable_rename,[status(thm)],[f_654_1]) ).

fof(f_654_3,plain,
    ! [U_2480,U_2479,U_2481] :
      ( ti(U_2481,U_2479) = zero_zero(U_2481)
      | ti(U_2481,U_2480) = zero_zero(U_2481)
      | hAPP(U_2481,U_2481,hAPP(U_2481,fun(U_2481,U_2481),times_times(U_2481),U_2480),U_2479) != zero_zero(U_2481)
      | ~ no_zero_divisors(U_2481) ),
    inference(definitional_conversion,[status(esa)],[f_654_2]) ).

cnf(f_654_4,plain,
    ( ti(U_2481,U_2479) = zero_zero(U_2481)
    | ti(U_2481,U_2480) = zero_zero(U_2481)
    | hAPP(U_2481,U_2481,hAPP(U_2481,fun(U_2481,U_2481),times_times(U_2481),U_2480),U_2479) != zero_zero(U_2481)
    | ~ no_zero_divisors(U_2481) ),
    inference(clausify,[status(thm)],[f_654_3]) ).

fof(f_655_1,plain,
    ! [N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),zero_zero(nat)),N) = zero_zero(nat),
    inference(fof_nnf,[status(thm)],[fact_584_mult__0]) ).

fof(f_655_2,plain,
    ! [U_2482] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),zero_zero(nat)),U_2482) = zero_zero(nat),
    inference(variable_rename,[status(thm)],[f_655_1]) ).

fof(f_655_3,plain,
    ! [U_2482] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),zero_zero(nat)),U_2482) = zero_zero(nat),
    inference(definitional_conversion,[status(esa)],[f_655_2]) ).

cnf(f_655_4,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),zero_zero(nat)),U_2482) = zero_zero(nat),
    inference(clausify,[status(thm)],[f_655_3]) ).

fof(f_656_1,plain,
    ! [M_1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),zero_zero(nat)) = zero_zero(nat),
    inference(fof_nnf,[status(thm)],[fact_585_mult__0__right]) ).

fof(f_656_2,plain,
    ! [U_2483] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2483),zero_zero(nat)) = zero_zero(nat),
    inference(variable_rename,[status(thm)],[f_656_1]) ).

fof(f_656_3,plain,
    ! [U_2483] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2483),zero_zero(nat)) = zero_zero(nat),
    inference(definitional_conversion,[status(esa)],[f_656_2]) ).

cnf(f_656_4,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2483),zero_zero(nat)) = zero_zero(nat),
    inference(clausify,[status(thm)],[f_656_3]) ).

fof(f_657_1,plain,
    ! [M,Na] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na) = zero_zero(nat)
        | ( Na != zero_zero(nat)
          & M != zero_zero(nat) ) )
      & ( Na = zero_zero(nat)
        | M = zero_zero(nat)
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na) != zero_zero(nat) ) ),
    inference(fof_nnf,[status(thm)],[fact_586_mult__is__0]) ).

fof(f_657_2,plain,
    ! [U_2485,U_2484] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2485),U_2484) = zero_zero(nat)
        | ( U_2484 != zero_zero(nat)
          & U_2485 != zero_zero(nat) ) )
      & ( U_2484 = zero_zero(nat)
        | U_2485 = zero_zero(nat)
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2485),U_2484) != zero_zero(nat) ) ),
    inference(variable_rename,[status(thm)],[f_657_1]) ).

fof(f_657_3,plain,
    ( ! [U_2489,U_2487] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2489),U_2487) = zero_zero(nat)
        | ( U_2487 != zero_zero(nat)
          & U_2489 != zero_zero(nat) ) )
    & ! [U_2488,U_2486] :
        ( U_2486 = zero_zero(nat)
        | U_2488 = zero_zero(nat)
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2488),U_2486) != zero_zero(nat) ) ),
    inference(miniscope,[status(thm)],[f_657_2]) ).

fof(f_657_4,plain,
    ( ! [U_2489,U_2487] :
        ( U_2487 != zero_zero(nat)
        | ~ sP172(U_2489,U_2487) )
    & ! [U_2489,U_2487] :
        ( U_2489 != zero_zero(nat)
        | ~ sP172(U_2489,U_2487) )
    & ! [U_2489,U_2487] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2489),U_2487) = zero_zero(nat)
        | sP172(U_2489,U_2487) )
    & ! [U_2486,U_2488] :
        ( U_2486 = zero_zero(nat)
        | U_2488 = zero_zero(nat)
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2488),U_2486) != zero_zero(nat) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP172])],[f_657_3]) ).

cnf(f_657_5,plain,
    ( U_2486 = zero_zero(nat)
    | U_2488 = zero_zero(nat)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2488),U_2486) != zero_zero(nat) ),
    inference(clausify,[status(thm)],[f_657_4]) ).

cnf(f_657_6,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2489),U_2487) = zero_zero(nat)
    | sP172(U_2489,U_2487) ),
    inference(clausify,[status(thm)],[f_657_4]) ).

cnf(f_657_7,plain,
    ( U_2489 != zero_zero(nat)
    | ~ sP172(U_2489,U_2487) ),
    inference(clausify,[status(thm)],[f_657_4]) ).

cnf(f_657_8,plain,
    ( U_2487 != zero_zero(nat)
    | ~ sP172(U_2489,U_2487) ),
    inference(clausify,[status(thm)],[f_657_4]) ).

fof(f_658_1,plain,
    ! [K,M,Na] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na)
        | ( K != zero_zero(nat)
          & M != Na ) )
      & ( K = zero_zero(nat)
        | M = Na
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na) ) ),
    inference(fof_nnf,[status(thm)],[fact_587_mult__cancel1]) ).

fof(f_658_2,plain,
    ! [U_2492,U_2491,U_2490] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2492),U_2491) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2492),U_2490)
        | ( U_2492 != zero_zero(nat)
          & U_2491 != U_2490 ) )
      & ( U_2492 = zero_zero(nat)
        | U_2491 = U_2490
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2492),U_2491) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2492),U_2490) ) ),
    inference(variable_rename,[status(thm)],[f_658_1]) ).

fof(f_658_3,plain,
    ( ! [U_2498,U_2496,U_2494] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2498),U_2496) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2498),U_2494)
        | ( U_2498 != zero_zero(nat)
          & U_2496 != U_2494 ) )
    & ! [U_2497,U_2495,U_2493] :
        ( U_2497 = zero_zero(nat)
        | U_2495 = U_2493
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2497),U_2495) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2497),U_2493) ) ),
    inference(miniscope,[status(thm)],[f_658_2]) ).

fof(f_658_4,plain,
    ( ! [U_2498,U_2496,U_2494] :
        ( U_2498 != zero_zero(nat)
        | ~ sP173(U_2498,U_2496,U_2494) )
    & ! [U_2498,U_2496,U_2494] :
        ( U_2496 != U_2494
        | ~ sP173(U_2498,U_2496,U_2494) )
    & ! [U_2498,U_2496,U_2494] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2498),U_2496) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2498),U_2494)
        | sP173(U_2498,U_2496,U_2494) )
    & ! [U_2497,U_2493,U_2495] :
        ( U_2497 = zero_zero(nat)
        | U_2495 = U_2493
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2497),U_2495) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2497),U_2493) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP173])],[f_658_3]) ).

cnf(f_658_5,plain,
    ( U_2497 = zero_zero(nat)
    | U_2495 = U_2493
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2497),U_2495) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2497),U_2493) ),
    inference(clausify,[status(thm)],[f_658_4]) ).

cnf(f_658_6,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2498),U_2496) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2498),U_2494)
    | sP173(U_2498,U_2496,U_2494) ),
    inference(clausify,[status(thm)],[f_658_4]) ).

cnf(f_658_7,plain,
    ( U_2496 != U_2494
    | ~ sP173(U_2498,U_2496,U_2494) ),
    inference(clausify,[status(thm)],[f_658_4]) ).

cnf(f_658_8,plain,
    ( U_2498 != zero_zero(nat)
    | ~ sP173(U_2498,U_2496,U_2494) ),
    inference(clausify,[status(thm)],[f_658_4]) ).

fof(f_659_1,plain,
    ! [M,K,Na] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Na),K)
        | ( K != zero_zero(nat)
          & M != Na ) )
      & ( K = zero_zero(nat)
        | M = Na
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Na),K) ) ),
    inference(fof_nnf,[status(thm)],[fact_588_mult__cancel2]) ).

fof(f_659_2,plain,
    ! [U_2501,U_2500,U_2499] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2501),U_2500) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2499),U_2500)
        | ( U_2500 != zero_zero(nat)
          & U_2501 != U_2499 ) )
      & ( U_2500 = zero_zero(nat)
        | U_2501 = U_2499
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2501),U_2500) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2499),U_2500) ) ),
    inference(variable_rename,[status(thm)],[f_659_1]) ).

fof(f_659_3,plain,
    ( ! [U_2507,U_2505,U_2503] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2507),U_2505) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2503),U_2505)
        | ( U_2505 != zero_zero(nat)
          & U_2507 != U_2503 ) )
    & ! [U_2506,U_2504,U_2502] :
        ( U_2504 = zero_zero(nat)
        | U_2506 = U_2502
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2506),U_2504) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2502),U_2504) ) ),
    inference(miniscope,[status(thm)],[f_659_2]) ).

fof(f_659_4,plain,
    ( ! [U_2507,U_2505,U_2503] :
        ( U_2505 != zero_zero(nat)
        | ~ sP174(U_2507,U_2505,U_2503) )
    & ! [U_2507,U_2505,U_2503] :
        ( U_2507 != U_2503
        | ~ sP174(U_2507,U_2505,U_2503) )
    & ! [U_2507,U_2505,U_2503] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2507),U_2505) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2503),U_2505)
        | sP174(U_2507,U_2505,U_2503) )
    & ! [U_2502,U_2506,U_2504] :
        ( U_2504 = zero_zero(nat)
        | U_2506 = U_2502
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2506),U_2504) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2502),U_2504) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP174])],[f_659_3]) ).

cnf(f_659_5,plain,
    ( U_2504 = zero_zero(nat)
    | U_2506 = U_2502
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2506),U_2504) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2502),U_2504) ),
    inference(clausify,[status(thm)],[f_659_4]) ).

cnf(f_659_6,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2507),U_2505) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2503),U_2505)
    | sP174(U_2507,U_2505,U_2503) ),
    inference(clausify,[status(thm)],[f_659_4]) ).

cnf(f_659_7,plain,
    ( U_2507 != U_2503
    | ~ sP174(U_2507,U_2505,U_2503) ),
    inference(clausify,[status(thm)],[f_659_4]) ).

cnf(f_659_8,plain,
    ( U_2505 != zero_zero(nat)
    | ~ sP174(U_2507,U_2505,U_2503) ),
    inference(clausify,[status(thm)],[f_659_4]) ).

fof(f_660_1,plain,
    ! [X_b] :
      ( hBOOL(hAPP(fun(X_b,fun(X_b,X_b)),bool,finite_comp_fun_idem(X_b,X_b),times_times(X_b)))
      | ~ ab_sem1668676832m_mult(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_589_comp__fun__idem]) ).

fof(f_660_2,plain,
    ! [U_2508] :
      ( hBOOL(hAPP(fun(U_2508,fun(U_2508,U_2508)),bool,finite_comp_fun_idem(U_2508,U_2508),times_times(U_2508)))
      | ~ ab_sem1668676832m_mult(U_2508) ),
    inference(variable_rename,[status(thm)],[f_660_1]) ).

fof(f_660_3,plain,
    ! [U_2508] :
      ( hBOOL(hAPP(fun(U_2508,fun(U_2508,U_2508)),bool,finite_comp_fun_idem(U_2508,U_2508),times_times(U_2508)))
      | ~ ab_sem1668676832m_mult(U_2508) ),
    inference(definitional_conversion,[status(esa)],[f_660_2]) ).

cnf(f_660_4,plain,
    ( hBOOL(hAPP(fun(U_2508,fun(U_2508,U_2508)),bool,finite_comp_fun_idem(U_2508,U_2508),times_times(U_2508)))
    | ~ ab_sem1668676832m_mult(U_2508) ),
    inference(clausify,[status(thm)],[f_660_3]) ).

fof(f_661_1,plain,
    ! [X_a] :
      ( ! [A_1,B,C] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),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),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C))
      | ~ comm_semiring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_590_comm__semiring__class_Odistrib]) ).

fof(f_661_2,plain,
    ! [U_2512] :
      ( ! [U_2511,U_2510,U_2509] : hAPP(U_2512,U_2512,hAPP(U_2512,fun(U_2512,U_2512),times_times(U_2512),hAPP(U_2512,U_2512,hAPP(U_2512,fun(U_2512,U_2512),plus_plus(U_2512),U_2511),U_2510)),U_2509) = hAPP(U_2512,U_2512,hAPP(U_2512,fun(U_2512,U_2512),plus_plus(U_2512),hAPP(U_2512,U_2512,hAPP(U_2512,fun(U_2512,U_2512),times_times(U_2512),U_2511),U_2509)),hAPP(U_2512,U_2512,hAPP(U_2512,fun(U_2512,U_2512),times_times(U_2512),U_2510),U_2509))
      | ~ comm_semiring(U_2512) ),
    inference(variable_rename,[status(thm)],[f_661_1]) ).

fof(f_661_3,plain,
    ! [U_2509,U_2512,U_2510,U_2511] :
      ( hAPP(U_2512,U_2512,hAPP(U_2512,fun(U_2512,U_2512),times_times(U_2512),hAPP(U_2512,U_2512,hAPP(U_2512,fun(U_2512,U_2512),plus_plus(U_2512),U_2511),U_2510)),U_2509) = hAPP(U_2512,U_2512,hAPP(U_2512,fun(U_2512,U_2512),plus_plus(U_2512),hAPP(U_2512,U_2512,hAPP(U_2512,fun(U_2512,U_2512),times_times(U_2512),U_2511),U_2509)),hAPP(U_2512,U_2512,hAPP(U_2512,fun(U_2512,U_2512),times_times(U_2512),U_2510),U_2509))
      | ~ comm_semiring(U_2512) ),
    inference(definitional_conversion,[status(esa)],[f_661_2]) ).

cnf(f_661_4,plain,
    ( hAPP(U_2512,U_2512,hAPP(U_2512,fun(U_2512,U_2512),times_times(U_2512),hAPP(U_2512,U_2512,hAPP(U_2512,fun(U_2512,U_2512),plus_plus(U_2512),U_2511),U_2510)),U_2509) = hAPP(U_2512,U_2512,hAPP(U_2512,fun(U_2512,U_2512),plus_plus(U_2512),hAPP(U_2512,U_2512,hAPP(U_2512,fun(U_2512,U_2512),times_times(U_2512),U_2511),U_2509)),hAPP(U_2512,U_2512,hAPP(U_2512,fun(U_2512,U_2512),times_times(U_2512),U_2510),U_2509))
    | ~ comm_semiring(U_2512) ),
    inference(clausify,[status(thm)],[f_661_3]) ).

fof(f_662_1,plain,
    ! [X_a] :
      ( ! [A_1,E_1,B,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),times_times(X_a),A_1),E_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),times_times(X_a),B),E_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),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),E_1)),C)
      | ~ semiring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_591_combine__common__factor]) ).

fof(f_662_2,plain,
    ! [U_2517] :
      ( ! [U_2516,U_2515,U_2514,U_2513] : hAPP(U_2517,U_2517,hAPP(U_2517,fun(U_2517,U_2517),plus_plus(U_2517),hAPP(U_2517,U_2517,hAPP(U_2517,fun(U_2517,U_2517),times_times(U_2517),U_2516),U_2515)),hAPP(U_2517,U_2517,hAPP(U_2517,fun(U_2517,U_2517),plus_plus(U_2517),hAPP(U_2517,U_2517,hAPP(U_2517,fun(U_2517,U_2517),times_times(U_2517),U_2514),U_2515)),U_2513)) = hAPP(U_2517,U_2517,hAPP(U_2517,fun(U_2517,U_2517),plus_plus(U_2517),hAPP(U_2517,U_2517,hAPP(U_2517,fun(U_2517,U_2517),times_times(U_2517),hAPP(U_2517,U_2517,hAPP(U_2517,fun(U_2517,U_2517),plus_plus(U_2517),U_2516),U_2514)),U_2515)),U_2513)
      | ~ semiring(U_2517) ),
    inference(variable_rename,[status(thm)],[f_662_1]) ).

fof(f_662_3,plain,
    ! [U_2517,U_2513,U_2514,U_2515,U_2516] :
      ( hAPP(U_2517,U_2517,hAPP(U_2517,fun(U_2517,U_2517),plus_plus(U_2517),hAPP(U_2517,U_2517,hAPP(U_2517,fun(U_2517,U_2517),times_times(U_2517),U_2516),U_2515)),hAPP(U_2517,U_2517,hAPP(U_2517,fun(U_2517,U_2517),plus_plus(U_2517),hAPP(U_2517,U_2517,hAPP(U_2517,fun(U_2517,U_2517),times_times(U_2517),U_2514),U_2515)),U_2513)) = hAPP(U_2517,U_2517,hAPP(U_2517,fun(U_2517,U_2517),plus_plus(U_2517),hAPP(U_2517,U_2517,hAPP(U_2517,fun(U_2517,U_2517),times_times(U_2517),hAPP(U_2517,U_2517,hAPP(U_2517,fun(U_2517,U_2517),plus_plus(U_2517),U_2516),U_2514)),U_2515)),U_2513)
      | ~ semiring(U_2517) ),
    inference(definitional_conversion,[status(esa)],[f_662_2]) ).

cnf(f_662_4,plain,
    ( hAPP(U_2517,U_2517,hAPP(U_2517,fun(U_2517,U_2517),plus_plus(U_2517),hAPP(U_2517,U_2517,hAPP(U_2517,fun(U_2517,U_2517),times_times(U_2517),U_2516),U_2515)),hAPP(U_2517,U_2517,hAPP(U_2517,fun(U_2517,U_2517),plus_plus(U_2517),hAPP(U_2517,U_2517,hAPP(U_2517,fun(U_2517,U_2517),times_times(U_2517),U_2514),U_2515)),U_2513)) = hAPP(U_2517,U_2517,hAPP(U_2517,fun(U_2517,U_2517),plus_plus(U_2517),hAPP(U_2517,U_2517,hAPP(U_2517,fun(U_2517,U_2517),times_times(U_2517),hAPP(U_2517,U_2517,hAPP(U_2517,fun(U_2517,U_2517),plus_plus(U_2517),U_2516),U_2514)),U_2515)),U_2513)
    | ~ semiring(U_2517) ),
    inference(clausify,[status(thm)],[f_662_3]) ).

fof(f_663_1,plain,
    ! [X_a] :
      ( ! [A_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),one_one(X_a)) = ti(X_a,A_1)
      | ~ comm_monoid_mult(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_592_mult_Ocomm__neutral]) ).

fof(f_663_2,plain,
    ! [U_2519] :
      ( ! [U_2518] : hAPP(U_2519,U_2519,hAPP(U_2519,fun(U_2519,U_2519),times_times(U_2519),U_2518),one_one(U_2519)) = ti(U_2519,U_2518)
      | ~ comm_monoid_mult(U_2519) ),
    inference(variable_rename,[status(thm)],[f_663_1]) ).

fof(f_663_3,plain,
    ! [U_2518,U_2519] :
      ( hAPP(U_2519,U_2519,hAPP(U_2519,fun(U_2519,U_2519),times_times(U_2519),U_2518),one_one(U_2519)) = ti(U_2519,U_2518)
      | ~ comm_monoid_mult(U_2519) ),
    inference(definitional_conversion,[status(esa)],[f_663_2]) ).

cnf(f_663_4,plain,
    ( hAPP(U_2519,U_2519,hAPP(U_2519,fun(U_2519,U_2519),times_times(U_2519),U_2518),one_one(U_2519)) = ti(U_2519,U_2518)
    | ~ comm_monoid_mult(U_2519) ),
    inference(clausify,[status(thm)],[f_663_3]) ).

fof(f_664_1,plain,
    ! [X_a] :
      ( ! [A_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),one_one(X_a)) = ti(X_a,A_1)
      | ~ monoid_mult(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_593_mult__1__right]) ).

fof(f_664_2,plain,
    ! [U_2521] :
      ( ! [U_2520] : hAPP(U_2521,U_2521,hAPP(U_2521,fun(U_2521,U_2521),times_times(U_2521),U_2520),one_one(U_2521)) = ti(U_2521,U_2520)
      | ~ monoid_mult(U_2521) ),
    inference(variable_rename,[status(thm)],[f_664_1]) ).

fof(f_664_3,plain,
    ! [U_2520,U_2521] :
      ( hAPP(U_2521,U_2521,hAPP(U_2521,fun(U_2521,U_2521),times_times(U_2521),U_2520),one_one(U_2521)) = ti(U_2521,U_2520)
      | ~ monoid_mult(U_2521) ),
    inference(definitional_conversion,[status(esa)],[f_664_2]) ).

cnf(f_664_4,plain,
    ( hAPP(U_2521,U_2521,hAPP(U_2521,fun(U_2521,U_2521),times_times(U_2521),U_2520),one_one(U_2521)) = ti(U_2521,U_2520)
    | ~ monoid_mult(U_2521) ),
    inference(clausify,[status(thm)],[f_664_3]) ).

fof(f_665_1,plain,
    ! [X_a] :
      ( ! [A_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),one_one(X_a)),A_1) = ti(X_a,A_1)
      | ~ comm_monoid_mult(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_594_mult__1]) ).

fof(f_665_2,plain,
    ! [U_2523] :
      ( ! [U_2522] : hAPP(U_2523,U_2523,hAPP(U_2523,fun(U_2523,U_2523),times_times(U_2523),one_one(U_2523)),U_2522) = ti(U_2523,U_2522)
      | ~ comm_monoid_mult(U_2523) ),
    inference(variable_rename,[status(thm)],[f_665_1]) ).

fof(f_665_3,plain,
    ! [U_2522,U_2523] :
      ( hAPP(U_2523,U_2523,hAPP(U_2523,fun(U_2523,U_2523),times_times(U_2523),one_one(U_2523)),U_2522) = ti(U_2523,U_2522)
      | ~ comm_monoid_mult(U_2523) ),
    inference(definitional_conversion,[status(esa)],[f_665_2]) ).

cnf(f_665_4,plain,
    ( hAPP(U_2523,U_2523,hAPP(U_2523,fun(U_2523,U_2523),times_times(U_2523),one_one(U_2523)),U_2522) = ti(U_2523,U_2522)
    | ~ comm_monoid_mult(U_2523) ),
    inference(clausify,[status(thm)],[f_665_3]) ).

fof(f_666_1,plain,
    ! [X_a] :
      ( ! [A_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),one_one(X_a)),A_1) = ti(X_a,A_1)
      | ~ monoid_mult(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_595_mult__1__left]) ).

fof(f_666_2,plain,
    ! [U_2525] :
      ( ! [U_2524] : hAPP(U_2525,U_2525,hAPP(U_2525,fun(U_2525,U_2525),times_times(U_2525),one_one(U_2525)),U_2524) = ti(U_2525,U_2524)
      | ~ monoid_mult(U_2525) ),
    inference(variable_rename,[status(thm)],[f_666_1]) ).

fof(f_666_3,plain,
    ! [U_2524,U_2525] :
      ( hAPP(U_2525,U_2525,hAPP(U_2525,fun(U_2525,U_2525),times_times(U_2525),one_one(U_2525)),U_2524) = ti(U_2525,U_2524)
      | ~ monoid_mult(U_2525) ),
    inference(definitional_conversion,[status(esa)],[f_666_2]) ).

cnf(f_666_4,plain,
    ( hAPP(U_2525,U_2525,hAPP(U_2525,fun(U_2525,U_2525),times_times(U_2525),one_one(U_2525)),U_2524) = ti(U_2525,U_2524)
    | ~ monoid_mult(U_2525) ),
    inference(clausify,[status(thm)],[f_666_3]) ).

fof(f_667_1,plain,
    ! [K,M,Na] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),M) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),Na)
        | M != Na )
      & ( M = Na
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),M) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),Na) ) ),
    inference(fof_nnf,[status(thm)],[fact_596_Suc__mult__cancel1]) ).

fof(f_667_2,plain,
    ! [U_2528,U_2527,U_2526] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2528)),U_2527) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2528)),U_2526)
        | U_2527 != U_2526 )
      & ( U_2527 = U_2526
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2528)),U_2527) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2528)),U_2526) ) ),
    inference(variable_rename,[status(thm)],[f_667_1]) ).

fof(f_667_3,plain,
    ( ! [U_2534,U_2532,U_2530] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2534)),U_2532) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2534)),U_2530)
        | U_2532 != U_2530 )
    & ! [U_2533,U_2531,U_2529] :
        ( U_2531 = U_2529
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2533)),U_2531) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2533)),U_2529) ) ),
    inference(miniscope,[status(thm)],[f_667_2]) ).

fof(f_667_4,plain,
    ( ! [U_2532,U_2530,U_2534] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2534)),U_2532) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2534)),U_2530)
        | U_2532 != U_2530 )
    & ! [U_2529,U_2531,U_2533] :
        ( U_2531 = U_2529
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2533)),U_2531) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2533)),U_2529) ) ),
    inference(definitional_conversion,[status(esa)],[f_667_3]) ).

cnf(f_667_5,plain,
    ( U_2531 = U_2529
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2533)),U_2531) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2533)),U_2529) ),
    inference(clausify,[status(thm)],[f_667_4]) ).

cnf(f_667_6,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2534)),U_2532) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2534)),U_2530)
    | U_2532 != U_2530 ),
    inference(clausify,[status(thm)],[f_667_4]) ).

fof(f_668_1,plain,
    ! [M_1,N,K_1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N)),K_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),K_1)),
    inference(fof_nnf,[status(thm)],[fact_597_add__mult__distrib]) ).

fof(f_668_2,plain,
    ! [U_2537,U_2536,U_2535] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2537),U_2536)),U_2535) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2537),U_2535)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2536),U_2535)),
    inference(variable_rename,[status(thm)],[f_668_1]) ).

fof(f_668_3,plain,
    ! [U_2535,U_2536,U_2537] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2537),U_2536)),U_2535) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2537),U_2535)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2536),U_2535)),
    inference(definitional_conversion,[status(esa)],[f_668_2]) ).

cnf(f_668_4,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2537),U_2536)),U_2535) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2537),U_2535)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2536),U_2535)),
    inference(clausify,[status(thm)],[f_668_3]) ).

fof(f_669_1,plain,
    ! [K_1,M_1,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N)),
    inference(fof_nnf,[status(thm)],[fact_598_add__mult__distrib2]) ).

fof(f_669_2,plain,
    ! [U_2540,U_2539,U_2538] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2540),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2539),U_2538)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2540),U_2539)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2540),U_2538)),
    inference(variable_rename,[status(thm)],[f_669_1]) ).

fof(f_669_3,plain,
    ! [U_2540,U_2538,U_2539] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2540),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2539),U_2538)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2540),U_2539)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2540),U_2538)),
    inference(definitional_conversion,[status(esa)],[f_669_2]) ).

cnf(f_669_4,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2540),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2539),U_2538)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2540),U_2539)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2540),U_2538)),
    inference(clausify,[status(thm)],[f_669_3]) ).

fof(f_670_1,plain,
    ! [K_1,L_1,I_2,J] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_2),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),L_1)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),L_1))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),J)) ),
    inference(fof_nnf,[status(thm)],[fact_599_mult__le__mono]) ).

fof(f_670_2,plain,
    ! [U_2544,U_2543,U_2542,U_2541] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2542),U_2544)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2541),U_2543)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2544),U_2543))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2542),U_2541)) ),
    inference(variable_rename,[status(thm)],[f_670_1]) ).

fof(f_670_3,plain,
    ! [U_2541,U_2542,U_2543,U_2544] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2542),U_2544)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2541),U_2543)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2544),U_2543))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2542),U_2541)) ),
    inference(definitional_conversion,[status(esa)],[f_670_2]) ).

cnf(f_670_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2542),U_2544)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2541),U_2543)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2544),U_2543))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2542),U_2541)) ),
    inference(clausify,[status(thm)],[f_670_3]) ).

fof(f_671_1,plain,
    ! [K_1,I_2,J] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),I_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),J)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),J)) ),
    inference(fof_nnf,[status(thm)],[fact_600_mult__le__mono2]) ).

fof(f_671_2,plain,
    ! [U_2547,U_2546,U_2545] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2547),U_2546)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2547),U_2545)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2546),U_2545)) ),
    inference(variable_rename,[status(thm)],[f_671_1]) ).

fof(f_671_3,plain,
    ! [U_2545,U_2546,U_2547] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2547),U_2546)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2547),U_2545)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2546),U_2545)) ),
    inference(definitional_conversion,[status(esa)],[f_671_2]) ).

cnf(f_671_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2547),U_2546)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2547),U_2545)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2546),U_2545)) ),
    inference(clausify,[status(thm)],[f_671_3]) ).

fof(f_672_1,plain,
    ! [K_1,I_2,J] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_2),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),K_1)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),J)) ),
    inference(fof_nnf,[status(thm)],[fact_601_mult__le__mono1]) ).

fof(f_672_2,plain,
    ! [U_2550,U_2549,U_2548] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2549),U_2550)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2548),U_2550)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2549),U_2548)) ),
    inference(variable_rename,[status(thm)],[f_672_1]) ).

fof(f_672_3,plain,
    ! [U_2548,U_2549,U_2550] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2549),U_2550)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2548),U_2550)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2549),U_2548)) ),
    inference(definitional_conversion,[status(esa)],[f_672_2]) ).

cnf(f_672_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2549),U_2550)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2548),U_2550)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2549),U_2548)) ),
    inference(clausify,[status(thm)],[f_672_3]) ).

fof(f_673_1,plain,
    ! [M_1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),M_1)))),
    inference(fof_nnf,[status(thm)],[fact_602_le__cube]) ).

fof(f_673_2,plain,
    ! [U_2551] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2551),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2551),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2551),U_2551)))),
    inference(variable_rename,[status(thm)],[f_673_1]) ).

fof(f_673_3,plain,
    ! [U_2551] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2551),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2551),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2551),U_2551)))),
    inference(definitional_conversion,[status(esa)],[f_673_2]) ).

cnf(f_673_4,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2551),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2551),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2551),U_2551)))),
    inference(clausify,[status(thm)],[f_673_3]) ).

fof(f_674_1,plain,
    ! [M_1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),M_1))),
    inference(fof_nnf,[status(thm)],[fact_603_le__square]) ).

fof(f_674_2,plain,
    ! [U_2552] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2552),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2552),U_2552))),
    inference(variable_rename,[status(thm)],[f_674_1]) ).

fof(f_674_3,plain,
    ! [U_2552] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2552),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2552),U_2552))),
    inference(definitional_conversion,[status(esa)],[f_674_2]) ).

cnf(f_674_4,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2552),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2552),U_2552))),
    inference(clausify,[status(thm)],[f_674_3]) ).

fof(f_675_1,plain,
    ! [M_1,N,K_1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N)),K_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),K_1)),
    inference(fof_nnf,[status(thm)],[fact_604_diff__mult__distrib]) ).

fof(f_675_2,plain,
    ! [U_2555,U_2554,U_2553] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2555),U_2554)),U_2553) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2555),U_2553)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2554),U_2553)),
    inference(variable_rename,[status(thm)],[f_675_1]) ).

fof(f_675_3,plain,
    ! [U_2553,U_2554,U_2555] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2555),U_2554)),U_2553) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2555),U_2553)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2554),U_2553)),
    inference(definitional_conversion,[status(esa)],[f_675_2]) ).

cnf(f_675_4,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2555),U_2554)),U_2553) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2555),U_2553)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2554),U_2553)),
    inference(clausify,[status(thm)],[f_675_3]) ).

fof(f_676_1,plain,
    ! [K_1,M_1,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N)),
    inference(fof_nnf,[status(thm)],[fact_605_diff__mult__distrib2]) ).

fof(f_676_2,plain,
    ! [U_2558,U_2557,U_2556] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2558),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2557),U_2556)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2558),U_2557)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2558),U_2556)),
    inference(variable_rename,[status(thm)],[f_676_1]) ).

fof(f_676_3,plain,
    ! [U_2558,U_2556,U_2557] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2558),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2557),U_2556)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2558),U_2557)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2558),U_2556)),
    inference(definitional_conversion,[status(esa)],[f_676_2]) ).

cnf(f_676_4,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2558),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2557),U_2556)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2558),U_2557)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2558),U_2556)),
    inference(clausify,[status(thm)],[f_676_3]) ).

fof(f_677_1,plain,
    ! [X_a] :
      ( ! [A_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),A_1) = ti(X_a,A_1)
      | ~ ab_sem1668676832m_mult(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_606_times_Oidem]) ).

fof(f_677_2,plain,
    ! [U_2560] :
      ( ! [U_2559] : hAPP(U_2560,U_2560,hAPP(U_2560,fun(U_2560,U_2560),times_times(U_2560),U_2559),U_2559) = ti(U_2560,U_2559)
      | ~ ab_sem1668676832m_mult(U_2560) ),
    inference(variable_rename,[status(thm)],[f_677_1]) ).

fof(f_677_3,plain,
    ! [U_2559,U_2560] :
      ( hAPP(U_2560,U_2560,hAPP(U_2560,fun(U_2560,U_2560),times_times(U_2560),U_2559),U_2559) = ti(U_2560,U_2559)
      | ~ ab_sem1668676832m_mult(U_2560) ),
    inference(definitional_conversion,[status(esa)],[f_677_2]) ).

cnf(f_677_4,plain,
    ( hAPP(U_2560,U_2560,hAPP(U_2560,fun(U_2560,U_2560),times_times(U_2560),U_2559),U_2559) = ti(U_2560,U_2559)
    | ~ ab_sem1668676832m_mult(U_2560) ),
    inference(clausify,[status(thm)],[f_677_3]) ).

fof(f_678_1,plain,
    ! [X_a] :
      ( ! [X] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),X) = ti(X_a,X)
      | ~ ab_sem1668676832m_mult(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_607_mult__idem]) ).

fof(f_678_2,plain,
    ! [U_2562] :
      ( ! [U_2561] : hAPP(U_2562,U_2562,hAPP(U_2562,fun(U_2562,U_2562),times_times(U_2562),U_2561),U_2561) = ti(U_2562,U_2561)
      | ~ ab_sem1668676832m_mult(U_2562) ),
    inference(variable_rename,[status(thm)],[f_678_1]) ).

fof(f_678_3,plain,
    ! [U_2561,U_2562] :
      ( hAPP(U_2562,U_2562,hAPP(U_2562,fun(U_2562,U_2562),times_times(U_2562),U_2561),U_2561) = ti(U_2562,U_2561)
      | ~ ab_sem1668676832m_mult(U_2562) ),
    inference(definitional_conversion,[status(esa)],[f_678_2]) ).

cnf(f_678_4,plain,
    ( hAPP(U_2562,U_2562,hAPP(U_2562,fun(U_2562,U_2562),times_times(U_2562),U_2561),U_2561) = ti(U_2562,U_2561)
    | ~ ab_sem1668676832m_mult(U_2562) ),
    inference(clausify,[status(thm)],[f_678_3]) ).

fof(f_679_1,plain,
    ! [X_a] :
      ( ! [A_1,B] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)
      | ~ ab_sem1668676832m_mult(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_608_mult__left__idem]) ).

fof(f_679_2,plain,
    ! [U_2565] :
      ( ! [U_2564,U_2563] : hAPP(U_2565,U_2565,hAPP(U_2565,fun(U_2565,U_2565),times_times(U_2565),U_2564),hAPP(U_2565,U_2565,hAPP(U_2565,fun(U_2565,U_2565),times_times(U_2565),U_2564),U_2563)) = hAPP(U_2565,U_2565,hAPP(U_2565,fun(U_2565,U_2565),times_times(U_2565),U_2564),U_2563)
      | ~ ab_sem1668676832m_mult(U_2565) ),
    inference(variable_rename,[status(thm)],[f_679_1]) ).

fof(f_679_3,plain,
    ! [U_2563,U_2565,U_2564] :
      ( hAPP(U_2565,U_2565,hAPP(U_2565,fun(U_2565,U_2565),times_times(U_2565),U_2564),hAPP(U_2565,U_2565,hAPP(U_2565,fun(U_2565,U_2565),times_times(U_2565),U_2564),U_2563)) = hAPP(U_2565,U_2565,hAPP(U_2565,fun(U_2565,U_2565),times_times(U_2565),U_2564),U_2563)
      | ~ ab_sem1668676832m_mult(U_2565) ),
    inference(definitional_conversion,[status(esa)],[f_679_2]) ).

cnf(f_679_4,plain,
    ( hAPP(U_2565,U_2565,hAPP(U_2565,fun(U_2565,U_2565),times_times(U_2565),U_2564),hAPP(U_2565,U_2565,hAPP(U_2565,fun(U_2565,U_2565),times_times(U_2565),U_2564),U_2563)) = hAPP(U_2565,U_2565,hAPP(U_2565,fun(U_2565,U_2565),times_times(U_2565),U_2564),U_2563)
    | ~ ab_sem1668676832m_mult(U_2565) ),
    inference(clausify,[status(thm)],[f_679_3]) ).

fof(f_680_1,plain,
    ! [X_a] :
      ( ! [A_1,B,C] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C))
      | ~ ab_semigroup_mult(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_609_ab__semigroup__mult__class_Omult__ac_I1_J]) ).

fof(f_680_2,plain,
    ! [U_2569] :
      ( ! [U_2568,U_2567,U_2566] : hAPP(U_2569,U_2569,hAPP(U_2569,fun(U_2569,U_2569),times_times(U_2569),hAPP(U_2569,U_2569,hAPP(U_2569,fun(U_2569,U_2569),times_times(U_2569),U_2568),U_2567)),U_2566) = hAPP(U_2569,U_2569,hAPP(U_2569,fun(U_2569,U_2569),times_times(U_2569),U_2568),hAPP(U_2569,U_2569,hAPP(U_2569,fun(U_2569,U_2569),times_times(U_2569),U_2567),U_2566))
      | ~ ab_semigroup_mult(U_2569) ),
    inference(variable_rename,[status(thm)],[f_680_1]) ).

fof(f_680_3,plain,
    ! [U_2566,U_2569,U_2567,U_2568] :
      ( hAPP(U_2569,U_2569,hAPP(U_2569,fun(U_2569,U_2569),times_times(U_2569),hAPP(U_2569,U_2569,hAPP(U_2569,fun(U_2569,U_2569),times_times(U_2569),U_2568),U_2567)),U_2566) = hAPP(U_2569,U_2569,hAPP(U_2569,fun(U_2569,U_2569),times_times(U_2569),U_2568),hAPP(U_2569,U_2569,hAPP(U_2569,fun(U_2569,U_2569),times_times(U_2569),U_2567),U_2566))
      | ~ ab_semigroup_mult(U_2569) ),
    inference(definitional_conversion,[status(esa)],[f_680_2]) ).

cnf(f_680_4,plain,
    ( hAPP(U_2569,U_2569,hAPP(U_2569,fun(U_2569,U_2569),times_times(U_2569),hAPP(U_2569,U_2569,hAPP(U_2569,fun(U_2569,U_2569),times_times(U_2569),U_2568),U_2567)),U_2566) = hAPP(U_2569,U_2569,hAPP(U_2569,fun(U_2569,U_2569),times_times(U_2569),U_2568),hAPP(U_2569,U_2569,hAPP(U_2569,fun(U_2569,U_2569),times_times(U_2569),U_2567),U_2566))
    | ~ ab_semigroup_mult(U_2569) ),
    inference(clausify,[status(thm)],[f_680_3]) ).

fof(f_681_1,plain,
    ! [M,Na] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na) = one_one(nat)
        | Na != one_one(nat)
        | M != one_one(nat) )
      & ( ( Na = one_one(nat)
          & M = one_one(nat) )
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na) != one_one(nat) ) ),
    inference(fof_nnf,[status(thm)],[fact_610_nat__mult__eq__1__iff]) ).

fof(f_681_2,plain,
    ! [U_2571,U_2570] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2571),U_2570) = one_one(nat)
        | U_2570 != one_one(nat)
        | U_2571 != one_one(nat) )
      & ( ( U_2570 = one_one(nat)
          & U_2571 = one_one(nat) )
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2571),U_2570) != one_one(nat) ) ),
    inference(variable_rename,[status(thm)],[f_681_1]) ).

fof(f_681_3,plain,
    ( ! [U_2575,U_2573] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2575),U_2573) = one_one(nat)
        | U_2573 != one_one(nat)
        | U_2575 != one_one(nat) )
    & ! [U_2574,U_2572] :
        ( ( U_2572 = one_one(nat)
          & U_2574 = one_one(nat) )
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2574),U_2572) != one_one(nat) ) ),
    inference(miniscope,[status(thm)],[f_681_2]) ).

fof(f_681_4,plain,
    ( ! [U_2572,U_2574] :
        ( U_2572 = one_one(nat)
        | ~ sP175(U_2572,U_2574) )
    & ! [U_2572,U_2574] :
        ( U_2574 = one_one(nat)
        | ~ sP175(U_2572,U_2574) )
    & ! [U_2575,U_2573] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2575),U_2573) = one_one(nat)
        | U_2573 != one_one(nat)
        | U_2575 != one_one(nat) )
    & ! [U_2572,U_2574] :
        ( sP175(U_2572,U_2574)
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2574),U_2572) != one_one(nat) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP175])],[f_681_3]) ).

cnf(f_681_5,plain,
    ( sP175(U_2572,U_2574)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2574),U_2572) != one_one(nat) ),
    inference(clausify,[status(thm)],[f_681_4]) ).

cnf(f_681_6,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2575),U_2573) = one_one(nat)
    | U_2573 != one_one(nat)
    | U_2575 != one_one(nat) ),
    inference(clausify,[status(thm)],[f_681_4]) ).

cnf(f_681_7,plain,
    ( U_2574 = one_one(nat)
    | ~ sP175(U_2572,U_2574) ),
    inference(clausify,[status(thm)],[f_681_4]) ).

cnf(f_681_8,plain,
    ( U_2572 = one_one(nat)
    | ~ sP175(U_2572,U_2574) ),
    inference(clausify,[status(thm)],[f_681_4]) ).

fof(f_682_1,plain,
    ! [N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),one_one(nat)) = N,
    inference(fof_nnf,[status(thm)],[fact_611_nat__mult__1__right]) ).

fof(f_682_2,plain,
    ! [U_2576] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2576),one_one(nat)) = U_2576,
    inference(variable_rename,[status(thm)],[f_682_1]) ).

fof(f_682_3,plain,
    ! [U_2576] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2576),one_one(nat)) = U_2576,
    inference(definitional_conversion,[status(esa)],[f_682_2]) ).

cnf(f_682_4,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2576),one_one(nat)) = U_2576,
    inference(clausify,[status(thm)],[f_682_3]) ).

fof(f_683_1,plain,
    ! [M,Na] :
      ( ( one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na)
        | Na != one_one(nat)
        | M != one_one(nat) )
      & ( ( Na = one_one(nat)
          & M = one_one(nat) )
        | one_one(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na) ) ),
    inference(fof_nnf,[status(thm)],[fact_612_nat__1__eq__mult__iff]) ).

fof(f_683_2,plain,
    ! [U_2578,U_2577] :
      ( ( one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2578),U_2577)
        | U_2577 != one_one(nat)
        | U_2578 != one_one(nat) )
      & ( ( U_2577 = one_one(nat)
          & U_2578 = one_one(nat) )
        | one_one(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2578),U_2577) ) ),
    inference(variable_rename,[status(thm)],[f_683_1]) ).

fof(f_683_3,plain,
    ( ! [U_2582,U_2580] :
        ( one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2582),U_2580)
        | U_2580 != one_one(nat)
        | U_2582 != one_one(nat) )
    & ! [U_2581,U_2579] :
        ( ( U_2579 = one_one(nat)
          & U_2581 = one_one(nat) )
        | one_one(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2581),U_2579) ) ),
    inference(miniscope,[status(thm)],[f_683_2]) ).

fof(f_683_4,plain,
    ( ! [U_2579,U_2581] :
        ( U_2579 = one_one(nat)
        | ~ sP176(U_2579,U_2581) )
    & ! [U_2579,U_2581] :
        ( U_2581 = one_one(nat)
        | ~ sP176(U_2579,U_2581) )
    & ! [U_2582,U_2580] :
        ( one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2582),U_2580)
        | U_2580 != one_one(nat)
        | U_2582 != one_one(nat) )
    & ! [U_2579,U_2581] :
        ( sP176(U_2579,U_2581)
        | one_one(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2581),U_2579) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP176])],[f_683_3]) ).

cnf(f_683_5,plain,
    ( sP176(U_2579,U_2581)
    | one_one(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2581),U_2579) ),
    inference(clausify,[status(thm)],[f_683_4]) ).

cnf(f_683_6,plain,
    ( one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2582),U_2580)
    | U_2580 != one_one(nat)
    | U_2582 != one_one(nat) ),
    inference(clausify,[status(thm)],[f_683_4]) ).

cnf(f_683_7,plain,
    ( U_2581 = one_one(nat)
    | ~ sP176(U_2579,U_2581) ),
    inference(clausify,[status(thm)],[f_683_4]) ).

cnf(f_683_8,plain,
    ( U_2579 = one_one(nat)
    | ~ sP176(U_2579,U_2581) ),
    inference(clausify,[status(thm)],[f_683_4]) ).

fof(f_684_1,plain,
    ! [N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),one_one(nat)),N) = N,
    inference(fof_nnf,[status(thm)],[fact_613_nat__mult__1]) ).

fof(f_684_2,plain,
    ! [U_2583] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),one_one(nat)),U_2583) = U_2583,
    inference(variable_rename,[status(thm)],[f_684_1]) ).

fof(f_684_3,plain,
    ! [U_2583] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),one_one(nat)),U_2583) = U_2583,
    inference(definitional_conversion,[status(esa)],[f_684_2]) ).

cnf(f_684_4,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),one_one(nat)),U_2583) = U_2583,
    inference(clausify,[status(thm)],[f_684_3]) ).

fof(f_685_1,plain,
    ! [X_b] :
      ( ! [X_1,Y_2] :
          ( ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(int,X_b,number_number_of(X_b),X_1)),hAPP(int,X_b,number_number_of(X_b),Y_2)))
            | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Y_2)) )
          & ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Y_2))
            | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(int,X_b,number_number_of(X_b),X_1)),hAPP(int,X_b,number_number_of(X_b),Y_2))) ) )
      | ~ linordered_idom(X_b)
      | ~ number_ring(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_614_less__number__of]) ).

fof(f_685_2,plain,
    ! [U_2586] :
      ( ! [U_2585,U_2584] :
          ( ( hBOOL(hAPP(U_2586,bool,hAPP(U_2586,fun(U_2586,bool),ord_less(U_2586),hAPP(int,U_2586,number_number_of(U_2586),U_2585)),hAPP(int,U_2586,number_number_of(U_2586),U_2584)))
            | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_2585),U_2584)) )
          & ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_2585),U_2584))
            | ~ hBOOL(hAPP(U_2586,bool,hAPP(U_2586,fun(U_2586,bool),ord_less(U_2586),hAPP(int,U_2586,number_number_of(U_2586),U_2585)),hAPP(int,U_2586,number_number_of(U_2586),U_2584))) ) )
      | ~ linordered_idom(U_2586)
      | ~ number_ring(U_2586) ),
    inference(variable_rename,[status(thm)],[f_685_1]) ).

fof(f_685_3,plain,
    ! [U_2586] :
      ( ( ! [U_2590,U_2588] :
            ( hBOOL(hAPP(U_2586,bool,hAPP(U_2586,fun(U_2586,bool),ord_less(U_2586),hAPP(int,U_2586,number_number_of(U_2586),U_2590)),hAPP(int,U_2586,number_number_of(U_2586),U_2588)))
            | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_2590),U_2588)) )
        & ! [U_2589,U_2587] :
            ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_2589),U_2587))
            | ~ hBOOL(hAPP(U_2586,bool,hAPP(U_2586,fun(U_2586,bool),ord_less(U_2586),hAPP(int,U_2586,number_number_of(U_2586),U_2589)),hAPP(int,U_2586,number_number_of(U_2586),U_2587))) ) )
      | ~ linordered_idom(U_2586)
      | ~ number_ring(U_2586) ),
    inference(miniscope,[status(thm)],[f_685_2]) ).

fof(f_685_4,plain,
    ( ! [U_2586,U_2587,U_2588,U_2589,U_2590] :
        ( hBOOL(hAPP(U_2586,bool,hAPP(U_2586,fun(U_2586,bool),ord_less(U_2586),hAPP(int,U_2586,number_number_of(U_2586),U_2590)),hAPP(int,U_2586,number_number_of(U_2586),U_2588)))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_2590),U_2588))
        | ~ sP177(U_2586,U_2587,U_2588,U_2589,U_2590) )
    & ! [U_2586,U_2587,U_2588,U_2589,U_2590] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_2589),U_2587))
        | ~ hBOOL(hAPP(U_2586,bool,hAPP(U_2586,fun(U_2586,bool),ord_less(U_2586),hAPP(int,U_2586,number_number_of(U_2586),U_2589)),hAPP(int,U_2586,number_number_of(U_2586),U_2587)))
        | ~ sP177(U_2586,U_2587,U_2588,U_2589,U_2590) )
    & ! [U_2586,U_2587,U_2588,U_2589,U_2590] :
        ( sP177(U_2586,U_2587,U_2588,U_2589,U_2590)
        | ~ linordered_idom(U_2586)
        | ~ number_ring(U_2586) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP177])],[f_685_3]) ).

cnf(f_685_5,plain,
    ( sP177(U_2586,U_2587,U_2588,U_2589,U_2590)
    | ~ linordered_idom(U_2586)
    | ~ number_ring(U_2586) ),
    inference(clausify,[status(thm)],[f_685_4]) ).

cnf(f_685_6,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_2589),U_2587))
    | ~ hBOOL(hAPP(U_2586,bool,hAPP(U_2586,fun(U_2586,bool),ord_less(U_2586),hAPP(int,U_2586,number_number_of(U_2586),U_2589)),hAPP(int,U_2586,number_number_of(U_2586),U_2587)))
    | ~ sP177(U_2586,U_2587,U_2588,U_2589,U_2590) ),
    inference(clausify,[status(thm)],[f_685_4]) ).

cnf(f_685_7,plain,
    ( hBOOL(hAPP(U_2586,bool,hAPP(U_2586,fun(U_2586,bool),ord_less(U_2586),hAPP(int,U_2586,number_number_of(U_2586),U_2590)),hAPP(int,U_2586,number_number_of(U_2586),U_2588)))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_2590),U_2588))
    | ~ sP177(U_2586,U_2587,U_2588,U_2589,U_2590) ),
    inference(clausify,[status(thm)],[f_685_4]) ).

fof(f_686_1,plain,
    ! [X_b] :
      ( ! [W_1] : hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(int,X_b,number_number_of(X_b),W_1)),ring_1_Ints(X_b)))
      | ~ number_ring(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_615_Ints__number__of]) ).

fof(f_686_2,plain,
    ! [U_2592] :
      ( ! [U_2591] : hBOOL(hAPP(fun(U_2592,bool),bool,hAPP(U_2592,fun(fun(U_2592,bool),bool),member(U_2592),hAPP(int,U_2592,number_number_of(U_2592),U_2591)),ring_1_Ints(U_2592)))
      | ~ number_ring(U_2592) ),
    inference(variable_rename,[status(thm)],[f_686_1]) ).

fof(f_686_3,plain,
    ! [U_2592,U_2591] :
      ( hBOOL(hAPP(fun(U_2592,bool),bool,hAPP(U_2592,fun(fun(U_2592,bool),bool),member(U_2592),hAPP(int,U_2592,number_number_of(U_2592),U_2591)),ring_1_Ints(U_2592)))
      | ~ number_ring(U_2592) ),
    inference(definitional_conversion,[status(esa)],[f_686_2]) ).

cnf(f_686_4,plain,
    ( hBOOL(hAPP(fun(U_2592,bool),bool,hAPP(U_2592,fun(fun(U_2592,bool),bool),member(U_2592),hAPP(int,U_2592,number_number_of(U_2592),U_2591)),ring_1_Ints(U_2592)))
    | ~ number_ring(U_2592) ),
    inference(clausify,[status(thm)],[f_686_3]) ).

fof(f_687_1,plain,
    ! [X_a] :
      ( ! [V,W] : hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),W)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),W))
      | ~ number_ring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_616_number__of__mult]) ).

fof(f_687_2,plain,
    ! [U_2595] :
      ( ! [U_2594,U_2593] : hAPP(int,U_2595,number_number_of(U_2595),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_2594),U_2593)) = hAPP(U_2595,U_2595,hAPP(U_2595,fun(U_2595,U_2595),times_times(U_2595),hAPP(int,U_2595,number_number_of(U_2595),U_2594)),hAPP(int,U_2595,number_number_of(U_2595),U_2593))
      | ~ number_ring(U_2595) ),
    inference(variable_rename,[status(thm)],[f_687_1]) ).

fof(f_687_3,plain,
    ! [U_2593,U_2595,U_2594] :
      ( hAPP(int,U_2595,number_number_of(U_2595),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_2594),U_2593)) = hAPP(U_2595,U_2595,hAPP(U_2595,fun(U_2595,U_2595),times_times(U_2595),hAPP(int,U_2595,number_number_of(U_2595),U_2594)),hAPP(int,U_2595,number_number_of(U_2595),U_2593))
      | ~ number_ring(U_2595) ),
    inference(definitional_conversion,[status(esa)],[f_687_2]) ).

cnf(f_687_4,plain,
    ( hAPP(int,U_2595,number_number_of(U_2595),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_2594),U_2593)) = hAPP(U_2595,U_2595,hAPP(U_2595,fun(U_2595,U_2595),times_times(U_2595),hAPP(int,U_2595,number_number_of(U_2595),U_2594)),hAPP(int,U_2595,number_number_of(U_2595),U_2593))
    | ~ number_ring(U_2595) ),
    inference(clausify,[status(thm)],[f_687_3]) ).

fof(f_688_1,plain,
    ! [X_b] :
      ( ! [W_1,X_1] :
          ( ( hAPP(int,X_b,number_number_of(X_b),W_1) = ti(X_b,X_1)
            | ti(X_b,X_1) != hAPP(int,X_b,number_number_of(X_b),W_1) )
          & ( ti(X_b,X_1) = hAPP(int,X_b,number_number_of(X_b),W_1)
            | hAPP(int,X_b,number_number_of(X_b),W_1) != ti(X_b,X_1) ) )
      | ~ number(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_617_number__of__reorient]) ).

fof(f_688_2,plain,
    ! [U_2598] :
      ( ! [U_2597,U_2596] :
          ( ( hAPP(int,U_2598,number_number_of(U_2598),U_2597) = ti(U_2598,U_2596)
            | ti(U_2598,U_2596) != hAPP(int,U_2598,number_number_of(U_2598),U_2597) )
          & ( ti(U_2598,U_2596) = hAPP(int,U_2598,number_number_of(U_2598),U_2597)
            | hAPP(int,U_2598,number_number_of(U_2598),U_2597) != ti(U_2598,U_2596) ) )
      | ~ number(U_2598) ),
    inference(variable_rename,[status(thm)],[f_688_1]) ).

fof(f_688_3,plain,
    ! [U_2598] :
      ( ( ! [U_2602,U_2600] :
            ( hAPP(int,U_2598,number_number_of(U_2598),U_2602) = ti(U_2598,U_2600)
            | ti(U_2598,U_2600) != hAPP(int,U_2598,number_number_of(U_2598),U_2602) )
        & ! [U_2601,U_2599] :
            ( ti(U_2598,U_2599) = hAPP(int,U_2598,number_number_of(U_2598),U_2601)
            | hAPP(int,U_2598,number_number_of(U_2598),U_2601) != ti(U_2598,U_2599) ) )
      | ~ number(U_2598) ),
    inference(miniscope,[status(thm)],[f_688_2]) ).

fof(f_688_4,plain,
    ( ! [U_2602,U_2598,U_2599,U_2600,U_2601] :
        ( hAPP(int,U_2598,number_number_of(U_2598),U_2602) = ti(U_2598,U_2600)
        | ti(U_2598,U_2600) != hAPP(int,U_2598,number_number_of(U_2598),U_2602)
        | ~ sP178(U_2602,U_2598,U_2599,U_2600,U_2601) )
    & ! [U_2602,U_2598,U_2599,U_2600,U_2601] :
        ( ti(U_2598,U_2599) = hAPP(int,U_2598,number_number_of(U_2598),U_2601)
        | hAPP(int,U_2598,number_number_of(U_2598),U_2601) != ti(U_2598,U_2599)
        | ~ sP178(U_2602,U_2598,U_2599,U_2600,U_2601) )
    & ! [U_2602,U_2598,U_2599,U_2600,U_2601] :
        ( sP178(U_2602,U_2598,U_2599,U_2600,U_2601)
        | ~ number(U_2598) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP178])],[f_688_3]) ).

cnf(f_688_5,plain,
    ( sP178(U_2602,U_2598,U_2599,U_2600,U_2601)
    | ~ number(U_2598) ),
    inference(clausify,[status(thm)],[f_688_4]) ).

cnf(f_688_6,plain,
    ( ti(U_2598,U_2599) = hAPP(int,U_2598,number_number_of(U_2598),U_2601)
    | hAPP(int,U_2598,number_number_of(U_2598),U_2601) != ti(U_2598,U_2599)
    | ~ sP178(U_2602,U_2598,U_2599,U_2600,U_2601) ),
    inference(clausify,[status(thm)],[f_688_4]) ).

cnf(f_688_7,plain,
    ( hAPP(int,U_2598,number_number_of(U_2598),U_2602) = ti(U_2598,U_2600)
    | ti(U_2598,U_2600) != hAPP(int,U_2598,number_number_of(U_2598),U_2602)
    | ~ sP178(U_2602,U_2598,U_2599,U_2600,U_2601) ),
    inference(clausify,[status(thm)],[f_688_4]) ).

fof(f_689_1,plain,
    ! [X_a] :
      ( ! [V,W] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),W)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),W))
      | ~ number_ring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_618_arith__simps_I32_J]) ).

fof(f_689_2,plain,
    ! [U_2605] :
      ( ! [U_2604,U_2603] : hAPP(U_2605,U_2605,hAPP(U_2605,fun(U_2605,U_2605),times_times(U_2605),hAPP(int,U_2605,number_number_of(U_2605),U_2604)),hAPP(int,U_2605,number_number_of(U_2605),U_2603)) = hAPP(int,U_2605,number_number_of(U_2605),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_2604),U_2603))
      | ~ number_ring(U_2605) ),
    inference(variable_rename,[status(thm)],[f_689_1]) ).

fof(f_689_3,plain,
    ! [U_2604,U_2605,U_2603] :
      ( hAPP(U_2605,U_2605,hAPP(U_2605,fun(U_2605,U_2605),times_times(U_2605),hAPP(int,U_2605,number_number_of(U_2605),U_2604)),hAPP(int,U_2605,number_number_of(U_2605),U_2603)) = hAPP(int,U_2605,number_number_of(U_2605),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_2604),U_2603))
      | ~ number_ring(U_2605) ),
    inference(definitional_conversion,[status(esa)],[f_689_2]) ).

cnf(f_689_4,plain,
    ( hAPP(U_2605,U_2605,hAPP(U_2605,fun(U_2605,U_2605),times_times(U_2605),hAPP(int,U_2605,number_number_of(U_2605),U_2604)),hAPP(int,U_2605,number_number_of(U_2605),U_2603)) = hAPP(int,U_2605,number_number_of(U_2605),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_2604),U_2603))
    | ~ number_ring(U_2605) ),
    inference(clausify,[status(thm)],[f_689_3]) ).

fof(f_690_1,plain,
    ! [X_b] :
      ( ! [X_1,Y_2] :
          ( ( hAPP(int,X_b,number_number_of(X_b),X_1) = hAPP(int,X_b,number_number_of(X_b),Y_2)
            | X_1 != Y_2 )
          & ( X_1 = Y_2
            | hAPP(int,X_b,number_number_of(X_b),X_1) != hAPP(int,X_b,number_number_of(X_b),Y_2) ) )
      | ~ ring_char_0(X_b)
      | ~ number_ring(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_619_eq__number__of]) ).

fof(f_690_2,plain,
    ! [U_2608] :
      ( ! [U_2607,U_2606] :
          ( ( hAPP(int,U_2608,number_number_of(U_2608),U_2607) = hAPP(int,U_2608,number_number_of(U_2608),U_2606)
            | U_2607 != U_2606 )
          & ( U_2607 = U_2606
            | hAPP(int,U_2608,number_number_of(U_2608),U_2607) != hAPP(int,U_2608,number_number_of(U_2608),U_2606) ) )
      | ~ ring_char_0(U_2608)
      | ~ number_ring(U_2608) ),
    inference(variable_rename,[status(thm)],[f_690_1]) ).

fof(f_690_3,plain,
    ! [U_2608] :
      ( ( ! [U_2612,U_2610] :
            ( hAPP(int,U_2608,number_number_of(U_2608),U_2612) = hAPP(int,U_2608,number_number_of(U_2608),U_2610)
            | U_2612 != U_2610 )
        & ! [U_2611,U_2609] :
            ( U_2611 = U_2609
            | hAPP(int,U_2608,number_number_of(U_2608),U_2611) != hAPP(int,U_2608,number_number_of(U_2608),U_2609) ) )
      | ~ ring_char_0(U_2608)
      | ~ number_ring(U_2608) ),
    inference(miniscope,[status(thm)],[f_690_2]) ).

fof(f_690_4,plain,
    ( ! [U_2608,U_2610,U_2609,U_2612,U_2611] :
        ( hAPP(int,U_2608,number_number_of(U_2608),U_2612) = hAPP(int,U_2608,number_number_of(U_2608),U_2610)
        | U_2612 != U_2610
        | ~ sP179(U_2608,U_2610,U_2609,U_2612,U_2611) )
    & ! [U_2608,U_2610,U_2609,U_2612,U_2611] :
        ( U_2611 = U_2609
        | hAPP(int,U_2608,number_number_of(U_2608),U_2611) != hAPP(int,U_2608,number_number_of(U_2608),U_2609)
        | ~ sP179(U_2608,U_2610,U_2609,U_2612,U_2611) )
    & ! [U_2608,U_2610,U_2609,U_2612,U_2611] :
        ( sP179(U_2608,U_2610,U_2609,U_2612,U_2611)
        | ~ ring_char_0(U_2608)
        | ~ number_ring(U_2608) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP179])],[f_690_3]) ).

cnf(f_690_5,plain,
    ( sP179(U_2608,U_2610,U_2609,U_2612,U_2611)
    | ~ ring_char_0(U_2608)
    | ~ number_ring(U_2608) ),
    inference(clausify,[status(thm)],[f_690_4]) ).

cnf(f_690_6,plain,
    ( U_2611 = U_2609
    | hAPP(int,U_2608,number_number_of(U_2608),U_2611) != hAPP(int,U_2608,number_number_of(U_2608),U_2609)
    | ~ sP179(U_2608,U_2610,U_2609,U_2612,U_2611) ),
    inference(clausify,[status(thm)],[f_690_4]) ).

cnf(f_690_7,plain,
    ( hAPP(int,U_2608,number_number_of(U_2608),U_2612) = hAPP(int,U_2608,number_number_of(U_2608),U_2610)
    | U_2612 != U_2610
    | ~ sP179(U_2608,U_2610,U_2609,U_2612,U_2611) ),
    inference(clausify,[status(thm)],[f_690_4]) ).

fof(f_691_1,plain,
    ! [X_a] :
      ( ! [V,W,Z] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),W)),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),W))),Z)
      | ~ number_ring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_620_mult__number__of__left]) ).

fof(f_691_2,plain,
    ! [U_2616] :
      ( ! [U_2615,U_2614,U_2613] : hAPP(U_2616,U_2616,hAPP(U_2616,fun(U_2616,U_2616),times_times(U_2616),hAPP(int,U_2616,number_number_of(U_2616),U_2615)),hAPP(U_2616,U_2616,hAPP(U_2616,fun(U_2616,U_2616),times_times(U_2616),hAPP(int,U_2616,number_number_of(U_2616),U_2614)),U_2613)) = hAPP(U_2616,U_2616,hAPP(U_2616,fun(U_2616,U_2616),times_times(U_2616),hAPP(int,U_2616,number_number_of(U_2616),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_2615),U_2614))),U_2613)
      | ~ number_ring(U_2616) ),
    inference(variable_rename,[status(thm)],[f_691_1]) ).

fof(f_691_3,plain,
    ! [U_2614,U_2615,U_2616,U_2613] :
      ( hAPP(U_2616,U_2616,hAPP(U_2616,fun(U_2616,U_2616),times_times(U_2616),hAPP(int,U_2616,number_number_of(U_2616),U_2615)),hAPP(U_2616,U_2616,hAPP(U_2616,fun(U_2616,U_2616),times_times(U_2616),hAPP(int,U_2616,number_number_of(U_2616),U_2614)),U_2613)) = hAPP(U_2616,U_2616,hAPP(U_2616,fun(U_2616,U_2616),times_times(U_2616),hAPP(int,U_2616,number_number_of(U_2616),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_2615),U_2614))),U_2613)
      | ~ number_ring(U_2616) ),
    inference(definitional_conversion,[status(esa)],[f_691_2]) ).

cnf(f_691_4,plain,
    ( hAPP(U_2616,U_2616,hAPP(U_2616,fun(U_2616,U_2616),times_times(U_2616),hAPP(int,U_2616,number_number_of(U_2616),U_2615)),hAPP(U_2616,U_2616,hAPP(U_2616,fun(U_2616,U_2616),times_times(U_2616),hAPP(int,U_2616,number_number_of(U_2616),U_2614)),U_2613)) = hAPP(U_2616,U_2616,hAPP(U_2616,fun(U_2616,U_2616),times_times(U_2616),hAPP(int,U_2616,number_number_of(U_2616),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_2615),U_2614))),U_2613)
    | ~ number_ring(U_2616) ),
    inference(clausify,[status(thm)],[f_691_3]) ).

fof(f_692_1,plain,
    ! [X_b] :
      ( ! [B_3,A_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),times_times(X_b),A_2),B_3)),ring_1_Ints(X_b)))
          | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_3),ring_1_Ints(X_b)))
          | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),ring_1_Ints(X_b))) )
      | ~ ring_1(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_621_Ints__mult]) ).

fof(f_692_2,plain,
    ! [U_2619] :
      ( ! [U_2618,U_2617] :
          ( hBOOL(hAPP(fun(U_2619,bool),bool,hAPP(U_2619,fun(fun(U_2619,bool),bool),member(U_2619),hAPP(U_2619,U_2619,hAPP(U_2619,fun(U_2619,U_2619),times_times(U_2619),U_2617),U_2618)),ring_1_Ints(U_2619)))
          | ~ hBOOL(hAPP(fun(U_2619,bool),bool,hAPP(U_2619,fun(fun(U_2619,bool),bool),member(U_2619),U_2618),ring_1_Ints(U_2619)))
          | ~ hBOOL(hAPP(fun(U_2619,bool),bool,hAPP(U_2619,fun(fun(U_2619,bool),bool),member(U_2619),U_2617),ring_1_Ints(U_2619))) )
      | ~ ring_1(U_2619) ),
    inference(variable_rename,[status(thm)],[f_692_1]) ).

fof(f_692_3,plain,
    ! [U_2618,U_2619,U_2617] :
      ( hBOOL(hAPP(fun(U_2619,bool),bool,hAPP(U_2619,fun(fun(U_2619,bool),bool),member(U_2619),hAPP(U_2619,U_2619,hAPP(U_2619,fun(U_2619,U_2619),times_times(U_2619),U_2617),U_2618)),ring_1_Ints(U_2619)))
      | ~ hBOOL(hAPP(fun(U_2619,bool),bool,hAPP(U_2619,fun(fun(U_2619,bool),bool),member(U_2619),U_2618),ring_1_Ints(U_2619)))
      | ~ hBOOL(hAPP(fun(U_2619,bool),bool,hAPP(U_2619,fun(fun(U_2619,bool),bool),member(U_2619),U_2617),ring_1_Ints(U_2619)))
      | ~ ring_1(U_2619) ),
    inference(definitional_conversion,[status(esa)],[f_692_2]) ).

cnf(f_692_4,plain,
    ( hBOOL(hAPP(fun(U_2619,bool),bool,hAPP(U_2619,fun(fun(U_2619,bool),bool),member(U_2619),hAPP(U_2619,U_2619,hAPP(U_2619,fun(U_2619,U_2619),times_times(U_2619),U_2617),U_2618)),ring_1_Ints(U_2619)))
    | ~ hBOOL(hAPP(fun(U_2619,bool),bool,hAPP(U_2619,fun(fun(U_2619,bool),bool),member(U_2619),U_2618),ring_1_Ints(U_2619)))
    | ~ hBOOL(hAPP(fun(U_2619,bool),bool,hAPP(U_2619,fun(fun(U_2619,bool),bool),member(U_2619),U_2617),ring_1_Ints(U_2619)))
    | ~ ring_1(U_2619) ),
    inference(clausify,[status(thm)],[f_692_3]) ).

fof(f_693_1,plain,
    ! [X_b] :
      ( ! [X_1,Y_2] :
          ( ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(int,X_b,number_number_of(X_b),X_1)),hAPP(int,X_b,number_number_of(X_b),Y_2)))
            | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X_1),Y_2)) )
          & ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X_1),Y_2))
            | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(int,X_b,number_number_of(X_b),X_1)),hAPP(int,X_b,number_number_of(X_b),Y_2))) ) )
      | ~ linordered_idom(X_b)
      | ~ number_ring(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_622_le__number__of]) ).

fof(f_693_2,plain,
    ! [U_2622] :
      ( ! [U_2621,U_2620] :
          ( ( hBOOL(hAPP(U_2622,bool,hAPP(U_2622,fun(U_2622,bool),ord_less_eq(U_2622),hAPP(int,U_2622,number_number_of(U_2622),U_2621)),hAPP(int,U_2622,number_number_of(U_2622),U_2620)))
            | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_2621),U_2620)) )
          & ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_2621),U_2620))
            | ~ hBOOL(hAPP(U_2622,bool,hAPP(U_2622,fun(U_2622,bool),ord_less_eq(U_2622),hAPP(int,U_2622,number_number_of(U_2622),U_2621)),hAPP(int,U_2622,number_number_of(U_2622),U_2620))) ) )
      | ~ linordered_idom(U_2622)
      | ~ number_ring(U_2622) ),
    inference(variable_rename,[status(thm)],[f_693_1]) ).

fof(f_693_3,plain,
    ! [U_2622] :
      ( ( ! [U_2626,U_2624] :
            ( hBOOL(hAPP(U_2622,bool,hAPP(U_2622,fun(U_2622,bool),ord_less_eq(U_2622),hAPP(int,U_2622,number_number_of(U_2622),U_2626)),hAPP(int,U_2622,number_number_of(U_2622),U_2624)))
            | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_2626),U_2624)) )
        & ! [U_2625,U_2623] :
            ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_2625),U_2623))
            | ~ hBOOL(hAPP(U_2622,bool,hAPP(U_2622,fun(U_2622,bool),ord_less_eq(U_2622),hAPP(int,U_2622,number_number_of(U_2622),U_2625)),hAPP(int,U_2622,number_number_of(U_2622),U_2623))) ) )
      | ~ linordered_idom(U_2622)
      | ~ number_ring(U_2622) ),
    inference(miniscope,[status(thm)],[f_693_2]) ).

fof(f_693_4,plain,
    ( ! [U_2625,U_2622,U_2623,U_2624,U_2626] :
        ( hBOOL(hAPP(U_2622,bool,hAPP(U_2622,fun(U_2622,bool),ord_less_eq(U_2622),hAPP(int,U_2622,number_number_of(U_2622),U_2626)),hAPP(int,U_2622,number_number_of(U_2622),U_2624)))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_2626),U_2624))
        | ~ sP180(U_2625,U_2622,U_2623,U_2624,U_2626) )
    & ! [U_2625,U_2622,U_2623,U_2624,U_2626] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_2625),U_2623))
        | ~ hBOOL(hAPP(U_2622,bool,hAPP(U_2622,fun(U_2622,bool),ord_less_eq(U_2622),hAPP(int,U_2622,number_number_of(U_2622),U_2625)),hAPP(int,U_2622,number_number_of(U_2622),U_2623)))
        | ~ sP180(U_2625,U_2622,U_2623,U_2624,U_2626) )
    & ! [U_2625,U_2622,U_2623,U_2624,U_2626] :
        ( sP180(U_2625,U_2622,U_2623,U_2624,U_2626)
        | ~ linordered_idom(U_2622)
        | ~ number_ring(U_2622) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP180])],[f_693_3]) ).

cnf(f_693_5,plain,
    ( sP180(U_2625,U_2622,U_2623,U_2624,U_2626)
    | ~ linordered_idom(U_2622)
    | ~ number_ring(U_2622) ),
    inference(clausify,[status(thm)],[f_693_4]) ).

cnf(f_693_6,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_2625),U_2623))
    | ~ hBOOL(hAPP(U_2622,bool,hAPP(U_2622,fun(U_2622,bool),ord_less_eq(U_2622),hAPP(int,U_2622,number_number_of(U_2622),U_2625)),hAPP(int,U_2622,number_number_of(U_2622),U_2623)))
    | ~ sP180(U_2625,U_2622,U_2623,U_2624,U_2626) ),
    inference(clausify,[status(thm)],[f_693_4]) ).

cnf(f_693_7,plain,
    ( hBOOL(hAPP(U_2622,bool,hAPP(U_2622,fun(U_2622,bool),ord_less_eq(U_2622),hAPP(int,U_2622,number_number_of(U_2622),U_2626)),hAPP(int,U_2622,number_number_of(U_2622),U_2624)))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_2626),U_2624))
    | ~ sP180(U_2625,U_2622,U_2623,U_2624,U_2626) ),
    inference(clausify,[status(thm)],[f_693_4]) ).

fof(f_694_1,plain,
    ! [X_a] :
      ( ! [V,W] : hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),V),W)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),W))
      | ~ number_ring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_623_number__of__diff]) ).

fof(f_694_2,plain,
    ! [U_2629] :
      ( ! [U_2628,U_2627] : hAPP(int,U_2629,number_number_of(U_2629),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_2628),U_2627)) = hAPP(U_2629,U_2629,hAPP(U_2629,fun(U_2629,U_2629),minus_minus(U_2629),hAPP(int,U_2629,number_number_of(U_2629),U_2628)),hAPP(int,U_2629,number_number_of(U_2629),U_2627))
      | ~ number_ring(U_2629) ),
    inference(variable_rename,[status(thm)],[f_694_1]) ).

fof(f_694_3,plain,
    ! [U_2628,U_2627,U_2629] :
      ( hAPP(int,U_2629,number_number_of(U_2629),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_2628),U_2627)) = hAPP(U_2629,U_2629,hAPP(U_2629,fun(U_2629,U_2629),minus_minus(U_2629),hAPP(int,U_2629,number_number_of(U_2629),U_2628)),hAPP(int,U_2629,number_number_of(U_2629),U_2627))
      | ~ number_ring(U_2629) ),
    inference(definitional_conversion,[status(esa)],[f_694_2]) ).

cnf(f_694_4,plain,
    ( hAPP(int,U_2629,number_number_of(U_2629),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_2628),U_2627)) = hAPP(U_2629,U_2629,hAPP(U_2629,fun(U_2629,U_2629),minus_minus(U_2629),hAPP(int,U_2629,number_number_of(U_2629),U_2628)),hAPP(int,U_2629,number_number_of(U_2629),U_2627))
    | ~ number_ring(U_2629) ),
    inference(clausify,[status(thm)],[f_694_3]) ).

fof(f_695_1,plain,
    ! [X_b] :
      ( ! [A_1,B,V] : hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_1),B)),hAPP(int,X_b,number_number_of(X_b),V)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_1),hAPP(int,X_b,number_number_of(X_b),V))),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B),hAPP(int,X_b,number_number_of(X_b),V)))
      | ~ ring(X_b)
      | ~ number(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_624_left__diff__distrib__number__of]) ).

fof(f_695_2,plain,
    ! [U_2633] :
      ( ! [U_2632,U_2631,U_2630] : hAPP(U_2633,U_2633,hAPP(U_2633,fun(U_2633,U_2633),times_times(U_2633),hAPP(U_2633,U_2633,hAPP(U_2633,fun(U_2633,U_2633),minus_minus(U_2633),U_2632),U_2631)),hAPP(int,U_2633,number_number_of(U_2633),U_2630)) = hAPP(U_2633,U_2633,hAPP(U_2633,fun(U_2633,U_2633),minus_minus(U_2633),hAPP(U_2633,U_2633,hAPP(U_2633,fun(U_2633,U_2633),times_times(U_2633),U_2632),hAPP(int,U_2633,number_number_of(U_2633),U_2630))),hAPP(U_2633,U_2633,hAPP(U_2633,fun(U_2633,U_2633),times_times(U_2633),U_2631),hAPP(int,U_2633,number_number_of(U_2633),U_2630)))
      | ~ ring(U_2633)
      | ~ number(U_2633) ),
    inference(variable_rename,[status(thm)],[f_695_1]) ).

fof(f_695_3,plain,
    ! [U_2630,U_2633,U_2631,U_2632] :
      ( hAPP(U_2633,U_2633,hAPP(U_2633,fun(U_2633,U_2633),times_times(U_2633),hAPP(U_2633,U_2633,hAPP(U_2633,fun(U_2633,U_2633),minus_minus(U_2633),U_2632),U_2631)),hAPP(int,U_2633,number_number_of(U_2633),U_2630)) = hAPP(U_2633,U_2633,hAPP(U_2633,fun(U_2633,U_2633),minus_minus(U_2633),hAPP(U_2633,U_2633,hAPP(U_2633,fun(U_2633,U_2633),times_times(U_2633),U_2632),hAPP(int,U_2633,number_number_of(U_2633),U_2630))),hAPP(U_2633,U_2633,hAPP(U_2633,fun(U_2633,U_2633),times_times(U_2633),U_2631),hAPP(int,U_2633,number_number_of(U_2633),U_2630)))
      | ~ ring(U_2633)
      | ~ number(U_2633) ),
    inference(definitional_conversion,[status(esa)],[f_695_2]) ).

cnf(f_695_4,plain,
    ( hAPP(U_2633,U_2633,hAPP(U_2633,fun(U_2633,U_2633),times_times(U_2633),hAPP(U_2633,U_2633,hAPP(U_2633,fun(U_2633,U_2633),minus_minus(U_2633),U_2632),U_2631)),hAPP(int,U_2633,number_number_of(U_2633),U_2630)) = hAPP(U_2633,U_2633,hAPP(U_2633,fun(U_2633,U_2633),minus_minus(U_2633),hAPP(U_2633,U_2633,hAPP(U_2633,fun(U_2633,U_2633),times_times(U_2633),U_2632),hAPP(int,U_2633,number_number_of(U_2633),U_2630))),hAPP(U_2633,U_2633,hAPP(U_2633,fun(U_2633,U_2633),times_times(U_2633),U_2631),hAPP(int,U_2633,number_number_of(U_2633),U_2630)))
    | ~ ring(U_2633)
    | ~ number(U_2633) ),
    inference(clausify,[status(thm)],[f_695_3]) ).

fof(f_696_1,plain,
    ! [X_b] :
      ( ! [V,B,C] : hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),V)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),B),C)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),V)),B)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),V)),C))
      | ~ ring(X_b)
      | ~ number(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_625_right__diff__distrib__number__of]) ).

fof(f_696_2,plain,
    ! [U_2637] :
      ( ! [U_2636,U_2635,U_2634] : hAPP(U_2637,U_2637,hAPP(U_2637,fun(U_2637,U_2637),times_times(U_2637),hAPP(int,U_2637,number_number_of(U_2637),U_2636)),hAPP(U_2637,U_2637,hAPP(U_2637,fun(U_2637,U_2637),minus_minus(U_2637),U_2635),U_2634)) = hAPP(U_2637,U_2637,hAPP(U_2637,fun(U_2637,U_2637),minus_minus(U_2637),hAPP(U_2637,U_2637,hAPP(U_2637,fun(U_2637,U_2637),times_times(U_2637),hAPP(int,U_2637,number_number_of(U_2637),U_2636)),U_2635)),hAPP(U_2637,U_2637,hAPP(U_2637,fun(U_2637,U_2637),times_times(U_2637),hAPP(int,U_2637,number_number_of(U_2637),U_2636)),U_2634))
      | ~ ring(U_2637)
      | ~ number(U_2637) ),
    inference(variable_rename,[status(thm)],[f_696_1]) ).

fof(f_696_3,plain,
    ! [U_2636,U_2634,U_2637,U_2635] :
      ( hAPP(U_2637,U_2637,hAPP(U_2637,fun(U_2637,U_2637),times_times(U_2637),hAPP(int,U_2637,number_number_of(U_2637),U_2636)),hAPP(U_2637,U_2637,hAPP(U_2637,fun(U_2637,U_2637),minus_minus(U_2637),U_2635),U_2634)) = hAPP(U_2637,U_2637,hAPP(U_2637,fun(U_2637,U_2637),minus_minus(U_2637),hAPP(U_2637,U_2637,hAPP(U_2637,fun(U_2637,U_2637),times_times(U_2637),hAPP(int,U_2637,number_number_of(U_2637),U_2636)),U_2635)),hAPP(U_2637,U_2637,hAPP(U_2637,fun(U_2637,U_2637),times_times(U_2637),hAPP(int,U_2637,number_number_of(U_2637),U_2636)),U_2634))
      | ~ ring(U_2637)
      | ~ number(U_2637) ),
    inference(definitional_conversion,[status(esa)],[f_696_2]) ).

cnf(f_696_4,plain,
    ( hAPP(U_2637,U_2637,hAPP(U_2637,fun(U_2637,U_2637),times_times(U_2637),hAPP(int,U_2637,number_number_of(U_2637),U_2636)),hAPP(U_2637,U_2637,hAPP(U_2637,fun(U_2637,U_2637),minus_minus(U_2637),U_2635),U_2634)) = hAPP(U_2637,U_2637,hAPP(U_2637,fun(U_2637,U_2637),minus_minus(U_2637),hAPP(U_2637,U_2637,hAPP(U_2637,fun(U_2637,U_2637),times_times(U_2637),hAPP(int,U_2637,number_number_of(U_2637),U_2636)),U_2635)),hAPP(U_2637,U_2637,hAPP(U_2637,fun(U_2637,U_2637),times_times(U_2637),hAPP(int,U_2637,number_number_of(U_2637),U_2636)),U_2634))
    | ~ ring(U_2637)
    | ~ number(U_2637) ),
    inference(clausify,[status(thm)],[f_696_3]) ).

fof(f_697_1,plain,
    ! [X_b] :
      ( ! [B_3,A_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),plus_plus(X_b),A_2),B_3)),ring_1_Ints(X_b)))
          | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_3),ring_1_Ints(X_b)))
          | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),ring_1_Ints(X_b))) )
      | ~ ring_1(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_626_Ints__add]) ).

fof(f_697_2,plain,
    ! [U_2640] :
      ( ! [U_2639,U_2638] :
          ( hBOOL(hAPP(fun(U_2640,bool),bool,hAPP(U_2640,fun(fun(U_2640,bool),bool),member(U_2640),hAPP(U_2640,U_2640,hAPP(U_2640,fun(U_2640,U_2640),plus_plus(U_2640),U_2638),U_2639)),ring_1_Ints(U_2640)))
          | ~ hBOOL(hAPP(fun(U_2640,bool),bool,hAPP(U_2640,fun(fun(U_2640,bool),bool),member(U_2640),U_2639),ring_1_Ints(U_2640)))
          | ~ hBOOL(hAPP(fun(U_2640,bool),bool,hAPP(U_2640,fun(fun(U_2640,bool),bool),member(U_2640),U_2638),ring_1_Ints(U_2640))) )
      | ~ ring_1(U_2640) ),
    inference(variable_rename,[status(thm)],[f_697_1]) ).

fof(f_697_3,plain,
    ! [U_2638,U_2640,U_2639] :
      ( hBOOL(hAPP(fun(U_2640,bool),bool,hAPP(U_2640,fun(fun(U_2640,bool),bool),member(U_2640),hAPP(U_2640,U_2640,hAPP(U_2640,fun(U_2640,U_2640),plus_plus(U_2640),U_2638),U_2639)),ring_1_Ints(U_2640)))
      | ~ hBOOL(hAPP(fun(U_2640,bool),bool,hAPP(U_2640,fun(fun(U_2640,bool),bool),member(U_2640),U_2639),ring_1_Ints(U_2640)))
      | ~ hBOOL(hAPP(fun(U_2640,bool),bool,hAPP(U_2640,fun(fun(U_2640,bool),bool),member(U_2640),U_2638),ring_1_Ints(U_2640)))
      | ~ ring_1(U_2640) ),
    inference(definitional_conversion,[status(esa)],[f_697_2]) ).

cnf(f_697_4,plain,
    ( hBOOL(hAPP(fun(U_2640,bool),bool,hAPP(U_2640,fun(fun(U_2640,bool),bool),member(U_2640),hAPP(U_2640,U_2640,hAPP(U_2640,fun(U_2640,U_2640),plus_plus(U_2640),U_2638),U_2639)),ring_1_Ints(U_2640)))
    | ~ hBOOL(hAPP(fun(U_2640,bool),bool,hAPP(U_2640,fun(fun(U_2640,bool),bool),member(U_2640),U_2639),ring_1_Ints(U_2640)))
    | ~ hBOOL(hAPP(fun(U_2640,bool),bool,hAPP(U_2640,fun(fun(U_2640,bool),bool),member(U_2640),U_2638),ring_1_Ints(U_2640)))
    | ~ ring_1(U_2640) ),
    inference(clausify,[status(thm)],[f_697_3]) ).

fof(f_698_1,plain,
    ! [X_a] :
      ( ! [V,W] : hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),W)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),W))
      | ~ number_ring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_627_number__of__add]) ).

fof(f_698_2,plain,
    ! [U_2643] :
      ( ! [U_2642,U_2641] : hAPP(int,U_2643,number_number_of(U_2643),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_2642),U_2641)) = hAPP(U_2643,U_2643,hAPP(U_2643,fun(U_2643,U_2643),plus_plus(U_2643),hAPP(int,U_2643,number_number_of(U_2643),U_2642)),hAPP(int,U_2643,number_number_of(U_2643),U_2641))
      | ~ number_ring(U_2643) ),
    inference(variable_rename,[status(thm)],[f_698_1]) ).

fof(f_698_3,plain,
    ! [U_2642,U_2641,U_2643] :
      ( hAPP(int,U_2643,number_number_of(U_2643),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_2642),U_2641)) = hAPP(U_2643,U_2643,hAPP(U_2643,fun(U_2643,U_2643),plus_plus(U_2643),hAPP(int,U_2643,number_number_of(U_2643),U_2642)),hAPP(int,U_2643,number_number_of(U_2643),U_2641))
      | ~ number_ring(U_2643) ),
    inference(definitional_conversion,[status(esa)],[f_698_2]) ).

cnf(f_698_4,plain,
    ( hAPP(int,U_2643,number_number_of(U_2643),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_2642),U_2641)) = hAPP(U_2643,U_2643,hAPP(U_2643,fun(U_2643,U_2643),plus_plus(U_2643),hAPP(int,U_2643,number_number_of(U_2643),U_2642)),hAPP(int,U_2643,number_number_of(U_2643),U_2641))
    | ~ number_ring(U_2643) ),
    inference(clausify,[status(thm)],[f_698_3]) ).

fof(f_699_1,plain,
    ! [X_a] :
      ( ! [V,W] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),W)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),W))
      | ~ number_ring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_628_add__number__of__eq]) ).

fof(f_699_2,plain,
    ! [U_2646] :
      ( ! [U_2645,U_2644] : hAPP(U_2646,U_2646,hAPP(U_2646,fun(U_2646,U_2646),plus_plus(U_2646),hAPP(int,U_2646,number_number_of(U_2646),U_2645)),hAPP(int,U_2646,number_number_of(U_2646),U_2644)) = hAPP(int,U_2646,number_number_of(U_2646),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_2645),U_2644))
      | ~ number_ring(U_2646) ),
    inference(variable_rename,[status(thm)],[f_699_1]) ).

fof(f_699_3,plain,
    ! [U_2646,U_2644,U_2645] :
      ( hAPP(U_2646,U_2646,hAPP(U_2646,fun(U_2646,U_2646),plus_plus(U_2646),hAPP(int,U_2646,number_number_of(U_2646),U_2645)),hAPP(int,U_2646,number_number_of(U_2646),U_2644)) = hAPP(int,U_2646,number_number_of(U_2646),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_2645),U_2644))
      | ~ number_ring(U_2646) ),
    inference(definitional_conversion,[status(esa)],[f_699_2]) ).

cnf(f_699_4,plain,
    ( hAPP(U_2646,U_2646,hAPP(U_2646,fun(U_2646,U_2646),plus_plus(U_2646),hAPP(int,U_2646,number_number_of(U_2646),U_2645)),hAPP(int,U_2646,number_number_of(U_2646),U_2644)) = hAPP(int,U_2646,number_number_of(U_2646),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_2645),U_2644))
    | ~ number_ring(U_2646) ),
    inference(clausify,[status(thm)],[f_699_3]) ).

fof(f_700_1,plain,
    ! [X_b] :
      ( ! [V,B,C] : hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),V)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),B),C)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),V)),B)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),V)),C))
      | ~ semiring(X_b)
      | ~ number(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_629_right__distrib__number__of]) ).

fof(f_700_2,plain,
    ! [U_2650] :
      ( ! [U_2649,U_2648,U_2647] : hAPP(U_2650,U_2650,hAPP(U_2650,fun(U_2650,U_2650),times_times(U_2650),hAPP(int,U_2650,number_number_of(U_2650),U_2649)),hAPP(U_2650,U_2650,hAPP(U_2650,fun(U_2650,U_2650),plus_plus(U_2650),U_2648),U_2647)) = hAPP(U_2650,U_2650,hAPP(U_2650,fun(U_2650,U_2650),plus_plus(U_2650),hAPP(U_2650,U_2650,hAPP(U_2650,fun(U_2650,U_2650),times_times(U_2650),hAPP(int,U_2650,number_number_of(U_2650),U_2649)),U_2648)),hAPP(U_2650,U_2650,hAPP(U_2650,fun(U_2650,U_2650),times_times(U_2650),hAPP(int,U_2650,number_number_of(U_2650),U_2649)),U_2647))
      | ~ semiring(U_2650)
      | ~ number(U_2650) ),
    inference(variable_rename,[status(thm)],[f_700_1]) ).

fof(f_700_3,plain,
    ! [U_2647,U_2650,U_2648,U_2649] :
      ( hAPP(U_2650,U_2650,hAPP(U_2650,fun(U_2650,U_2650),times_times(U_2650),hAPP(int,U_2650,number_number_of(U_2650),U_2649)),hAPP(U_2650,U_2650,hAPP(U_2650,fun(U_2650,U_2650),plus_plus(U_2650),U_2648),U_2647)) = hAPP(U_2650,U_2650,hAPP(U_2650,fun(U_2650,U_2650),plus_plus(U_2650),hAPP(U_2650,U_2650,hAPP(U_2650,fun(U_2650,U_2650),times_times(U_2650),hAPP(int,U_2650,number_number_of(U_2650),U_2649)),U_2648)),hAPP(U_2650,U_2650,hAPP(U_2650,fun(U_2650,U_2650),times_times(U_2650),hAPP(int,U_2650,number_number_of(U_2650),U_2649)),U_2647))
      | ~ semiring(U_2650)
      | ~ number(U_2650) ),
    inference(definitional_conversion,[status(esa)],[f_700_2]) ).

cnf(f_700_4,plain,
    ( hAPP(U_2650,U_2650,hAPP(U_2650,fun(U_2650,U_2650),times_times(U_2650),hAPP(int,U_2650,number_number_of(U_2650),U_2649)),hAPP(U_2650,U_2650,hAPP(U_2650,fun(U_2650,U_2650),plus_plus(U_2650),U_2648),U_2647)) = hAPP(U_2650,U_2650,hAPP(U_2650,fun(U_2650,U_2650),plus_plus(U_2650),hAPP(U_2650,U_2650,hAPP(U_2650,fun(U_2650,U_2650),times_times(U_2650),hAPP(int,U_2650,number_number_of(U_2650),U_2649)),U_2648)),hAPP(U_2650,U_2650,hAPP(U_2650,fun(U_2650,U_2650),times_times(U_2650),hAPP(int,U_2650,number_number_of(U_2650),U_2649)),U_2647))
    | ~ semiring(U_2650)
    | ~ number(U_2650) ),
    inference(clausify,[status(thm)],[f_700_3]) ).

fof(f_701_1,plain,
    ! [X_a] :
      ( ! [V,W,Z] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),W)),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),W))),Z)
      | ~ number_ring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_630_add__number__of__left]) ).

fof(f_701_2,plain,
    ! [U_2654] :
      ( ! [U_2653,U_2652,U_2651] : hAPP(U_2654,U_2654,hAPP(U_2654,fun(U_2654,U_2654),plus_plus(U_2654),hAPP(int,U_2654,number_number_of(U_2654),U_2653)),hAPP(U_2654,U_2654,hAPP(U_2654,fun(U_2654,U_2654),plus_plus(U_2654),hAPP(int,U_2654,number_number_of(U_2654),U_2652)),U_2651)) = hAPP(U_2654,U_2654,hAPP(U_2654,fun(U_2654,U_2654),plus_plus(U_2654),hAPP(int,U_2654,number_number_of(U_2654),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_2653),U_2652))),U_2651)
      | ~ number_ring(U_2654) ),
    inference(variable_rename,[status(thm)],[f_701_1]) ).

fof(f_701_3,plain,
    ! [U_2652,U_2651,U_2654,U_2653] :
      ( hAPP(U_2654,U_2654,hAPP(U_2654,fun(U_2654,U_2654),plus_plus(U_2654),hAPP(int,U_2654,number_number_of(U_2654),U_2653)),hAPP(U_2654,U_2654,hAPP(U_2654,fun(U_2654,U_2654),plus_plus(U_2654),hAPP(int,U_2654,number_number_of(U_2654),U_2652)),U_2651)) = hAPP(U_2654,U_2654,hAPP(U_2654,fun(U_2654,U_2654),plus_plus(U_2654),hAPP(int,U_2654,number_number_of(U_2654),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_2653),U_2652))),U_2651)
      | ~ number_ring(U_2654) ),
    inference(definitional_conversion,[status(esa)],[f_701_2]) ).

cnf(f_701_4,plain,
    ( hAPP(U_2654,U_2654,hAPP(U_2654,fun(U_2654,U_2654),plus_plus(U_2654),hAPP(int,U_2654,number_number_of(U_2654),U_2653)),hAPP(U_2654,U_2654,hAPP(U_2654,fun(U_2654,U_2654),plus_plus(U_2654),hAPP(int,U_2654,number_number_of(U_2654),U_2652)),U_2651)) = hAPP(U_2654,U_2654,hAPP(U_2654,fun(U_2654,U_2654),plus_plus(U_2654),hAPP(int,U_2654,number_number_of(U_2654),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_2653),U_2652))),U_2651)
    | ~ number_ring(U_2654) ),
    inference(clausify,[status(thm)],[f_701_3]) ).

fof(f_702_1,plain,
    ! [X_b] :
      ( ! [A_1,B,V] : hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_1),B)),hAPP(int,X_b,number_number_of(X_b),V)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_1),hAPP(int,X_b,number_number_of(X_b),V))),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B),hAPP(int,X_b,number_number_of(X_b),V)))
      | ~ semiring(X_b)
      | ~ number(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_631_left__distrib__number__of]) ).

fof(f_702_2,plain,
    ! [U_2658] :
      ( ! [U_2657,U_2656,U_2655] : hAPP(U_2658,U_2658,hAPP(U_2658,fun(U_2658,U_2658),times_times(U_2658),hAPP(U_2658,U_2658,hAPP(U_2658,fun(U_2658,U_2658),plus_plus(U_2658),U_2657),U_2656)),hAPP(int,U_2658,number_number_of(U_2658),U_2655)) = hAPP(U_2658,U_2658,hAPP(U_2658,fun(U_2658,U_2658),plus_plus(U_2658),hAPP(U_2658,U_2658,hAPP(U_2658,fun(U_2658,U_2658),times_times(U_2658),U_2657),hAPP(int,U_2658,number_number_of(U_2658),U_2655))),hAPP(U_2658,U_2658,hAPP(U_2658,fun(U_2658,U_2658),times_times(U_2658),U_2656),hAPP(int,U_2658,number_number_of(U_2658),U_2655)))
      | ~ semiring(U_2658)
      | ~ number(U_2658) ),
    inference(variable_rename,[status(thm)],[f_702_1]) ).

fof(f_702_3,plain,
    ! [U_2655,U_2658,U_2656,U_2657] :
      ( hAPP(U_2658,U_2658,hAPP(U_2658,fun(U_2658,U_2658),times_times(U_2658),hAPP(U_2658,U_2658,hAPP(U_2658,fun(U_2658,U_2658),plus_plus(U_2658),U_2657),U_2656)),hAPP(int,U_2658,number_number_of(U_2658),U_2655)) = hAPP(U_2658,U_2658,hAPP(U_2658,fun(U_2658,U_2658),plus_plus(U_2658),hAPP(U_2658,U_2658,hAPP(U_2658,fun(U_2658,U_2658),times_times(U_2658),U_2657),hAPP(int,U_2658,number_number_of(U_2658),U_2655))),hAPP(U_2658,U_2658,hAPP(U_2658,fun(U_2658,U_2658),times_times(U_2658),U_2656),hAPP(int,U_2658,number_number_of(U_2658),U_2655)))
      | ~ semiring(U_2658)
      | ~ number(U_2658) ),
    inference(definitional_conversion,[status(esa)],[f_702_2]) ).

cnf(f_702_4,plain,
    ( hAPP(U_2658,U_2658,hAPP(U_2658,fun(U_2658,U_2658),times_times(U_2658),hAPP(U_2658,U_2658,hAPP(U_2658,fun(U_2658,U_2658),plus_plus(U_2658),U_2657),U_2656)),hAPP(int,U_2658,number_number_of(U_2658),U_2655)) = hAPP(U_2658,U_2658,hAPP(U_2658,fun(U_2658,U_2658),plus_plus(U_2658),hAPP(U_2658,U_2658,hAPP(U_2658,fun(U_2658,U_2658),times_times(U_2658),U_2657),hAPP(int,U_2658,number_number_of(U_2658),U_2655))),hAPP(U_2658,U_2658,hAPP(U_2658,fun(U_2658,U_2658),times_times(U_2658),U_2656),hAPP(int,U_2658,number_number_of(U_2658),U_2655)))
    | ~ semiring(U_2658)
    | ~ number(U_2658) ),
    inference(clausify,[status(thm)],[f_702_3]) ).

fof(f_703_1,plain,
    ! [X_b] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),zero_zero(X_b)),ring_1_Ints(X_b)))
      | ~ ring_1(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_632_Ints__0]) ).

fof(f_703_2,plain,
    ! [U_2659] :
      ( hBOOL(hAPP(fun(U_2659,bool),bool,hAPP(U_2659,fun(fun(U_2659,bool),bool),member(U_2659),zero_zero(U_2659)),ring_1_Ints(U_2659)))
      | ~ ring_1(U_2659) ),
    inference(variable_rename,[status(thm)],[f_703_1]) ).

fof(f_703_3,plain,
    ! [U_2659] :
      ( hBOOL(hAPP(fun(U_2659,bool),bool,hAPP(U_2659,fun(fun(U_2659,bool),bool),member(U_2659),zero_zero(U_2659)),ring_1_Ints(U_2659)))
      | ~ ring_1(U_2659) ),
    inference(definitional_conversion,[status(esa)],[f_703_2]) ).

cnf(f_703_4,plain,
    ( hBOOL(hAPP(fun(U_2659,bool),bool,hAPP(U_2659,fun(fun(U_2659,bool),bool),member(U_2659),zero_zero(U_2659)),ring_1_Ints(U_2659)))
    | ~ ring_1(U_2659) ),
    inference(clausify,[status(thm)],[f_703_3]) ).

fof(f_704_1,plain,
    ! [X_b] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),one_one(X_b)),ring_1_Ints(X_b)))
      | ~ ring_1(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_633_Ints__1]) ).

fof(f_704_2,plain,
    ! [U_2660] :
      ( hBOOL(hAPP(fun(U_2660,bool),bool,hAPP(U_2660,fun(fun(U_2660,bool),bool),member(U_2660),one_one(U_2660)),ring_1_Ints(U_2660)))
      | ~ ring_1(U_2660) ),
    inference(variable_rename,[status(thm)],[f_704_1]) ).

fof(f_704_3,plain,
    ! [U_2660] :
      ( hBOOL(hAPP(fun(U_2660,bool),bool,hAPP(U_2660,fun(fun(U_2660,bool),bool),member(U_2660),one_one(U_2660)),ring_1_Ints(U_2660)))
      | ~ ring_1(U_2660) ),
    inference(definitional_conversion,[status(esa)],[f_704_2]) ).

cnf(f_704_4,plain,
    ( hBOOL(hAPP(fun(U_2660,bool),bool,hAPP(U_2660,fun(fun(U_2660,bool),bool),member(U_2660),one_one(U_2660)),ring_1_Ints(U_2660)))
    | ~ ring_1(U_2660) ),
    inference(clausify,[status(thm)],[f_704_3]) ).

fof(f_705_1,plain,
    ! [X_a] :
      ( ! [A_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),one_one(X_a)),A_1) = ti(X_a,A_1)
      | ~ comm_semiring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_634_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J]) ).

fof(f_705_2,plain,
    ! [U_2662] :
      ( ! [U_2661] : hAPP(U_2662,U_2662,hAPP(U_2662,fun(U_2662,U_2662),times_times(U_2662),one_one(U_2662)),U_2661) = ti(U_2662,U_2661)
      | ~ comm_semiring_1(U_2662) ),
    inference(variable_rename,[status(thm)],[f_705_1]) ).

fof(f_705_3,plain,
    ! [U_2661,U_2662] :
      ( hAPP(U_2662,U_2662,hAPP(U_2662,fun(U_2662,U_2662),times_times(U_2662),one_one(U_2662)),U_2661) = ti(U_2662,U_2661)
      | ~ comm_semiring_1(U_2662) ),
    inference(definitional_conversion,[status(esa)],[f_705_2]) ).

cnf(f_705_4,plain,
    ( hAPP(U_2662,U_2662,hAPP(U_2662,fun(U_2662,U_2662),times_times(U_2662),one_one(U_2662)),U_2661) = ti(U_2662,U_2661)
    | ~ comm_semiring_1(U_2662) ),
    inference(clausify,[status(thm)],[f_705_3]) ).

fof(f_706_1,plain,
    ! [X_a] :
      ( ! [A_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),one_one(X_a)) = ti(X_a,A_1)
      | ~ comm_semiring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_635_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J]) ).

fof(f_706_2,plain,
    ! [U_2664] :
      ( ! [U_2663] : hAPP(U_2664,U_2664,hAPP(U_2664,fun(U_2664,U_2664),times_times(U_2664),U_2663),one_one(U_2664)) = ti(U_2664,U_2663)
      | ~ comm_semiring_1(U_2664) ),
    inference(variable_rename,[status(thm)],[f_706_1]) ).

fof(f_706_3,plain,
    ! [U_2663,U_2664] :
      ( hAPP(U_2664,U_2664,hAPP(U_2664,fun(U_2664,U_2664),times_times(U_2664),U_2663),one_one(U_2664)) = ti(U_2664,U_2663)
      | ~ comm_semiring_1(U_2664) ),
    inference(definitional_conversion,[status(esa)],[f_706_2]) ).

cnf(f_706_4,plain,
    ( hAPP(U_2664,U_2664,hAPP(U_2664,fun(U_2664,U_2664),times_times(U_2664),U_2663),one_one(U_2664)) = ti(U_2664,U_2663)
    | ~ comm_semiring_1(U_2664) ),
    inference(clausify,[status(thm)],[f_706_3]) ).

fof(f_707_1,plain,
    ! [X_a] :
      ( ! [A_1,B] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),A_1)
      | ~ comm_semiring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_636_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J]) ).

fof(f_707_2,plain,
    ! [U_2667] :
      ( ! [U_2666,U_2665] : hAPP(U_2667,U_2667,hAPP(U_2667,fun(U_2667,U_2667),times_times(U_2667),U_2666),U_2665) = hAPP(U_2667,U_2667,hAPP(U_2667,fun(U_2667,U_2667),times_times(U_2667),U_2665),U_2666)
      | ~ comm_semiring_1(U_2667) ),
    inference(variable_rename,[status(thm)],[f_707_1]) ).

fof(f_707_3,plain,
    ! [U_2667,U_2665,U_2666] :
      ( hAPP(U_2667,U_2667,hAPP(U_2667,fun(U_2667,U_2667),times_times(U_2667),U_2666),U_2665) = hAPP(U_2667,U_2667,hAPP(U_2667,fun(U_2667,U_2667),times_times(U_2667),U_2665),U_2666)
      | ~ comm_semiring_1(U_2667) ),
    inference(definitional_conversion,[status(esa)],[f_707_2]) ).

cnf(f_707_4,plain,
    ( hAPP(U_2667,U_2667,hAPP(U_2667,fun(U_2667,U_2667),times_times(U_2667),U_2666),U_2665) = hAPP(U_2667,U_2667,hAPP(U_2667,fun(U_2667,U_2667),times_times(U_2667),U_2665),U_2666)
    | ~ comm_semiring_1(U_2667) ),
    inference(clausify,[status(thm)],[f_707_3]) ).

fof(f_708_1,plain,
    ! [X_a] :
      ( ! [Lx,Rx,Ry] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ry))
      | ~ comm_semiring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_637_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J]) ).

fof(f_708_2,plain,
    ! [U_2671] :
      ( ! [U_2670,U_2669,U_2668] : hAPP(U_2671,U_2671,hAPP(U_2671,fun(U_2671,U_2671),times_times(U_2671),U_2670),hAPP(U_2671,U_2671,hAPP(U_2671,fun(U_2671,U_2671),times_times(U_2671),U_2669),U_2668)) = hAPP(U_2671,U_2671,hAPP(U_2671,fun(U_2671,U_2671),times_times(U_2671),U_2669),hAPP(U_2671,U_2671,hAPP(U_2671,fun(U_2671,U_2671),times_times(U_2671),U_2670),U_2668))
      | ~ comm_semiring_1(U_2671) ),
    inference(variable_rename,[status(thm)],[f_708_1]) ).

fof(f_708_3,plain,
    ! [U_2670,U_2671,U_2668,U_2669] :
      ( hAPP(U_2671,U_2671,hAPP(U_2671,fun(U_2671,U_2671),times_times(U_2671),U_2670),hAPP(U_2671,U_2671,hAPP(U_2671,fun(U_2671,U_2671),times_times(U_2671),U_2669),U_2668)) = hAPP(U_2671,U_2671,hAPP(U_2671,fun(U_2671,U_2671),times_times(U_2671),U_2669),hAPP(U_2671,U_2671,hAPP(U_2671,fun(U_2671,U_2671),times_times(U_2671),U_2670),U_2668))
      | ~ comm_semiring_1(U_2671) ),
    inference(definitional_conversion,[status(esa)],[f_708_2]) ).

cnf(f_708_4,plain,
    ( hAPP(U_2671,U_2671,hAPP(U_2671,fun(U_2671,U_2671),times_times(U_2671),U_2670),hAPP(U_2671,U_2671,hAPP(U_2671,fun(U_2671,U_2671),times_times(U_2671),U_2669),U_2668)) = hAPP(U_2671,U_2671,hAPP(U_2671,fun(U_2671,U_2671),times_times(U_2671),U_2669),hAPP(U_2671,U_2671,hAPP(U_2671,fun(U_2671,U_2671),times_times(U_2671),U_2670),U_2668))
    | ~ comm_semiring_1(U_2671) ),
    inference(clausify,[status(thm)],[f_708_3]) ).

fof(f_709_1,plain,
    ! [X_a] :
      ( ! [Lx,Rx,Ry] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Rx)),Ry)
      | ~ comm_semiring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_638_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J]) ).

fof(f_709_2,plain,
    ! [U_2675] :
      ( ! [U_2674,U_2673,U_2672] : hAPP(U_2675,U_2675,hAPP(U_2675,fun(U_2675,U_2675),times_times(U_2675),U_2674),hAPP(U_2675,U_2675,hAPP(U_2675,fun(U_2675,U_2675),times_times(U_2675),U_2673),U_2672)) = hAPP(U_2675,U_2675,hAPP(U_2675,fun(U_2675,U_2675),times_times(U_2675),hAPP(U_2675,U_2675,hAPP(U_2675,fun(U_2675,U_2675),times_times(U_2675),U_2674),U_2673)),U_2672)
      | ~ comm_semiring_1(U_2675) ),
    inference(variable_rename,[status(thm)],[f_709_1]) ).

fof(f_709_3,plain,
    ! [U_2672,U_2675,U_2674,U_2673] :
      ( hAPP(U_2675,U_2675,hAPP(U_2675,fun(U_2675,U_2675),times_times(U_2675),U_2674),hAPP(U_2675,U_2675,hAPP(U_2675,fun(U_2675,U_2675),times_times(U_2675),U_2673),U_2672)) = hAPP(U_2675,U_2675,hAPP(U_2675,fun(U_2675,U_2675),times_times(U_2675),hAPP(U_2675,U_2675,hAPP(U_2675,fun(U_2675,U_2675),times_times(U_2675),U_2674),U_2673)),U_2672)
      | ~ comm_semiring_1(U_2675) ),
    inference(definitional_conversion,[status(esa)],[f_709_2]) ).

cnf(f_709_4,plain,
    ( hAPP(U_2675,U_2675,hAPP(U_2675,fun(U_2675,U_2675),times_times(U_2675),U_2674),hAPP(U_2675,U_2675,hAPP(U_2675,fun(U_2675,U_2675),times_times(U_2675),U_2673),U_2672)) = hAPP(U_2675,U_2675,hAPP(U_2675,fun(U_2675,U_2675),times_times(U_2675),hAPP(U_2675,U_2675,hAPP(U_2675,fun(U_2675,U_2675),times_times(U_2675),U_2674),U_2673)),U_2672)
    | ~ comm_semiring_1(U_2675) ),
    inference(clausify,[status(thm)],[f_709_3]) ).

fof(f_710_1,plain,
    ! [X_a] :
      ( ! [Lx,Ly,Rx] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),Rx) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ly),Rx))
      | ~ comm_semiring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_639_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J]) ).

fof(f_710_2,plain,
    ! [U_2679] :
      ( ! [U_2678,U_2677,U_2676] : hAPP(U_2679,U_2679,hAPP(U_2679,fun(U_2679,U_2679),times_times(U_2679),hAPP(U_2679,U_2679,hAPP(U_2679,fun(U_2679,U_2679),times_times(U_2679),U_2678),U_2677)),U_2676) = hAPP(U_2679,U_2679,hAPP(U_2679,fun(U_2679,U_2679),times_times(U_2679),U_2678),hAPP(U_2679,U_2679,hAPP(U_2679,fun(U_2679,U_2679),times_times(U_2679),U_2677),U_2676))
      | ~ comm_semiring_1(U_2679) ),
    inference(variable_rename,[status(thm)],[f_710_1]) ).

fof(f_710_3,plain,
    ! [U_2676,U_2679,U_2677,U_2678] :
      ( hAPP(U_2679,U_2679,hAPP(U_2679,fun(U_2679,U_2679),times_times(U_2679),hAPP(U_2679,U_2679,hAPP(U_2679,fun(U_2679,U_2679),times_times(U_2679),U_2678),U_2677)),U_2676) = hAPP(U_2679,U_2679,hAPP(U_2679,fun(U_2679,U_2679),times_times(U_2679),U_2678),hAPP(U_2679,U_2679,hAPP(U_2679,fun(U_2679,U_2679),times_times(U_2679),U_2677),U_2676))
      | ~ comm_semiring_1(U_2679) ),
    inference(definitional_conversion,[status(esa)],[f_710_2]) ).

cnf(f_710_4,plain,
    ( hAPP(U_2679,U_2679,hAPP(U_2679,fun(U_2679,U_2679),times_times(U_2679),hAPP(U_2679,U_2679,hAPP(U_2679,fun(U_2679,U_2679),times_times(U_2679),U_2678),U_2677)),U_2676) = hAPP(U_2679,U_2679,hAPP(U_2679,fun(U_2679,U_2679),times_times(U_2679),U_2678),hAPP(U_2679,U_2679,hAPP(U_2679,fun(U_2679,U_2679),times_times(U_2679),U_2677),U_2676))
    | ~ comm_semiring_1(U_2679) ),
    inference(clausify,[status(thm)],[f_710_3]) ).

fof(f_711_1,plain,
    ! [X_a] :
      ( ! [Lx,Ly,Rx] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),Rx) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Rx)),Ly)
      | ~ comm_semiring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_640_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J]) ).

fof(f_711_2,plain,
    ! [U_2683] :
      ( ! [U_2682,U_2681,U_2680] : hAPP(U_2683,U_2683,hAPP(U_2683,fun(U_2683,U_2683),times_times(U_2683),hAPP(U_2683,U_2683,hAPP(U_2683,fun(U_2683,U_2683),times_times(U_2683),U_2682),U_2681)),U_2680) = hAPP(U_2683,U_2683,hAPP(U_2683,fun(U_2683,U_2683),times_times(U_2683),hAPP(U_2683,U_2683,hAPP(U_2683,fun(U_2683,U_2683),times_times(U_2683),U_2682),U_2680)),U_2681)
      | ~ comm_semiring_1(U_2683) ),
    inference(variable_rename,[status(thm)],[f_711_1]) ).

fof(f_711_3,plain,
    ! [U_2683,U_2680,U_2681,U_2682] :
      ( hAPP(U_2683,U_2683,hAPP(U_2683,fun(U_2683,U_2683),times_times(U_2683),hAPP(U_2683,U_2683,hAPP(U_2683,fun(U_2683,U_2683),times_times(U_2683),U_2682),U_2681)),U_2680) = hAPP(U_2683,U_2683,hAPP(U_2683,fun(U_2683,U_2683),times_times(U_2683),hAPP(U_2683,U_2683,hAPP(U_2683,fun(U_2683,U_2683),times_times(U_2683),U_2682),U_2680)),U_2681)
      | ~ comm_semiring_1(U_2683) ),
    inference(definitional_conversion,[status(esa)],[f_711_2]) ).

cnf(f_711_4,plain,
    ( hAPP(U_2683,U_2683,hAPP(U_2683,fun(U_2683,U_2683),times_times(U_2683),hAPP(U_2683,U_2683,hAPP(U_2683,fun(U_2683,U_2683),times_times(U_2683),U_2682),U_2681)),U_2680) = hAPP(U_2683,U_2683,hAPP(U_2683,fun(U_2683,U_2683),times_times(U_2683),hAPP(U_2683,U_2683,hAPP(U_2683,fun(U_2683,U_2683),times_times(U_2683),U_2682),U_2680)),U_2681)
    | ~ comm_semiring_1(U_2683) ),
    inference(clausify,[status(thm)],[f_711_3]) ).

fof(f_712_1,plain,
    ! [X_a] :
      ( ! [Lx,Ly,Rx,Ry] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ly),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry)))
      | ~ comm_semiring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_641_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J]) ).

fof(f_712_2,plain,
    ! [U_2688] :
      ( ! [U_2687,U_2686,U_2685,U_2684] : hAPP(U_2688,U_2688,hAPP(U_2688,fun(U_2688,U_2688),times_times(U_2688),hAPP(U_2688,U_2688,hAPP(U_2688,fun(U_2688,U_2688),times_times(U_2688),U_2687),U_2686)),hAPP(U_2688,U_2688,hAPP(U_2688,fun(U_2688,U_2688),times_times(U_2688),U_2685),U_2684)) = hAPP(U_2688,U_2688,hAPP(U_2688,fun(U_2688,U_2688),times_times(U_2688),U_2687),hAPP(U_2688,U_2688,hAPP(U_2688,fun(U_2688,U_2688),times_times(U_2688),U_2686),hAPP(U_2688,U_2688,hAPP(U_2688,fun(U_2688,U_2688),times_times(U_2688),U_2685),U_2684)))
      | ~ comm_semiring_1(U_2688) ),
    inference(variable_rename,[status(thm)],[f_712_1]) ).

fof(f_712_3,plain,
    ! [U_2684,U_2688,U_2685,U_2686,U_2687] :
      ( hAPP(U_2688,U_2688,hAPP(U_2688,fun(U_2688,U_2688),times_times(U_2688),hAPP(U_2688,U_2688,hAPP(U_2688,fun(U_2688,U_2688),times_times(U_2688),U_2687),U_2686)),hAPP(U_2688,U_2688,hAPP(U_2688,fun(U_2688,U_2688),times_times(U_2688),U_2685),U_2684)) = hAPP(U_2688,U_2688,hAPP(U_2688,fun(U_2688,U_2688),times_times(U_2688),U_2687),hAPP(U_2688,U_2688,hAPP(U_2688,fun(U_2688,U_2688),times_times(U_2688),U_2686),hAPP(U_2688,U_2688,hAPP(U_2688,fun(U_2688,U_2688),times_times(U_2688),U_2685),U_2684)))
      | ~ comm_semiring_1(U_2688) ),
    inference(definitional_conversion,[status(esa)],[f_712_2]) ).

cnf(f_712_4,plain,
    ( hAPP(U_2688,U_2688,hAPP(U_2688,fun(U_2688,U_2688),times_times(U_2688),hAPP(U_2688,U_2688,hAPP(U_2688,fun(U_2688,U_2688),times_times(U_2688),U_2687),U_2686)),hAPP(U_2688,U_2688,hAPP(U_2688,fun(U_2688,U_2688),times_times(U_2688),U_2685),U_2684)) = hAPP(U_2688,U_2688,hAPP(U_2688,fun(U_2688,U_2688),times_times(U_2688),U_2687),hAPP(U_2688,U_2688,hAPP(U_2688,fun(U_2688,U_2688),times_times(U_2688),U_2686),hAPP(U_2688,U_2688,hAPP(U_2688,fun(U_2688,U_2688),times_times(U_2688),U_2685),U_2684)))
    | ~ comm_semiring_1(U_2688) ),
    inference(clausify,[status(thm)],[f_712_3]) ).

fof(f_713_1,plain,
    ! [X_a] :
      ( ! [Lx,Ly,Rx,Ry] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),Ry))
      | ~ comm_semiring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_642_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J]) ).

fof(f_713_2,plain,
    ! [U_2693] :
      ( ! [U_2692,U_2691,U_2690,U_2689] : hAPP(U_2693,U_2693,hAPP(U_2693,fun(U_2693,U_2693),times_times(U_2693),hAPP(U_2693,U_2693,hAPP(U_2693,fun(U_2693,U_2693),times_times(U_2693),U_2692),U_2691)),hAPP(U_2693,U_2693,hAPP(U_2693,fun(U_2693,U_2693),times_times(U_2693),U_2690),U_2689)) = hAPP(U_2693,U_2693,hAPP(U_2693,fun(U_2693,U_2693),times_times(U_2693),U_2690),hAPP(U_2693,U_2693,hAPP(U_2693,fun(U_2693,U_2693),times_times(U_2693),hAPP(U_2693,U_2693,hAPP(U_2693,fun(U_2693,U_2693),times_times(U_2693),U_2692),U_2691)),U_2689))
      | ~ comm_semiring_1(U_2693) ),
    inference(variable_rename,[status(thm)],[f_713_1]) ).

fof(f_713_3,plain,
    ! [U_2690,U_2693,U_2689,U_2691,U_2692] :
      ( hAPP(U_2693,U_2693,hAPP(U_2693,fun(U_2693,U_2693),times_times(U_2693),hAPP(U_2693,U_2693,hAPP(U_2693,fun(U_2693,U_2693),times_times(U_2693),U_2692),U_2691)),hAPP(U_2693,U_2693,hAPP(U_2693,fun(U_2693,U_2693),times_times(U_2693),U_2690),U_2689)) = hAPP(U_2693,U_2693,hAPP(U_2693,fun(U_2693,U_2693),times_times(U_2693),U_2690),hAPP(U_2693,U_2693,hAPP(U_2693,fun(U_2693,U_2693),times_times(U_2693),hAPP(U_2693,U_2693,hAPP(U_2693,fun(U_2693,U_2693),times_times(U_2693),U_2692),U_2691)),U_2689))
      | ~ comm_semiring_1(U_2693) ),
    inference(definitional_conversion,[status(esa)],[f_713_2]) ).

cnf(f_713_4,plain,
    ( hAPP(U_2693,U_2693,hAPP(U_2693,fun(U_2693,U_2693),times_times(U_2693),hAPP(U_2693,U_2693,hAPP(U_2693,fun(U_2693,U_2693),times_times(U_2693),U_2692),U_2691)),hAPP(U_2693,U_2693,hAPP(U_2693,fun(U_2693,U_2693),times_times(U_2693),U_2690),U_2689)) = hAPP(U_2693,U_2693,hAPP(U_2693,fun(U_2693,U_2693),times_times(U_2693),U_2690),hAPP(U_2693,U_2693,hAPP(U_2693,fun(U_2693,U_2693),times_times(U_2693),hAPP(U_2693,U_2693,hAPP(U_2693,fun(U_2693,U_2693),times_times(U_2693),U_2692),U_2691)),U_2689))
    | ~ comm_semiring_1(U_2693) ),
    inference(clausify,[status(thm)],[f_713_3]) ).

fof(f_714_1,plain,
    ! [X_a] :
      ( ! [Lx,Ly,Rx,Ry] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Rx)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ly),Ry))
      | ~ comm_semiring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_643_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J]) ).

fof(f_714_2,plain,
    ! [U_2698] :
      ( ! [U_2697,U_2696,U_2695,U_2694] : hAPP(U_2698,U_2698,hAPP(U_2698,fun(U_2698,U_2698),times_times(U_2698),hAPP(U_2698,U_2698,hAPP(U_2698,fun(U_2698,U_2698),times_times(U_2698),U_2697),U_2696)),hAPP(U_2698,U_2698,hAPP(U_2698,fun(U_2698,U_2698),times_times(U_2698),U_2695),U_2694)) = hAPP(U_2698,U_2698,hAPP(U_2698,fun(U_2698,U_2698),times_times(U_2698),hAPP(U_2698,U_2698,hAPP(U_2698,fun(U_2698,U_2698),times_times(U_2698),U_2697),U_2695)),hAPP(U_2698,U_2698,hAPP(U_2698,fun(U_2698,U_2698),times_times(U_2698),U_2696),U_2694))
      | ~ comm_semiring_1(U_2698) ),
    inference(variable_rename,[status(thm)],[f_714_1]) ).

fof(f_714_3,plain,
    ! [U_2695,U_2696,U_2697,U_2698,U_2694] :
      ( hAPP(U_2698,U_2698,hAPP(U_2698,fun(U_2698,U_2698),times_times(U_2698),hAPP(U_2698,U_2698,hAPP(U_2698,fun(U_2698,U_2698),times_times(U_2698),U_2697),U_2696)),hAPP(U_2698,U_2698,hAPP(U_2698,fun(U_2698,U_2698),times_times(U_2698),U_2695),U_2694)) = hAPP(U_2698,U_2698,hAPP(U_2698,fun(U_2698,U_2698),times_times(U_2698),hAPP(U_2698,U_2698,hAPP(U_2698,fun(U_2698,U_2698),times_times(U_2698),U_2697),U_2695)),hAPP(U_2698,U_2698,hAPP(U_2698,fun(U_2698,U_2698),times_times(U_2698),U_2696),U_2694))
      | ~ comm_semiring_1(U_2698) ),
    inference(definitional_conversion,[status(esa)],[f_714_2]) ).

cnf(f_714_4,plain,
    ( hAPP(U_2698,U_2698,hAPP(U_2698,fun(U_2698,U_2698),times_times(U_2698),hAPP(U_2698,U_2698,hAPP(U_2698,fun(U_2698,U_2698),times_times(U_2698),U_2697),U_2696)),hAPP(U_2698,U_2698,hAPP(U_2698,fun(U_2698,U_2698),times_times(U_2698),U_2695),U_2694)) = hAPP(U_2698,U_2698,hAPP(U_2698,fun(U_2698,U_2698),times_times(U_2698),hAPP(U_2698,U_2698,hAPP(U_2698,fun(U_2698,U_2698),times_times(U_2698),U_2697),U_2695)),hAPP(U_2698,U_2698,hAPP(U_2698,fun(U_2698,U_2698),times_times(U_2698),U_2696),U_2694))
    | ~ comm_semiring_1(U_2698) ),
    inference(clausify,[status(thm)],[f_714_3]) ).

fof(f_715_1,plain,
    ! [X_a] :
      ( ! [X,Y,Z] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Y),Z)) = 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),times_times(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Z))
      | ~ comm_semiring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_644_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J]) ).

fof(f_715_2,plain,
    ! [U_2702] :
      ( ! [U_2701,U_2700,U_2699] : hAPP(U_2702,U_2702,hAPP(U_2702,fun(U_2702,U_2702),times_times(U_2702),U_2701),hAPP(U_2702,U_2702,hAPP(U_2702,fun(U_2702,U_2702),plus_plus(U_2702),U_2700),U_2699)) = hAPP(U_2702,U_2702,hAPP(U_2702,fun(U_2702,U_2702),plus_plus(U_2702),hAPP(U_2702,U_2702,hAPP(U_2702,fun(U_2702,U_2702),times_times(U_2702),U_2701),U_2700)),hAPP(U_2702,U_2702,hAPP(U_2702,fun(U_2702,U_2702),times_times(U_2702),U_2701),U_2699))
      | ~ comm_semiring_1(U_2702) ),
    inference(variable_rename,[status(thm)],[f_715_1]) ).

fof(f_715_3,plain,
    ! [U_2702,U_2700,U_2699,U_2701] :
      ( hAPP(U_2702,U_2702,hAPP(U_2702,fun(U_2702,U_2702),times_times(U_2702),U_2701),hAPP(U_2702,U_2702,hAPP(U_2702,fun(U_2702,U_2702),plus_plus(U_2702),U_2700),U_2699)) = hAPP(U_2702,U_2702,hAPP(U_2702,fun(U_2702,U_2702),plus_plus(U_2702),hAPP(U_2702,U_2702,hAPP(U_2702,fun(U_2702,U_2702),times_times(U_2702),U_2701),U_2700)),hAPP(U_2702,U_2702,hAPP(U_2702,fun(U_2702,U_2702),times_times(U_2702),U_2701),U_2699))
      | ~ comm_semiring_1(U_2702) ),
    inference(definitional_conversion,[status(esa)],[f_715_2]) ).

cnf(f_715_4,plain,
    ( hAPP(U_2702,U_2702,hAPP(U_2702,fun(U_2702,U_2702),times_times(U_2702),U_2701),hAPP(U_2702,U_2702,hAPP(U_2702,fun(U_2702,U_2702),plus_plus(U_2702),U_2700),U_2699)) = hAPP(U_2702,U_2702,hAPP(U_2702,fun(U_2702,U_2702),plus_plus(U_2702),hAPP(U_2702,U_2702,hAPP(U_2702,fun(U_2702,U_2702),times_times(U_2702),U_2701),U_2700)),hAPP(U_2702,U_2702,hAPP(U_2702,fun(U_2702,U_2702),times_times(U_2702),U_2701),U_2699))
    | ~ comm_semiring_1(U_2702) ),
    inference(clausify,[status(thm)],[f_715_3]) ).

fof(f_716_1,plain,
    ! [X_b] :
      ( ! [C_1,D_1,A_2,B_3] :
          ( ( ( ti(X_b,C_1) != ti(X_b,D_1)
              & ti(X_b,A_2) != ti(X_b,B_3) )
            | hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),D_1)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),D_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),C_1)) )
          & ( hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),D_1)) != hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),D_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),C_1))
            | ti(X_b,C_1) = ti(X_b,D_1)
            | ti(X_b,A_2) = ti(X_b,B_3) ) )
      | ~ semiri456707255roduct(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_645_crossproduct__noteq]) ).

fof(f_716_2,plain,
    ! [U_2707] :
      ( ! [U_2706,U_2705,U_2704,U_2703] :
          ( ( ( ti(U_2707,U_2706) != ti(U_2707,U_2705)
              & ti(U_2707,U_2704) != ti(U_2707,U_2703) )
            | hAPP(U_2707,U_2707,hAPP(U_2707,fun(U_2707,U_2707),plus_plus(U_2707),hAPP(U_2707,U_2707,hAPP(U_2707,fun(U_2707,U_2707),times_times(U_2707),U_2704),U_2706)),hAPP(U_2707,U_2707,hAPP(U_2707,fun(U_2707,U_2707),times_times(U_2707),U_2703),U_2705)) = hAPP(U_2707,U_2707,hAPP(U_2707,fun(U_2707,U_2707),plus_plus(U_2707),hAPP(U_2707,U_2707,hAPP(U_2707,fun(U_2707,U_2707),times_times(U_2707),U_2704),U_2705)),hAPP(U_2707,U_2707,hAPP(U_2707,fun(U_2707,U_2707),times_times(U_2707),U_2703),U_2706)) )
          & ( hAPP(U_2707,U_2707,hAPP(U_2707,fun(U_2707,U_2707),plus_plus(U_2707),hAPP(U_2707,U_2707,hAPP(U_2707,fun(U_2707,U_2707),times_times(U_2707),U_2704),U_2706)),hAPP(U_2707,U_2707,hAPP(U_2707,fun(U_2707,U_2707),times_times(U_2707),U_2703),U_2705)) != hAPP(U_2707,U_2707,hAPP(U_2707,fun(U_2707,U_2707),plus_plus(U_2707),hAPP(U_2707,U_2707,hAPP(U_2707,fun(U_2707,U_2707),times_times(U_2707),U_2704),U_2705)),hAPP(U_2707,U_2707,hAPP(U_2707,fun(U_2707,U_2707),times_times(U_2707),U_2703),U_2706))
            | ti(U_2707,U_2706) = ti(U_2707,U_2705)
            | ti(U_2707,U_2704) = ti(U_2707,U_2703) ) )
      | ~ semiri456707255roduct(U_2707) ),
    inference(variable_rename,[status(thm)],[f_716_1]) ).

fof(f_716_3,plain,
    ! [U_2707] :
      ( ( ! [U_2715,U_2713,U_2711,U_2709] :
            ( ( ti(U_2707,U_2715) != ti(U_2707,U_2713)
              & ti(U_2707,U_2711) != ti(U_2707,U_2709) )
            | hAPP(U_2707,U_2707,hAPP(U_2707,fun(U_2707,U_2707),plus_plus(U_2707),hAPP(U_2707,U_2707,hAPP(U_2707,fun(U_2707,U_2707),times_times(U_2707),U_2711),U_2715)),hAPP(U_2707,U_2707,hAPP(U_2707,fun(U_2707,U_2707),times_times(U_2707),U_2709),U_2713)) = hAPP(U_2707,U_2707,hAPP(U_2707,fun(U_2707,U_2707),plus_plus(U_2707),hAPP(U_2707,U_2707,hAPP(U_2707,fun(U_2707,U_2707),times_times(U_2707),U_2711),U_2713)),hAPP(U_2707,U_2707,hAPP(U_2707,fun(U_2707,U_2707),times_times(U_2707),U_2709),U_2715)) )
        & ! [U_2714,U_2712,U_2710,U_2708] :
            ( hAPP(U_2707,U_2707,hAPP(U_2707,fun(U_2707,U_2707),plus_plus(U_2707),hAPP(U_2707,U_2707,hAPP(U_2707,fun(U_2707,U_2707),times_times(U_2707),U_2710),U_2714)),hAPP(U_2707,U_2707,hAPP(U_2707,fun(U_2707,U_2707),times_times(U_2707),U_2708),U_2712)) != hAPP(U_2707,U_2707,hAPP(U_2707,fun(U_2707,U_2707),plus_plus(U_2707),hAPP(U_2707,U_2707,hAPP(U_2707,fun(U_2707,U_2707),times_times(U_2707),U_2710),U_2712)),hAPP(U_2707,U_2707,hAPP(U_2707,fun(U_2707,U_2707),times_times(U_2707),U_2708),U_2714))
            | ti(U_2707,U_2714) = ti(U_2707,U_2712)
            | ti(U_2707,U_2710) = ti(U_2707,U_2708) ) )
      | ~ semiri456707255roduct(U_2707) ),
    inference(miniscope,[status(thm)],[f_716_2]) ).

fof(f_716_4,plain,
    ( ! [U_2707,U_2711,U_2709,U_2713,U_2715] :
        ( ti(U_2707,U_2715) != ti(U_2707,U_2713)
        | ~ sP181(U_2707,U_2711,U_2709,U_2713,U_2715) )
    & ! [U_2707,U_2711,U_2709,U_2713,U_2715] :
        ( ti(U_2707,U_2711) != ti(U_2707,U_2709)
        | ~ sP181(U_2707,U_2711,U_2709,U_2713,U_2715) )
    & ! [U_2714,U_2707,U_2708,U_2710,U_2711,U_2709,U_2712,U_2713,U_2715] :
        ( sP181(U_2707,U_2711,U_2709,U_2713,U_2715)
        | hAPP(U_2707,U_2707,hAPP(U_2707,fun(U_2707,U_2707),plus_plus(U_2707),hAPP(U_2707,U_2707,hAPP(U_2707,fun(U_2707,U_2707),times_times(U_2707),U_2711),U_2715)),hAPP(U_2707,U_2707,hAPP(U_2707,fun(U_2707,U_2707),times_times(U_2707),U_2709),U_2713)) = hAPP(U_2707,U_2707,hAPP(U_2707,fun(U_2707,U_2707),plus_plus(U_2707),hAPP(U_2707,U_2707,hAPP(U_2707,fun(U_2707,U_2707),times_times(U_2707),U_2711),U_2713)),hAPP(U_2707,U_2707,hAPP(U_2707,fun(U_2707,U_2707),times_times(U_2707),U_2709),U_2715))
        | ~ sP182(U_2714,U_2707,U_2708,U_2710,U_2711,U_2709,U_2712,U_2713,U_2715) )
    & ! [U_2714,U_2707,U_2708,U_2710,U_2711,U_2709,U_2712,U_2713,U_2715] :
        ( hAPP(U_2707,U_2707,hAPP(U_2707,fun(U_2707,U_2707),plus_plus(U_2707),hAPP(U_2707,U_2707,hAPP(U_2707,fun(U_2707,U_2707),times_times(U_2707),U_2710),U_2714)),hAPP(U_2707,U_2707,hAPP(U_2707,fun(U_2707,U_2707),times_times(U_2707),U_2708),U_2712)) != hAPP(U_2707,U_2707,hAPP(U_2707,fun(U_2707,U_2707),plus_plus(U_2707),hAPP(U_2707,U_2707,hAPP(U_2707,fun(U_2707,U_2707),times_times(U_2707),U_2710),U_2712)),hAPP(U_2707,U_2707,hAPP(U_2707,fun(U_2707,U_2707),times_times(U_2707),U_2708),U_2714))
        | ti(U_2707,U_2714) = ti(U_2707,U_2712)
        | ti(U_2707,U_2710) = ti(U_2707,U_2708)
        | ~ sP182(U_2714,U_2707,U_2708,U_2710,U_2711,U_2709,U_2712,U_2713,U_2715) )
    & ! [U_2714,U_2707,U_2708,U_2710,U_2711,U_2709,U_2712,U_2713,U_2715] :
        ( sP182(U_2714,U_2707,U_2708,U_2710,U_2711,U_2709,U_2712,U_2713,U_2715)
        | ~ semiri456707255roduct(U_2707) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP181,sP182])],[f_716_3]) ).

cnf(f_716_5,plain,
    ( sP182(U_2714,U_2707,U_2708,U_2710,U_2711,U_2709,U_2712,U_2713,U_2715)
    | ~ semiri456707255roduct(U_2707) ),
    inference(clausify,[status(thm)],[f_716_4]) ).

cnf(f_716_6,plain,
    ( hAPP(U_2707,U_2707,hAPP(U_2707,fun(U_2707,U_2707),plus_plus(U_2707),hAPP(U_2707,U_2707,hAPP(U_2707,fun(U_2707,U_2707),times_times(U_2707),U_2710),U_2714)),hAPP(U_2707,U_2707,hAPP(U_2707,fun(U_2707,U_2707),times_times(U_2707),U_2708),U_2712)) != hAPP(U_2707,U_2707,hAPP(U_2707,fun(U_2707,U_2707),plus_plus(U_2707),hAPP(U_2707,U_2707,hAPP(U_2707,fun(U_2707,U_2707),times_times(U_2707),U_2710),U_2712)),hAPP(U_2707,U_2707,hAPP(U_2707,fun(U_2707,U_2707),times_times(U_2707),U_2708),U_2714))
    | ti(U_2707,U_2714) = ti(U_2707,U_2712)
    | ti(U_2707,U_2710) = ti(U_2707,U_2708)
    | ~ sP182(U_2714,U_2707,U_2708,U_2710,U_2711,U_2709,U_2712,U_2713,U_2715) ),
    inference(clausify,[status(thm)],[f_716_4]) ).

cnf(f_716_7,plain,
    ( sP181(U_2707,U_2711,U_2709,U_2713,U_2715)
    | hAPP(U_2707,U_2707,hAPP(U_2707,fun(U_2707,U_2707),plus_plus(U_2707),hAPP(U_2707,U_2707,hAPP(U_2707,fun(U_2707,U_2707),times_times(U_2707),U_2711),U_2715)),hAPP(U_2707,U_2707,hAPP(U_2707,fun(U_2707,U_2707),times_times(U_2707),U_2709),U_2713)) = hAPP(U_2707,U_2707,hAPP(U_2707,fun(U_2707,U_2707),plus_plus(U_2707),hAPP(U_2707,U_2707,hAPP(U_2707,fun(U_2707,U_2707),times_times(U_2707),U_2711),U_2713)),hAPP(U_2707,U_2707,hAPP(U_2707,fun(U_2707,U_2707),times_times(U_2707),U_2709),U_2715))
    | ~ sP182(U_2714,U_2707,U_2708,U_2710,U_2711,U_2709,U_2712,U_2713,U_2715) ),
    inference(clausify,[status(thm)],[f_716_4]) ).

cnf(f_716_8,plain,
    ( ti(U_2707,U_2711) != ti(U_2707,U_2709)
    | ~ sP181(U_2707,U_2711,U_2709,U_2713,U_2715) ),
    inference(clausify,[status(thm)],[f_716_4]) ).

cnf(f_716_9,plain,
    ( ti(U_2707,U_2715) != ti(U_2707,U_2713)
    | ~ sP181(U_2707,U_2711,U_2709,U_2713,U_2715) ),
    inference(clausify,[status(thm)],[f_716_4]) ).

fof(f_717_1,plain,
    ! [X_a] :
      ( ! [A_1,B,C] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),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),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C))
      | ~ comm_semiring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_646_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J]) ).

fof(f_717_2,plain,
    ! [U_2719] :
      ( ! [U_2718,U_2717,U_2716] : hAPP(U_2719,U_2719,hAPP(U_2719,fun(U_2719,U_2719),times_times(U_2719),hAPP(U_2719,U_2719,hAPP(U_2719,fun(U_2719,U_2719),plus_plus(U_2719),U_2718),U_2717)),U_2716) = hAPP(U_2719,U_2719,hAPP(U_2719,fun(U_2719,U_2719),plus_plus(U_2719),hAPP(U_2719,U_2719,hAPP(U_2719,fun(U_2719,U_2719),times_times(U_2719),U_2718),U_2716)),hAPP(U_2719,U_2719,hAPP(U_2719,fun(U_2719,U_2719),times_times(U_2719),U_2717),U_2716))
      | ~ comm_semiring_1(U_2719) ),
    inference(variable_rename,[status(thm)],[f_717_1]) ).

fof(f_717_3,plain,
    ! [U_2718,U_2717,U_2719,U_2716] :
      ( hAPP(U_2719,U_2719,hAPP(U_2719,fun(U_2719,U_2719),times_times(U_2719),hAPP(U_2719,U_2719,hAPP(U_2719,fun(U_2719,U_2719),plus_plus(U_2719),U_2718),U_2717)),U_2716) = hAPP(U_2719,U_2719,hAPP(U_2719,fun(U_2719,U_2719),plus_plus(U_2719),hAPP(U_2719,U_2719,hAPP(U_2719,fun(U_2719,U_2719),times_times(U_2719),U_2718),U_2716)),hAPP(U_2719,U_2719,hAPP(U_2719,fun(U_2719,U_2719),times_times(U_2719),U_2717),U_2716))
      | ~ comm_semiring_1(U_2719) ),
    inference(definitional_conversion,[status(esa)],[f_717_2]) ).

cnf(f_717_4,plain,
    ( hAPP(U_2719,U_2719,hAPP(U_2719,fun(U_2719,U_2719),times_times(U_2719),hAPP(U_2719,U_2719,hAPP(U_2719,fun(U_2719,U_2719),plus_plus(U_2719),U_2718),U_2717)),U_2716) = hAPP(U_2719,U_2719,hAPP(U_2719,fun(U_2719,U_2719),plus_plus(U_2719),hAPP(U_2719,U_2719,hAPP(U_2719,fun(U_2719,U_2719),times_times(U_2719),U_2718),U_2716)),hAPP(U_2719,U_2719,hAPP(U_2719,fun(U_2719,U_2719),times_times(U_2719),U_2717),U_2716))
    | ~ comm_semiring_1(U_2719) ),
    inference(clausify,[status(thm)],[f_717_3]) ).

fof(f_718_1,plain,
    ! [X_a] :
      ( ! [A_1,M_1,B] : 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),times_times(X_a),A_1),M_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),M_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),M_1)
      | ~ comm_semiring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_647_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J]) ).

fof(f_718_2,plain,
    ! [U_2723] :
      ( ! [U_2722,U_2721,U_2720] : hAPP(U_2723,U_2723,hAPP(U_2723,fun(U_2723,U_2723),plus_plus(U_2723),hAPP(U_2723,U_2723,hAPP(U_2723,fun(U_2723,U_2723),times_times(U_2723),U_2722),U_2721)),hAPP(U_2723,U_2723,hAPP(U_2723,fun(U_2723,U_2723),times_times(U_2723),U_2720),U_2721)) = hAPP(U_2723,U_2723,hAPP(U_2723,fun(U_2723,U_2723),times_times(U_2723),hAPP(U_2723,U_2723,hAPP(U_2723,fun(U_2723,U_2723),plus_plus(U_2723),U_2722),U_2720)),U_2721)
      | ~ comm_semiring_1(U_2723) ),
    inference(variable_rename,[status(thm)],[f_718_1]) ).

fof(f_718_3,plain,
    ! [U_2720,U_2723,U_2721,U_2722] :
      ( hAPP(U_2723,U_2723,hAPP(U_2723,fun(U_2723,U_2723),plus_plus(U_2723),hAPP(U_2723,U_2723,hAPP(U_2723,fun(U_2723,U_2723),times_times(U_2723),U_2722),U_2721)),hAPP(U_2723,U_2723,hAPP(U_2723,fun(U_2723,U_2723),times_times(U_2723),U_2720),U_2721)) = hAPP(U_2723,U_2723,hAPP(U_2723,fun(U_2723,U_2723),times_times(U_2723),hAPP(U_2723,U_2723,hAPP(U_2723,fun(U_2723,U_2723),plus_plus(U_2723),U_2722),U_2720)),U_2721)
      | ~ comm_semiring_1(U_2723) ),
    inference(definitional_conversion,[status(esa)],[f_718_2]) ).

cnf(f_718_4,plain,
    ( hAPP(U_2723,U_2723,hAPP(U_2723,fun(U_2723,U_2723),plus_plus(U_2723),hAPP(U_2723,U_2723,hAPP(U_2723,fun(U_2723,U_2723),times_times(U_2723),U_2722),U_2721)),hAPP(U_2723,U_2723,hAPP(U_2723,fun(U_2723,U_2723),times_times(U_2723),U_2720),U_2721)) = hAPP(U_2723,U_2723,hAPP(U_2723,fun(U_2723,U_2723),times_times(U_2723),hAPP(U_2723,U_2723,hAPP(U_2723,fun(U_2723,U_2723),plus_plus(U_2723),U_2722),U_2720)),U_2721)
    | ~ comm_semiring_1(U_2723) ),
    inference(clausify,[status(thm)],[f_718_3]) ).

fof(f_719_1,plain,
    ! [X_b] :
      ( ! [W_1,Y_2,X_1,Z_2] :
          ( ( hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),W_1),Y_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),Z_2)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),W_1),Z_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),Y_2))
            | ( ti(X_b,Y_2) != ti(X_b,Z_2)
              & ti(X_b,W_1) != ti(X_b,X_1) ) )
          & ( ti(X_b,Y_2) = ti(X_b,Z_2)
            | ti(X_b,W_1) = ti(X_b,X_1)
            | hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),W_1),Y_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),Z_2)) != hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),W_1),Z_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),Y_2)) ) )
      | ~ semiri456707255roduct(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_648_crossproduct__eq]) ).

fof(f_719_2,plain,
    ! [U_2728] :
      ( ! [U_2727,U_2726,U_2725,U_2724] :
          ( ( hAPP(U_2728,U_2728,hAPP(U_2728,fun(U_2728,U_2728),plus_plus(U_2728),hAPP(U_2728,U_2728,hAPP(U_2728,fun(U_2728,U_2728),times_times(U_2728),U_2727),U_2726)),hAPP(U_2728,U_2728,hAPP(U_2728,fun(U_2728,U_2728),times_times(U_2728),U_2725),U_2724)) = hAPP(U_2728,U_2728,hAPP(U_2728,fun(U_2728,U_2728),plus_plus(U_2728),hAPP(U_2728,U_2728,hAPP(U_2728,fun(U_2728,U_2728),times_times(U_2728),U_2727),U_2724)),hAPP(U_2728,U_2728,hAPP(U_2728,fun(U_2728,U_2728),times_times(U_2728),U_2725),U_2726))
            | ( ti(U_2728,U_2726) != ti(U_2728,U_2724)
              & ti(U_2728,U_2727) != ti(U_2728,U_2725) ) )
          & ( ti(U_2728,U_2726) = ti(U_2728,U_2724)
            | ti(U_2728,U_2727) = ti(U_2728,U_2725)
            | hAPP(U_2728,U_2728,hAPP(U_2728,fun(U_2728,U_2728),plus_plus(U_2728),hAPP(U_2728,U_2728,hAPP(U_2728,fun(U_2728,U_2728),times_times(U_2728),U_2727),U_2726)),hAPP(U_2728,U_2728,hAPP(U_2728,fun(U_2728,U_2728),times_times(U_2728),U_2725),U_2724)) != hAPP(U_2728,U_2728,hAPP(U_2728,fun(U_2728,U_2728),plus_plus(U_2728),hAPP(U_2728,U_2728,hAPP(U_2728,fun(U_2728,U_2728),times_times(U_2728),U_2727),U_2724)),hAPP(U_2728,U_2728,hAPP(U_2728,fun(U_2728,U_2728),times_times(U_2728),U_2725),U_2726)) ) )
      | ~ semiri456707255roduct(U_2728) ),
    inference(variable_rename,[status(thm)],[f_719_1]) ).

fof(f_719_3,plain,
    ! [U_2728] :
      ( ( ! [U_2736,U_2734,U_2732,U_2730] :
            ( hAPP(U_2728,U_2728,hAPP(U_2728,fun(U_2728,U_2728),plus_plus(U_2728),hAPP(U_2728,U_2728,hAPP(U_2728,fun(U_2728,U_2728),times_times(U_2728),U_2736),U_2734)),hAPP(U_2728,U_2728,hAPP(U_2728,fun(U_2728,U_2728),times_times(U_2728),U_2732),U_2730)) = hAPP(U_2728,U_2728,hAPP(U_2728,fun(U_2728,U_2728),plus_plus(U_2728),hAPP(U_2728,U_2728,hAPP(U_2728,fun(U_2728,U_2728),times_times(U_2728),U_2736),U_2730)),hAPP(U_2728,U_2728,hAPP(U_2728,fun(U_2728,U_2728),times_times(U_2728),U_2732),U_2734))
            | ( ti(U_2728,U_2734) != ti(U_2728,U_2730)
              & ti(U_2728,U_2736) != ti(U_2728,U_2732) ) )
        & ! [U_2735,U_2733,U_2731,U_2729] :
            ( ti(U_2728,U_2733) = ti(U_2728,U_2729)
            | ti(U_2728,U_2735) = ti(U_2728,U_2731)
            | hAPP(U_2728,U_2728,hAPP(U_2728,fun(U_2728,U_2728),plus_plus(U_2728),hAPP(U_2728,U_2728,hAPP(U_2728,fun(U_2728,U_2728),times_times(U_2728),U_2735),U_2733)),hAPP(U_2728,U_2728,hAPP(U_2728,fun(U_2728,U_2728),times_times(U_2728),U_2731),U_2729)) != hAPP(U_2728,U_2728,hAPP(U_2728,fun(U_2728,U_2728),plus_plus(U_2728),hAPP(U_2728,U_2728,hAPP(U_2728,fun(U_2728,U_2728),times_times(U_2728),U_2735),U_2729)),hAPP(U_2728,U_2728,hAPP(U_2728,fun(U_2728,U_2728),times_times(U_2728),U_2731),U_2733)) ) )
      | ~ semiri456707255roduct(U_2728) ),
    inference(miniscope,[status(thm)],[f_719_2]) ).

fof(f_719_4,plain,
    ( ! [U_2728,U_2730,U_2732,U_2734,U_2736] :
        ( ti(U_2728,U_2734) != ti(U_2728,U_2730)
        | ~ sP183(U_2728,U_2730,U_2732,U_2734,U_2736) )
    & ! [U_2728,U_2730,U_2732,U_2734,U_2736] :
        ( ti(U_2728,U_2736) != ti(U_2728,U_2732)
        | ~ sP183(U_2728,U_2730,U_2732,U_2734,U_2736) )
    & ! [U_2731,U_2728,U_2729,U_2730,U_2732,U_2733,U_2734,U_2735,U_2736] :
        ( hAPP(U_2728,U_2728,hAPP(U_2728,fun(U_2728,U_2728),plus_plus(U_2728),hAPP(U_2728,U_2728,hAPP(U_2728,fun(U_2728,U_2728),times_times(U_2728),U_2736),U_2734)),hAPP(U_2728,U_2728,hAPP(U_2728,fun(U_2728,U_2728),times_times(U_2728),U_2732),U_2730)) = hAPP(U_2728,U_2728,hAPP(U_2728,fun(U_2728,U_2728),plus_plus(U_2728),hAPP(U_2728,U_2728,hAPP(U_2728,fun(U_2728,U_2728),times_times(U_2728),U_2736),U_2730)),hAPP(U_2728,U_2728,hAPP(U_2728,fun(U_2728,U_2728),times_times(U_2728),U_2732),U_2734))
        | sP183(U_2728,U_2730,U_2732,U_2734,U_2736)
        | ~ sP184(U_2731,U_2728,U_2729,U_2730,U_2732,U_2733,U_2734,U_2735,U_2736) )
    & ! [U_2731,U_2728,U_2729,U_2730,U_2732,U_2733,U_2734,U_2735,U_2736] :
        ( ti(U_2728,U_2733) = ti(U_2728,U_2729)
        | ti(U_2728,U_2735) = ti(U_2728,U_2731)
        | hAPP(U_2728,U_2728,hAPP(U_2728,fun(U_2728,U_2728),plus_plus(U_2728),hAPP(U_2728,U_2728,hAPP(U_2728,fun(U_2728,U_2728),times_times(U_2728),U_2735),U_2733)),hAPP(U_2728,U_2728,hAPP(U_2728,fun(U_2728,U_2728),times_times(U_2728),U_2731),U_2729)) != hAPP(U_2728,U_2728,hAPP(U_2728,fun(U_2728,U_2728),plus_plus(U_2728),hAPP(U_2728,U_2728,hAPP(U_2728,fun(U_2728,U_2728),times_times(U_2728),U_2735),U_2729)),hAPP(U_2728,U_2728,hAPP(U_2728,fun(U_2728,U_2728),times_times(U_2728),U_2731),U_2733))
        | ~ sP184(U_2731,U_2728,U_2729,U_2730,U_2732,U_2733,U_2734,U_2735,U_2736) )
    & ! [U_2731,U_2728,U_2729,U_2730,U_2732,U_2733,U_2734,U_2735,U_2736] :
        ( sP184(U_2731,U_2728,U_2729,U_2730,U_2732,U_2733,U_2734,U_2735,U_2736)
        | ~ semiri456707255roduct(U_2728) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP183,sP184])],[f_719_3]) ).

cnf(f_719_5,plain,
    ( sP184(U_2731,U_2728,U_2729,U_2730,U_2732,U_2733,U_2734,U_2735,U_2736)
    | ~ semiri456707255roduct(U_2728) ),
    inference(clausify,[status(thm)],[f_719_4]) ).

cnf(f_719_6,plain,
    ( ti(U_2728,U_2733) = ti(U_2728,U_2729)
    | ti(U_2728,U_2735) = ti(U_2728,U_2731)
    | hAPP(U_2728,U_2728,hAPP(U_2728,fun(U_2728,U_2728),plus_plus(U_2728),hAPP(U_2728,U_2728,hAPP(U_2728,fun(U_2728,U_2728),times_times(U_2728),U_2735),U_2733)),hAPP(U_2728,U_2728,hAPP(U_2728,fun(U_2728,U_2728),times_times(U_2728),U_2731),U_2729)) != hAPP(U_2728,U_2728,hAPP(U_2728,fun(U_2728,U_2728),plus_plus(U_2728),hAPP(U_2728,U_2728,hAPP(U_2728,fun(U_2728,U_2728),times_times(U_2728),U_2735),U_2729)),hAPP(U_2728,U_2728,hAPP(U_2728,fun(U_2728,U_2728),times_times(U_2728),U_2731),U_2733))
    | ~ sP184(U_2731,U_2728,U_2729,U_2730,U_2732,U_2733,U_2734,U_2735,U_2736) ),
    inference(clausify,[status(thm)],[f_719_4]) ).

cnf(f_719_7,plain,
    ( hAPP(U_2728,U_2728,hAPP(U_2728,fun(U_2728,U_2728),plus_plus(U_2728),hAPP(U_2728,U_2728,hAPP(U_2728,fun(U_2728,U_2728),times_times(U_2728),U_2736),U_2734)),hAPP(U_2728,U_2728,hAPP(U_2728,fun(U_2728,U_2728),times_times(U_2728),U_2732),U_2730)) = hAPP(U_2728,U_2728,hAPP(U_2728,fun(U_2728,U_2728),plus_plus(U_2728),hAPP(U_2728,U_2728,hAPP(U_2728,fun(U_2728,U_2728),times_times(U_2728),U_2736),U_2730)),hAPP(U_2728,U_2728,hAPP(U_2728,fun(U_2728,U_2728),times_times(U_2728),U_2732),U_2734))
    | sP183(U_2728,U_2730,U_2732,U_2734,U_2736)
    | ~ sP184(U_2731,U_2728,U_2729,U_2730,U_2732,U_2733,U_2734,U_2735,U_2736) ),
    inference(clausify,[status(thm)],[f_719_4]) ).

cnf(f_719_8,plain,
    ( ti(U_2728,U_2736) != ti(U_2728,U_2732)
    | ~ sP183(U_2728,U_2730,U_2732,U_2734,U_2736) ),
    inference(clausify,[status(thm)],[f_719_4]) ).

cnf(f_719_9,plain,
    ( ti(U_2728,U_2734) != ti(U_2728,U_2730)
    | ~ sP183(U_2728,U_2730,U_2732,U_2734,U_2736) ),
    inference(clausify,[status(thm)],[f_719_4]) ).

fof(f_720_1,plain,
    ! [X_a] :
      ( ! [A_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),zero_zero(X_a)),A_1) = zero_zero(X_a)
      | ~ comm_semiring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_649_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J]) ).

fof(f_720_2,plain,
    ! [U_2738] :
      ( ! [U_2737] : hAPP(U_2738,U_2738,hAPP(U_2738,fun(U_2738,U_2738),times_times(U_2738),zero_zero(U_2738)),U_2737) = zero_zero(U_2738)
      | ~ comm_semiring_1(U_2738) ),
    inference(variable_rename,[status(thm)],[f_720_1]) ).

fof(f_720_3,plain,
    ! [U_2737,U_2738] :
      ( hAPP(U_2738,U_2738,hAPP(U_2738,fun(U_2738,U_2738),times_times(U_2738),zero_zero(U_2738)),U_2737) = zero_zero(U_2738)
      | ~ comm_semiring_1(U_2738) ),
    inference(definitional_conversion,[status(esa)],[f_720_2]) ).

cnf(f_720_4,plain,
    ( hAPP(U_2738,U_2738,hAPP(U_2738,fun(U_2738,U_2738),times_times(U_2738),zero_zero(U_2738)),U_2737) = zero_zero(U_2738)
    | ~ comm_semiring_1(U_2738) ),
    inference(clausify,[status(thm)],[f_720_3]) ).

fof(f_721_1,plain,
    ! [X_a] :
      ( ! [A_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),zero_zero(X_a)) = zero_zero(X_a)
      | ~ comm_semiring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_650_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J]) ).

fof(f_721_2,plain,
    ! [U_2740] :
      ( ! [U_2739] : hAPP(U_2740,U_2740,hAPP(U_2740,fun(U_2740,U_2740),times_times(U_2740),U_2739),zero_zero(U_2740)) = zero_zero(U_2740)
      | ~ comm_semiring_1(U_2740) ),
    inference(variable_rename,[status(thm)],[f_721_1]) ).

fof(f_721_3,plain,
    ! [U_2740,U_2739] :
      ( hAPP(U_2740,U_2740,hAPP(U_2740,fun(U_2740,U_2740),times_times(U_2740),U_2739),zero_zero(U_2740)) = zero_zero(U_2740)
      | ~ comm_semiring_1(U_2740) ),
    inference(definitional_conversion,[status(esa)],[f_721_2]) ).

cnf(f_721_4,plain,
    ( hAPP(U_2740,U_2740,hAPP(U_2740,fun(U_2740,U_2740),times_times(U_2740),U_2739),zero_zero(U_2740)) = zero_zero(U_2740)
    | ~ comm_semiring_1(U_2740) ),
    inference(clausify,[status(thm)],[f_721_3]) ).

fof(f_722_1,plain,
    ! [X_b] :
      ( ! [V_3,W_1] :
          ( ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(int,X_b,number_number_of(X_b),V_3)),hAPP(int,X_b,number_number_of(X_b),W_1)))
            | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(int,X_b,number_number_of(X_b),W_1)),hAPP(int,X_b,number_number_of(X_b),V_3))) )
          & ( ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(int,X_b,number_number_of(X_b),W_1)),hAPP(int,X_b,number_number_of(X_b),V_3)))
            | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(int,X_b,number_number_of(X_b),V_3)),hAPP(int,X_b,number_number_of(X_b),W_1))) ) )
      | ~ linorder(X_b)
      | ~ number(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_651_le__number__of__eq__not__less]) ).

fof(f_722_2,plain,
    ! [U_2743] :
      ( ! [U_2742,U_2741] :
          ( ( hBOOL(hAPP(U_2743,bool,hAPP(U_2743,fun(U_2743,bool),ord_less_eq(U_2743),hAPP(int,U_2743,number_number_of(U_2743),U_2742)),hAPP(int,U_2743,number_number_of(U_2743),U_2741)))
            | hBOOL(hAPP(U_2743,bool,hAPP(U_2743,fun(U_2743,bool),ord_less(U_2743),hAPP(int,U_2743,number_number_of(U_2743),U_2741)),hAPP(int,U_2743,number_number_of(U_2743),U_2742))) )
          & ( ~ hBOOL(hAPP(U_2743,bool,hAPP(U_2743,fun(U_2743,bool),ord_less(U_2743),hAPP(int,U_2743,number_number_of(U_2743),U_2741)),hAPP(int,U_2743,number_number_of(U_2743),U_2742)))
            | ~ hBOOL(hAPP(U_2743,bool,hAPP(U_2743,fun(U_2743,bool),ord_less_eq(U_2743),hAPP(int,U_2743,number_number_of(U_2743),U_2742)),hAPP(int,U_2743,number_number_of(U_2743),U_2741))) ) )
      | ~ linorder(U_2743)
      | ~ number(U_2743) ),
    inference(variable_rename,[status(thm)],[f_722_1]) ).

fof(f_722_3,plain,
    ! [U_2743] :
      ( ( ! [U_2747,U_2745] :
            ( hBOOL(hAPP(U_2743,bool,hAPP(U_2743,fun(U_2743,bool),ord_less_eq(U_2743),hAPP(int,U_2743,number_number_of(U_2743),U_2747)),hAPP(int,U_2743,number_number_of(U_2743),U_2745)))
            | hBOOL(hAPP(U_2743,bool,hAPP(U_2743,fun(U_2743,bool),ord_less(U_2743),hAPP(int,U_2743,number_number_of(U_2743),U_2745)),hAPP(int,U_2743,number_number_of(U_2743),U_2747))) )
        & ! [U_2746,U_2744] :
            ( ~ hBOOL(hAPP(U_2743,bool,hAPP(U_2743,fun(U_2743,bool),ord_less(U_2743),hAPP(int,U_2743,number_number_of(U_2743),U_2744)),hAPP(int,U_2743,number_number_of(U_2743),U_2746)))
            | ~ hBOOL(hAPP(U_2743,bool,hAPP(U_2743,fun(U_2743,bool),ord_less_eq(U_2743),hAPP(int,U_2743,number_number_of(U_2743),U_2746)),hAPP(int,U_2743,number_number_of(U_2743),U_2744))) ) )
      | ~ linorder(U_2743)
      | ~ number(U_2743) ),
    inference(miniscope,[status(thm)],[f_722_2]) ).

fof(f_722_4,plain,
    ( ! [U_2743,U_2744,U_2746,U_2745,U_2747] :
        ( hBOOL(hAPP(U_2743,bool,hAPP(U_2743,fun(U_2743,bool),ord_less_eq(U_2743),hAPP(int,U_2743,number_number_of(U_2743),U_2747)),hAPP(int,U_2743,number_number_of(U_2743),U_2745)))
        | hBOOL(hAPP(U_2743,bool,hAPP(U_2743,fun(U_2743,bool),ord_less(U_2743),hAPP(int,U_2743,number_number_of(U_2743),U_2745)),hAPP(int,U_2743,number_number_of(U_2743),U_2747)))
        | ~ sP185(U_2743,U_2744,U_2746,U_2745,U_2747) )
    & ! [U_2743,U_2744,U_2746,U_2745,U_2747] :
        ( ~ hBOOL(hAPP(U_2743,bool,hAPP(U_2743,fun(U_2743,bool),ord_less(U_2743),hAPP(int,U_2743,number_number_of(U_2743),U_2744)),hAPP(int,U_2743,number_number_of(U_2743),U_2746)))
        | ~ hBOOL(hAPP(U_2743,bool,hAPP(U_2743,fun(U_2743,bool),ord_less_eq(U_2743),hAPP(int,U_2743,number_number_of(U_2743),U_2746)),hAPP(int,U_2743,number_number_of(U_2743),U_2744)))
        | ~ sP185(U_2743,U_2744,U_2746,U_2745,U_2747) )
    & ! [U_2743,U_2744,U_2746,U_2745,U_2747] :
        ( sP185(U_2743,U_2744,U_2746,U_2745,U_2747)
        | ~ linorder(U_2743)
        | ~ number(U_2743) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP185])],[f_722_3]) ).

cnf(f_722_5,plain,
    ( sP185(U_2743,U_2744,U_2746,U_2745,U_2747)
    | ~ linorder(U_2743)
    | ~ number(U_2743) ),
    inference(clausify,[status(thm)],[f_722_4]) ).

cnf(f_722_6,plain,
    ( ~ hBOOL(hAPP(U_2743,bool,hAPP(U_2743,fun(U_2743,bool),ord_less(U_2743),hAPP(int,U_2743,number_number_of(U_2743),U_2744)),hAPP(int,U_2743,number_number_of(U_2743),U_2746)))
    | ~ hBOOL(hAPP(U_2743,bool,hAPP(U_2743,fun(U_2743,bool),ord_less_eq(U_2743),hAPP(int,U_2743,number_number_of(U_2743),U_2746)),hAPP(int,U_2743,number_number_of(U_2743),U_2744)))
    | ~ sP185(U_2743,U_2744,U_2746,U_2745,U_2747) ),
    inference(clausify,[status(thm)],[f_722_4]) ).

cnf(f_722_7,plain,
    ( hBOOL(hAPP(U_2743,bool,hAPP(U_2743,fun(U_2743,bool),ord_less_eq(U_2743),hAPP(int,U_2743,number_number_of(U_2743),U_2747)),hAPP(int,U_2743,number_number_of(U_2743),U_2745)))
    | hBOOL(hAPP(U_2743,bool,hAPP(U_2743,fun(U_2743,bool),ord_less(U_2743),hAPP(int,U_2743,number_number_of(U_2743),U_2745)),hAPP(int,U_2743,number_number_of(U_2743),U_2747)))
    | ~ sP185(U_2743,U_2744,U_2746,U_2745,U_2747) ),
    inference(clausify,[status(thm)],[f_722_4]) ).

fof(f_723_1,plain,
    ! [X_a] :
      ( ! [V,W,C] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),W)),C)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),W))),C)
      | ~ number_ring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_652_add__number__of__diff1]) ).

fof(f_723_2,plain,
    ! [U_2751] :
      ( ! [U_2750,U_2749,U_2748] : hAPP(U_2751,U_2751,hAPP(U_2751,fun(U_2751,U_2751),plus_plus(U_2751),hAPP(int,U_2751,number_number_of(U_2751),U_2750)),hAPP(U_2751,U_2751,hAPP(U_2751,fun(U_2751,U_2751),minus_minus(U_2751),hAPP(int,U_2751,number_number_of(U_2751),U_2749)),U_2748)) = hAPP(U_2751,U_2751,hAPP(U_2751,fun(U_2751,U_2751),minus_minus(U_2751),hAPP(int,U_2751,number_number_of(U_2751),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_2750),U_2749))),U_2748)
      | ~ number_ring(U_2751) ),
    inference(variable_rename,[status(thm)],[f_723_1]) ).

fof(f_723_3,plain,
    ! [U_2751,U_2748,U_2750,U_2749] :
      ( hAPP(U_2751,U_2751,hAPP(U_2751,fun(U_2751,U_2751),plus_plus(U_2751),hAPP(int,U_2751,number_number_of(U_2751),U_2750)),hAPP(U_2751,U_2751,hAPP(U_2751,fun(U_2751,U_2751),minus_minus(U_2751),hAPP(int,U_2751,number_number_of(U_2751),U_2749)),U_2748)) = hAPP(U_2751,U_2751,hAPP(U_2751,fun(U_2751,U_2751),minus_minus(U_2751),hAPP(int,U_2751,number_number_of(U_2751),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_2750),U_2749))),U_2748)
      | ~ number_ring(U_2751) ),
    inference(definitional_conversion,[status(esa)],[f_723_2]) ).

cnf(f_723_4,plain,
    ( hAPP(U_2751,U_2751,hAPP(U_2751,fun(U_2751,U_2751),plus_plus(U_2751),hAPP(int,U_2751,number_number_of(U_2751),U_2750)),hAPP(U_2751,U_2751,hAPP(U_2751,fun(U_2751,U_2751),minus_minus(U_2751),hAPP(int,U_2751,number_number_of(U_2751),U_2749)),U_2748)) = hAPP(U_2751,U_2751,hAPP(U_2751,fun(U_2751,U_2751),minus_minus(U_2751),hAPP(int,U_2751,number_number_of(U_2751),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_2750),U_2749))),U_2748)
    | ~ number_ring(U_2751) ),
    inference(clausify,[status(thm)],[f_723_3]) ).

fof(f_724_1,plain,
    ! [X_a] :
      ( ! [B,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),times_times(X_a),A_1),B)),zero_zero(X_a)))
          | ( ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B))
              | ~ 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),zero_zero(X_a)))
              | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) ) ) )
      | ~ ordere453448008miring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_653_split__mult__neg__le]) ).

fof(f_724_2,plain,
    ! [U_2754] :
      ( ! [U_2753,U_2752] :
          ( hBOOL(hAPP(U_2754,bool,hAPP(U_2754,fun(U_2754,bool),ord_less_eq(U_2754),hAPP(U_2754,U_2754,hAPP(U_2754,fun(U_2754,U_2754),times_times(U_2754),U_2752),U_2753)),zero_zero(U_2754)))
          | ( ( ~ hBOOL(hAPP(U_2754,bool,hAPP(U_2754,fun(U_2754,bool),ord_less_eq(U_2754),zero_zero(U_2754)),U_2753))
              | ~ hBOOL(hAPP(U_2754,bool,hAPP(U_2754,fun(U_2754,bool),ord_less_eq(U_2754),U_2752),zero_zero(U_2754))) )
            & ( ~ hBOOL(hAPP(U_2754,bool,hAPP(U_2754,fun(U_2754,bool),ord_less_eq(U_2754),U_2753),zero_zero(U_2754)))
              | ~ hBOOL(hAPP(U_2754,bool,hAPP(U_2754,fun(U_2754,bool),ord_less_eq(U_2754),zero_zero(U_2754)),U_2752)) ) ) )
      | ~ ordere453448008miring(U_2754) ),
    inference(variable_rename,[status(thm)],[f_724_1]) ).

fof(f_724_3,plain,
    ( ! [U_2754,U_2753,U_2752] :
        ( ~ hBOOL(hAPP(U_2754,bool,hAPP(U_2754,fun(U_2754,bool),ord_less_eq(U_2754),zero_zero(U_2754)),U_2753))
        | ~ hBOOL(hAPP(U_2754,bool,hAPP(U_2754,fun(U_2754,bool),ord_less_eq(U_2754),U_2752),zero_zero(U_2754)))
        | ~ sP186(U_2754,U_2753,U_2752) )
    & ! [U_2754,U_2753,U_2752] :
        ( ~ hBOOL(hAPP(U_2754,bool,hAPP(U_2754,fun(U_2754,bool),ord_less_eq(U_2754),U_2753),zero_zero(U_2754)))
        | ~ hBOOL(hAPP(U_2754,bool,hAPP(U_2754,fun(U_2754,bool),ord_less_eq(U_2754),zero_zero(U_2754)),U_2752))
        | ~ sP186(U_2754,U_2753,U_2752) )
    & ! [U_2754,U_2753,U_2752] :
        ( hBOOL(hAPP(U_2754,bool,hAPP(U_2754,fun(U_2754,bool),ord_less_eq(U_2754),hAPP(U_2754,U_2754,hAPP(U_2754,fun(U_2754,U_2754),times_times(U_2754),U_2752),U_2753)),zero_zero(U_2754)))
        | sP186(U_2754,U_2753,U_2752)
        | ~ ordere453448008miring(U_2754) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP186])],[f_724_2]) ).

cnf(f_724_4,plain,
    ( hBOOL(hAPP(U_2754,bool,hAPP(U_2754,fun(U_2754,bool),ord_less_eq(U_2754),hAPP(U_2754,U_2754,hAPP(U_2754,fun(U_2754,U_2754),times_times(U_2754),U_2752),U_2753)),zero_zero(U_2754)))
    | sP186(U_2754,U_2753,U_2752)
    | ~ ordere453448008miring(U_2754) ),
    inference(clausify,[status(thm)],[f_724_3]) ).

cnf(f_724_5,plain,
    ( ~ hBOOL(hAPP(U_2754,bool,hAPP(U_2754,fun(U_2754,bool),ord_less_eq(U_2754),U_2753),zero_zero(U_2754)))
    | ~ hBOOL(hAPP(U_2754,bool,hAPP(U_2754,fun(U_2754,bool),ord_less_eq(U_2754),zero_zero(U_2754)),U_2752))
    | ~ sP186(U_2754,U_2753,U_2752) ),
    inference(clausify,[status(thm)],[f_724_3]) ).

cnf(f_724_6,plain,
    ( ~ hBOOL(hAPP(U_2754,bool,hAPP(U_2754,fun(U_2754,bool),ord_less_eq(U_2754),zero_zero(U_2754)),U_2753))
    | ~ hBOOL(hAPP(U_2754,bool,hAPP(U_2754,fun(U_2754,bool),ord_less_eq(U_2754),U_2752),zero_zero(U_2754)))
    | ~ sP186(U_2754,U_2753,U_2752) ),
    inference(clausify,[status(thm)],[f_724_3]) ).

fof(f_725_1,plain,
    ! [X_a] :
      ( ! [B,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),times_times(X_a),A_1),B)))
          | ( ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),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))) )
            & ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B))
              | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) ) ) )
      | ~ ordered_ring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_654_split__mult__pos__le]) ).

fof(f_725_2,plain,
    ! [U_2757] :
      ( ! [U_2756,U_2755] :
          ( hBOOL(hAPP(U_2757,bool,hAPP(U_2757,fun(U_2757,bool),ord_less_eq(U_2757),zero_zero(U_2757)),hAPP(U_2757,U_2757,hAPP(U_2757,fun(U_2757,U_2757),times_times(U_2757),U_2755),U_2756)))
          | ( ( ~ hBOOL(hAPP(U_2757,bool,hAPP(U_2757,fun(U_2757,bool),ord_less_eq(U_2757),U_2756),zero_zero(U_2757)))
              | ~ hBOOL(hAPP(U_2757,bool,hAPP(U_2757,fun(U_2757,bool),ord_less_eq(U_2757),U_2755),zero_zero(U_2757))) )
            & ( ~ hBOOL(hAPP(U_2757,bool,hAPP(U_2757,fun(U_2757,bool),ord_less_eq(U_2757),zero_zero(U_2757)),U_2756))
              | ~ hBOOL(hAPP(U_2757,bool,hAPP(U_2757,fun(U_2757,bool),ord_less_eq(U_2757),zero_zero(U_2757)),U_2755)) ) ) )
      | ~ ordered_ring(U_2757) ),
    inference(variable_rename,[status(thm)],[f_725_1]) ).

fof(f_725_3,plain,
    ( ! [U_2757,U_2756,U_2755] :
        ( ~ hBOOL(hAPP(U_2757,bool,hAPP(U_2757,fun(U_2757,bool),ord_less_eq(U_2757),U_2756),zero_zero(U_2757)))
        | ~ hBOOL(hAPP(U_2757,bool,hAPP(U_2757,fun(U_2757,bool),ord_less_eq(U_2757),U_2755),zero_zero(U_2757)))
        | ~ sP187(U_2757,U_2756,U_2755) )
    & ! [U_2757,U_2756,U_2755] :
        ( ~ hBOOL(hAPP(U_2757,bool,hAPP(U_2757,fun(U_2757,bool),ord_less_eq(U_2757),zero_zero(U_2757)),U_2756))
        | ~ hBOOL(hAPP(U_2757,bool,hAPP(U_2757,fun(U_2757,bool),ord_less_eq(U_2757),zero_zero(U_2757)),U_2755))
        | ~ sP187(U_2757,U_2756,U_2755) )
    & ! [U_2757,U_2756,U_2755] :
        ( hBOOL(hAPP(U_2757,bool,hAPP(U_2757,fun(U_2757,bool),ord_less_eq(U_2757),zero_zero(U_2757)),hAPP(U_2757,U_2757,hAPP(U_2757,fun(U_2757,U_2757),times_times(U_2757),U_2755),U_2756)))
        | sP187(U_2757,U_2756,U_2755)
        | ~ ordered_ring(U_2757) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP187])],[f_725_2]) ).

cnf(f_725_4,plain,
    ( hBOOL(hAPP(U_2757,bool,hAPP(U_2757,fun(U_2757,bool),ord_less_eq(U_2757),zero_zero(U_2757)),hAPP(U_2757,U_2757,hAPP(U_2757,fun(U_2757,U_2757),times_times(U_2757),U_2755),U_2756)))
    | sP187(U_2757,U_2756,U_2755)
    | ~ ordered_ring(U_2757) ),
    inference(clausify,[status(thm)],[f_725_3]) ).

cnf(f_725_5,plain,
    ( ~ hBOOL(hAPP(U_2757,bool,hAPP(U_2757,fun(U_2757,bool),ord_less_eq(U_2757),zero_zero(U_2757)),U_2756))
    | ~ hBOOL(hAPP(U_2757,bool,hAPP(U_2757,fun(U_2757,bool),ord_less_eq(U_2757),zero_zero(U_2757)),U_2755))
    | ~ sP187(U_2757,U_2756,U_2755) ),
    inference(clausify,[status(thm)],[f_725_3]) ).

cnf(f_725_6,plain,
    ( ~ hBOOL(hAPP(U_2757,bool,hAPP(U_2757,fun(U_2757,bool),ord_less_eq(U_2757),U_2756),zero_zero(U_2757)))
    | ~ hBOOL(hAPP(U_2757,bool,hAPP(U_2757,fun(U_2757,bool),ord_less_eq(U_2757),U_2755),zero_zero(U_2757)))
    | ~ sP187(U_2757,U_2756,U_2755) ),
    inference(clausify,[status(thm)],[f_725_3]) ).

fof(f_726_1,plain,
    ! [X_a] :
      ( ! [C,D,A_1,B] :
          ( 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),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D)))
          | ~ 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),zero_zero(X_a)),B))
          | ~ 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)) )
      | ~ ordered_semiring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_655_mult__mono]) ).

fof(f_726_2,plain,
    ! [U_2762] :
      ( ! [U_2761,U_2760,U_2759,U_2758] :
          ( hBOOL(hAPP(U_2762,bool,hAPP(U_2762,fun(U_2762,bool),ord_less_eq(U_2762),hAPP(U_2762,U_2762,hAPP(U_2762,fun(U_2762,U_2762),times_times(U_2762),U_2759),U_2761)),hAPP(U_2762,U_2762,hAPP(U_2762,fun(U_2762,U_2762),times_times(U_2762),U_2758),U_2760)))
          | ~ hBOOL(hAPP(U_2762,bool,hAPP(U_2762,fun(U_2762,bool),ord_less_eq(U_2762),zero_zero(U_2762)),U_2761))
          | ~ hBOOL(hAPP(U_2762,bool,hAPP(U_2762,fun(U_2762,bool),ord_less_eq(U_2762),zero_zero(U_2762)),U_2758))
          | ~ hBOOL(hAPP(U_2762,bool,hAPP(U_2762,fun(U_2762,bool),ord_less_eq(U_2762),U_2761),U_2760))
          | ~ hBOOL(hAPP(U_2762,bool,hAPP(U_2762,fun(U_2762,bool),ord_less_eq(U_2762),U_2759),U_2758)) )
      | ~ ordered_semiring(U_2762) ),
    inference(variable_rename,[status(thm)],[f_726_1]) ).

fof(f_726_3,plain,
    ! [U_2760,U_2758,U_2762,U_2759,U_2761] :
      ( hBOOL(hAPP(U_2762,bool,hAPP(U_2762,fun(U_2762,bool),ord_less_eq(U_2762),hAPP(U_2762,U_2762,hAPP(U_2762,fun(U_2762,U_2762),times_times(U_2762),U_2759),U_2761)),hAPP(U_2762,U_2762,hAPP(U_2762,fun(U_2762,U_2762),times_times(U_2762),U_2758),U_2760)))
      | ~ hBOOL(hAPP(U_2762,bool,hAPP(U_2762,fun(U_2762,bool),ord_less_eq(U_2762),zero_zero(U_2762)),U_2761))
      | ~ hBOOL(hAPP(U_2762,bool,hAPP(U_2762,fun(U_2762,bool),ord_less_eq(U_2762),zero_zero(U_2762)),U_2758))
      | ~ hBOOL(hAPP(U_2762,bool,hAPP(U_2762,fun(U_2762,bool),ord_less_eq(U_2762),U_2761),U_2760))
      | ~ hBOOL(hAPP(U_2762,bool,hAPP(U_2762,fun(U_2762,bool),ord_less_eq(U_2762),U_2759),U_2758))
      | ~ ordered_semiring(U_2762) ),
    inference(definitional_conversion,[status(esa)],[f_726_2]) ).

cnf(f_726_4,plain,
    ( hBOOL(hAPP(U_2762,bool,hAPP(U_2762,fun(U_2762,bool),ord_less_eq(U_2762),hAPP(U_2762,U_2762,hAPP(U_2762,fun(U_2762,U_2762),times_times(U_2762),U_2759),U_2761)),hAPP(U_2762,U_2762,hAPP(U_2762,fun(U_2762,U_2762),times_times(U_2762),U_2758),U_2760)))
    | ~ hBOOL(hAPP(U_2762,bool,hAPP(U_2762,fun(U_2762,bool),ord_less_eq(U_2762),zero_zero(U_2762)),U_2761))
    | ~ hBOOL(hAPP(U_2762,bool,hAPP(U_2762,fun(U_2762,bool),ord_less_eq(U_2762),zero_zero(U_2762)),U_2758))
    | ~ hBOOL(hAPP(U_2762,bool,hAPP(U_2762,fun(U_2762,bool),ord_less_eq(U_2762),U_2761),U_2760))
    | ~ hBOOL(hAPP(U_2762,bool,hAPP(U_2762,fun(U_2762,bool),ord_less_eq(U_2762),U_2759),U_2758))
    | ~ ordered_semiring(U_2762) ),
    inference(clausify,[status(thm)],[f_726_3]) ).

fof(f_727_1,plain,
    ! [X_a] :
      ( ! [C,D,A_1,B] :
          ( 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),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D)))
          | ~ 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),zero_zero(X_a)),A_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),A_1),B)) )
      | ~ ordered_semiring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_656_mult__mono_H]) ).

fof(f_727_2,plain,
    ! [U_2767] :
      ( ! [U_2766,U_2765,U_2764,U_2763] :
          ( hBOOL(hAPP(U_2767,bool,hAPP(U_2767,fun(U_2767,bool),ord_less_eq(U_2767),hAPP(U_2767,U_2767,hAPP(U_2767,fun(U_2767,U_2767),times_times(U_2767),U_2764),U_2766)),hAPP(U_2767,U_2767,hAPP(U_2767,fun(U_2767,U_2767),times_times(U_2767),U_2763),U_2765)))
          | ~ hBOOL(hAPP(U_2767,bool,hAPP(U_2767,fun(U_2767,bool),ord_less_eq(U_2767),zero_zero(U_2767)),U_2766))
          | ~ hBOOL(hAPP(U_2767,bool,hAPP(U_2767,fun(U_2767,bool),ord_less_eq(U_2767),zero_zero(U_2767)),U_2764))
          | ~ hBOOL(hAPP(U_2767,bool,hAPP(U_2767,fun(U_2767,bool),ord_less_eq(U_2767),U_2766),U_2765))
          | ~ hBOOL(hAPP(U_2767,bool,hAPP(U_2767,fun(U_2767,bool),ord_less_eq(U_2767),U_2764),U_2763)) )
      | ~ ordered_semiring(U_2767) ),
    inference(variable_rename,[status(thm)],[f_727_1]) ).

fof(f_727_3,plain,
    ! [U_2765,U_2763,U_2767,U_2764,U_2766] :
      ( hBOOL(hAPP(U_2767,bool,hAPP(U_2767,fun(U_2767,bool),ord_less_eq(U_2767),hAPP(U_2767,U_2767,hAPP(U_2767,fun(U_2767,U_2767),times_times(U_2767),U_2764),U_2766)),hAPP(U_2767,U_2767,hAPP(U_2767,fun(U_2767,U_2767),times_times(U_2767),U_2763),U_2765)))
      | ~ hBOOL(hAPP(U_2767,bool,hAPP(U_2767,fun(U_2767,bool),ord_less_eq(U_2767),zero_zero(U_2767)),U_2766))
      | ~ hBOOL(hAPP(U_2767,bool,hAPP(U_2767,fun(U_2767,bool),ord_less_eq(U_2767),zero_zero(U_2767)),U_2764))
      | ~ hBOOL(hAPP(U_2767,bool,hAPP(U_2767,fun(U_2767,bool),ord_less_eq(U_2767),U_2766),U_2765))
      | ~ hBOOL(hAPP(U_2767,bool,hAPP(U_2767,fun(U_2767,bool),ord_less_eq(U_2767),U_2764),U_2763))
      | ~ ordered_semiring(U_2767) ),
    inference(definitional_conversion,[status(esa)],[f_727_2]) ).

cnf(f_727_4,plain,
    ( hBOOL(hAPP(U_2767,bool,hAPP(U_2767,fun(U_2767,bool),ord_less_eq(U_2767),hAPP(U_2767,U_2767,hAPP(U_2767,fun(U_2767,U_2767),times_times(U_2767),U_2764),U_2766)),hAPP(U_2767,U_2767,hAPP(U_2767,fun(U_2767,U_2767),times_times(U_2767),U_2763),U_2765)))
    | ~ hBOOL(hAPP(U_2767,bool,hAPP(U_2767,fun(U_2767,bool),ord_less_eq(U_2767),zero_zero(U_2767)),U_2766))
    | ~ hBOOL(hAPP(U_2767,bool,hAPP(U_2767,fun(U_2767,bool),ord_less_eq(U_2767),zero_zero(U_2767)),U_2764))
    | ~ hBOOL(hAPP(U_2767,bool,hAPP(U_2767,fun(U_2767,bool),ord_less_eq(U_2767),U_2766),U_2765))
    | ~ hBOOL(hAPP(U_2767,bool,hAPP(U_2767,fun(U_2767,bool),ord_less_eq(U_2767),U_2764),U_2763))
    | ~ ordered_semiring(U_2767) ),
    inference(clausify,[status(thm)],[f_727_3]) ).

fof(f_728_1,plain,
    ! [X_a] :
      ( ! [C,B,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),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),zero_zero(X_a)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1)) )
      | ~ ordered_ring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_657_mult__left__mono__neg]) ).

fof(f_728_2,plain,
    ! [U_2771] :
      ( ! [U_2770,U_2769,U_2768] :
          ( hBOOL(hAPP(U_2771,bool,hAPP(U_2771,fun(U_2771,bool),ord_less_eq(U_2771),hAPP(U_2771,U_2771,hAPP(U_2771,fun(U_2771,U_2771),times_times(U_2771),U_2770),U_2768)),hAPP(U_2771,U_2771,hAPP(U_2771,fun(U_2771,U_2771),times_times(U_2771),U_2770),U_2769)))
          | ~ hBOOL(hAPP(U_2771,bool,hAPP(U_2771,fun(U_2771,bool),ord_less_eq(U_2771),U_2770),zero_zero(U_2771)))
          | ~ hBOOL(hAPP(U_2771,bool,hAPP(U_2771,fun(U_2771,bool),ord_less_eq(U_2771),U_2769),U_2768)) )
      | ~ ordered_ring(U_2771) ),
    inference(variable_rename,[status(thm)],[f_728_1]) ).

fof(f_728_3,plain,
    ! [U_2770,U_2771,U_2768,U_2769] :
      ( hBOOL(hAPP(U_2771,bool,hAPP(U_2771,fun(U_2771,bool),ord_less_eq(U_2771),hAPP(U_2771,U_2771,hAPP(U_2771,fun(U_2771,U_2771),times_times(U_2771),U_2770),U_2768)),hAPP(U_2771,U_2771,hAPP(U_2771,fun(U_2771,U_2771),times_times(U_2771),U_2770),U_2769)))
      | ~ hBOOL(hAPP(U_2771,bool,hAPP(U_2771,fun(U_2771,bool),ord_less_eq(U_2771),U_2770),zero_zero(U_2771)))
      | ~ hBOOL(hAPP(U_2771,bool,hAPP(U_2771,fun(U_2771,bool),ord_less_eq(U_2771),U_2769),U_2768))
      | ~ ordered_ring(U_2771) ),
    inference(definitional_conversion,[status(esa)],[f_728_2]) ).

cnf(f_728_4,plain,
    ( hBOOL(hAPP(U_2771,bool,hAPP(U_2771,fun(U_2771,bool),ord_less_eq(U_2771),hAPP(U_2771,U_2771,hAPP(U_2771,fun(U_2771,U_2771),times_times(U_2771),U_2770),U_2768)),hAPP(U_2771,U_2771,hAPP(U_2771,fun(U_2771,U_2771),times_times(U_2771),U_2770),U_2769)))
    | ~ hBOOL(hAPP(U_2771,bool,hAPP(U_2771,fun(U_2771,bool),ord_less_eq(U_2771),U_2770),zero_zero(U_2771)))
    | ~ hBOOL(hAPP(U_2771,bool,hAPP(U_2771,fun(U_2771,bool),ord_less_eq(U_2771),U_2769),U_2768))
    | ~ ordered_ring(U_2771) ),
    inference(clausify,[status(thm)],[f_728_3]) ).

fof(f_729_1,plain,
    ! [X_a] :
      ( ! [C,B,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),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),zero_zero(X_a)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1)) )
      | ~ ordered_ring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_658_mult__right__mono__neg]) ).

fof(f_729_2,plain,
    ! [U_2775] :
      ( ! [U_2774,U_2773,U_2772] :
          ( hBOOL(hAPP(U_2775,bool,hAPP(U_2775,fun(U_2775,bool),ord_less_eq(U_2775),hAPP(U_2775,U_2775,hAPP(U_2775,fun(U_2775,U_2775),times_times(U_2775),U_2772),U_2774)),hAPP(U_2775,U_2775,hAPP(U_2775,fun(U_2775,U_2775),times_times(U_2775),U_2773),U_2774)))
          | ~ hBOOL(hAPP(U_2775,bool,hAPP(U_2775,fun(U_2775,bool),ord_less_eq(U_2775),U_2774),zero_zero(U_2775)))
          | ~ hBOOL(hAPP(U_2775,bool,hAPP(U_2775,fun(U_2775,bool),ord_less_eq(U_2775),U_2773),U_2772)) )
      | ~ ordered_ring(U_2775) ),
    inference(variable_rename,[status(thm)],[f_729_1]) ).

fof(f_729_3,plain,
    ! [U_2774,U_2773,U_2775,U_2772] :
      ( hBOOL(hAPP(U_2775,bool,hAPP(U_2775,fun(U_2775,bool),ord_less_eq(U_2775),hAPP(U_2775,U_2775,hAPP(U_2775,fun(U_2775,U_2775),times_times(U_2775),U_2772),U_2774)),hAPP(U_2775,U_2775,hAPP(U_2775,fun(U_2775,U_2775),times_times(U_2775),U_2773),U_2774)))
      | ~ hBOOL(hAPP(U_2775,bool,hAPP(U_2775,fun(U_2775,bool),ord_less_eq(U_2775),U_2774),zero_zero(U_2775)))
      | ~ hBOOL(hAPP(U_2775,bool,hAPP(U_2775,fun(U_2775,bool),ord_less_eq(U_2775),U_2773),U_2772))
      | ~ ordered_ring(U_2775) ),
    inference(definitional_conversion,[status(esa)],[f_729_2]) ).

cnf(f_729_4,plain,
    ( hBOOL(hAPP(U_2775,bool,hAPP(U_2775,fun(U_2775,bool),ord_less_eq(U_2775),hAPP(U_2775,U_2775,hAPP(U_2775,fun(U_2775,U_2775),times_times(U_2775),U_2772),U_2774)),hAPP(U_2775,U_2775,hAPP(U_2775,fun(U_2775,U_2775),times_times(U_2775),U_2773),U_2774)))
    | ~ hBOOL(hAPP(U_2775,bool,hAPP(U_2775,fun(U_2775,bool),ord_less_eq(U_2775),U_2774),zero_zero(U_2775)))
    | ~ hBOOL(hAPP(U_2775,bool,hAPP(U_2775,fun(U_2775,bool),ord_less_eq(U_2775),U_2773),U_2772))
    | ~ ordered_ring(U_2775) ),
    inference(clausify,[status(thm)],[f_729_3]) ).

fof(f_730_1,plain,
    ! [X_a] :
      ( ! [C,A_1,B] :
          ( 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),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B)))
          | ~ 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),A_1),B)) )
      | ~ ordere1490568538miring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_659_comm__mult__left__mono]) ).

fof(f_730_2,plain,
    ! [U_2779] :
      ( ! [U_2778,U_2777,U_2776] :
          ( hBOOL(hAPP(U_2779,bool,hAPP(U_2779,fun(U_2779,bool),ord_less_eq(U_2779),hAPP(U_2779,U_2779,hAPP(U_2779,fun(U_2779,U_2779),times_times(U_2779),U_2778),U_2777)),hAPP(U_2779,U_2779,hAPP(U_2779,fun(U_2779,U_2779),times_times(U_2779),U_2778),U_2776)))
          | ~ hBOOL(hAPP(U_2779,bool,hAPP(U_2779,fun(U_2779,bool),ord_less_eq(U_2779),zero_zero(U_2779)),U_2778))
          | ~ hBOOL(hAPP(U_2779,bool,hAPP(U_2779,fun(U_2779,bool),ord_less_eq(U_2779),U_2777),U_2776)) )
      | ~ ordere1490568538miring(U_2779) ),
    inference(variable_rename,[status(thm)],[f_730_1]) ).

fof(f_730_3,plain,
    ! [U_2778,U_2779,U_2777,U_2776] :
      ( hBOOL(hAPP(U_2779,bool,hAPP(U_2779,fun(U_2779,bool),ord_less_eq(U_2779),hAPP(U_2779,U_2779,hAPP(U_2779,fun(U_2779,U_2779),times_times(U_2779),U_2778),U_2777)),hAPP(U_2779,U_2779,hAPP(U_2779,fun(U_2779,U_2779),times_times(U_2779),U_2778),U_2776)))
      | ~ hBOOL(hAPP(U_2779,bool,hAPP(U_2779,fun(U_2779,bool),ord_less_eq(U_2779),zero_zero(U_2779)),U_2778))
      | ~ hBOOL(hAPP(U_2779,bool,hAPP(U_2779,fun(U_2779,bool),ord_less_eq(U_2779),U_2777),U_2776))
      | ~ ordere1490568538miring(U_2779) ),
    inference(definitional_conversion,[status(esa)],[f_730_2]) ).

cnf(f_730_4,plain,
    ( hBOOL(hAPP(U_2779,bool,hAPP(U_2779,fun(U_2779,bool),ord_less_eq(U_2779),hAPP(U_2779,U_2779,hAPP(U_2779,fun(U_2779,U_2779),times_times(U_2779),U_2778),U_2777)),hAPP(U_2779,U_2779,hAPP(U_2779,fun(U_2779,U_2779),times_times(U_2779),U_2778),U_2776)))
    | ~ hBOOL(hAPP(U_2779,bool,hAPP(U_2779,fun(U_2779,bool),ord_less_eq(U_2779),zero_zero(U_2779)),U_2778))
    | ~ hBOOL(hAPP(U_2779,bool,hAPP(U_2779,fun(U_2779,bool),ord_less_eq(U_2779),U_2777),U_2776))
    | ~ ordere1490568538miring(U_2779) ),
    inference(clausify,[status(thm)],[f_730_3]) ).

fof(f_731_1,plain,
    ! [X_a] :
      ( ! [C,A_1,B] :
          ( 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),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B)))
          | ~ 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),A_1),B)) )
      | ~ ordered_semiring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_660_mult__left__mono]) ).

fof(f_731_2,plain,
    ! [U_2783] :
      ( ! [U_2782,U_2781,U_2780] :
          ( hBOOL(hAPP(U_2783,bool,hAPP(U_2783,fun(U_2783,bool),ord_less_eq(U_2783),hAPP(U_2783,U_2783,hAPP(U_2783,fun(U_2783,U_2783),times_times(U_2783),U_2782),U_2781)),hAPP(U_2783,U_2783,hAPP(U_2783,fun(U_2783,U_2783),times_times(U_2783),U_2782),U_2780)))
          | ~ hBOOL(hAPP(U_2783,bool,hAPP(U_2783,fun(U_2783,bool),ord_less_eq(U_2783),zero_zero(U_2783)),U_2782))
          | ~ hBOOL(hAPP(U_2783,bool,hAPP(U_2783,fun(U_2783,bool),ord_less_eq(U_2783),U_2781),U_2780)) )
      | ~ ordered_semiring(U_2783) ),
    inference(variable_rename,[status(thm)],[f_731_1]) ).

fof(f_731_3,plain,
    ! [U_2782,U_2781,U_2780,U_2783] :
      ( hBOOL(hAPP(U_2783,bool,hAPP(U_2783,fun(U_2783,bool),ord_less_eq(U_2783),hAPP(U_2783,U_2783,hAPP(U_2783,fun(U_2783,U_2783),times_times(U_2783),U_2782),U_2781)),hAPP(U_2783,U_2783,hAPP(U_2783,fun(U_2783,U_2783),times_times(U_2783),U_2782),U_2780)))
      | ~ hBOOL(hAPP(U_2783,bool,hAPP(U_2783,fun(U_2783,bool),ord_less_eq(U_2783),zero_zero(U_2783)),U_2782))
      | ~ hBOOL(hAPP(U_2783,bool,hAPP(U_2783,fun(U_2783,bool),ord_less_eq(U_2783),U_2781),U_2780))
      | ~ ordered_semiring(U_2783) ),
    inference(definitional_conversion,[status(esa)],[f_731_2]) ).

cnf(f_731_4,plain,
    ( hBOOL(hAPP(U_2783,bool,hAPP(U_2783,fun(U_2783,bool),ord_less_eq(U_2783),hAPP(U_2783,U_2783,hAPP(U_2783,fun(U_2783,U_2783),times_times(U_2783),U_2782),U_2781)),hAPP(U_2783,U_2783,hAPP(U_2783,fun(U_2783,U_2783),times_times(U_2783),U_2782),U_2780)))
    | ~ hBOOL(hAPP(U_2783,bool,hAPP(U_2783,fun(U_2783,bool),ord_less_eq(U_2783),zero_zero(U_2783)),U_2782))
    | ~ hBOOL(hAPP(U_2783,bool,hAPP(U_2783,fun(U_2783,bool),ord_less_eq(U_2783),U_2781),U_2780))
    | ~ ordered_semiring(U_2783) ),
    inference(clausify,[status(thm)],[f_731_3]) ).

fof(f_732_1,plain,
    ! [X_a] :
      ( ! [C,A_1,B] :
          ( 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),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),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),A_1),B)) )
      | ~ ordered_semiring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_661_mult__right__mono]) ).

fof(f_732_2,plain,
    ! [U_2787] :
      ( ! [U_2786,U_2785,U_2784] :
          ( hBOOL(hAPP(U_2787,bool,hAPP(U_2787,fun(U_2787,bool),ord_less_eq(U_2787),hAPP(U_2787,U_2787,hAPP(U_2787,fun(U_2787,U_2787),times_times(U_2787),U_2785),U_2786)),hAPP(U_2787,U_2787,hAPP(U_2787,fun(U_2787,U_2787),times_times(U_2787),U_2784),U_2786)))
          | ~ hBOOL(hAPP(U_2787,bool,hAPP(U_2787,fun(U_2787,bool),ord_less_eq(U_2787),zero_zero(U_2787)),U_2786))
          | ~ hBOOL(hAPP(U_2787,bool,hAPP(U_2787,fun(U_2787,bool),ord_less_eq(U_2787),U_2785),U_2784)) )
      | ~ ordered_semiring(U_2787) ),
    inference(variable_rename,[status(thm)],[f_732_1]) ).

fof(f_732_3,plain,
    ! [U_2786,U_2787,U_2784,U_2785] :
      ( hBOOL(hAPP(U_2787,bool,hAPP(U_2787,fun(U_2787,bool),ord_less_eq(U_2787),hAPP(U_2787,U_2787,hAPP(U_2787,fun(U_2787,U_2787),times_times(U_2787),U_2785),U_2786)),hAPP(U_2787,U_2787,hAPP(U_2787,fun(U_2787,U_2787),times_times(U_2787),U_2784),U_2786)))
      | ~ hBOOL(hAPP(U_2787,bool,hAPP(U_2787,fun(U_2787,bool),ord_less_eq(U_2787),zero_zero(U_2787)),U_2786))
      | ~ hBOOL(hAPP(U_2787,bool,hAPP(U_2787,fun(U_2787,bool),ord_less_eq(U_2787),U_2785),U_2784))
      | ~ ordered_semiring(U_2787) ),
    inference(definitional_conversion,[status(esa)],[f_732_2]) ).

cnf(f_732_4,plain,
    ( hBOOL(hAPP(U_2787,bool,hAPP(U_2787,fun(U_2787,bool),ord_less_eq(U_2787),hAPP(U_2787,U_2787,hAPP(U_2787,fun(U_2787,U_2787),times_times(U_2787),U_2785),U_2786)),hAPP(U_2787,U_2787,hAPP(U_2787,fun(U_2787,U_2787),times_times(U_2787),U_2784),U_2786)))
    | ~ hBOOL(hAPP(U_2787,bool,hAPP(U_2787,fun(U_2787,bool),ord_less_eq(U_2787),zero_zero(U_2787)),U_2786))
    | ~ hBOOL(hAPP(U_2787,bool,hAPP(U_2787,fun(U_2787,bool),ord_less_eq(U_2787),U_2785),U_2784))
    | ~ ordered_semiring(U_2787) ),
    inference(clausify,[status(thm)],[f_732_3]) ).

fof(f_733_1,plain,
    ! [X_a] :
      ( ! [B,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),times_times(X_a),A_1),B)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),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))) )
      | ~ ordered_ring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_662_mult__nonpos__nonpos]) ).

fof(f_733_2,plain,
    ! [U_2790] :
      ( ! [U_2789,U_2788] :
          ( hBOOL(hAPP(U_2790,bool,hAPP(U_2790,fun(U_2790,bool),ord_less_eq(U_2790),zero_zero(U_2790)),hAPP(U_2790,U_2790,hAPP(U_2790,fun(U_2790,U_2790),times_times(U_2790),U_2788),U_2789)))
          | ~ hBOOL(hAPP(U_2790,bool,hAPP(U_2790,fun(U_2790,bool),ord_less_eq(U_2790),U_2789),zero_zero(U_2790)))
          | ~ hBOOL(hAPP(U_2790,bool,hAPP(U_2790,fun(U_2790,bool),ord_less_eq(U_2790),U_2788),zero_zero(U_2790))) )
      | ~ ordered_ring(U_2790) ),
    inference(variable_rename,[status(thm)],[f_733_1]) ).

fof(f_733_3,plain,
    ! [U_2790,U_2788,U_2789] :
      ( hBOOL(hAPP(U_2790,bool,hAPP(U_2790,fun(U_2790,bool),ord_less_eq(U_2790),zero_zero(U_2790)),hAPP(U_2790,U_2790,hAPP(U_2790,fun(U_2790,U_2790),times_times(U_2790),U_2788),U_2789)))
      | ~ hBOOL(hAPP(U_2790,bool,hAPP(U_2790,fun(U_2790,bool),ord_less_eq(U_2790),U_2789),zero_zero(U_2790)))
      | ~ hBOOL(hAPP(U_2790,bool,hAPP(U_2790,fun(U_2790,bool),ord_less_eq(U_2790),U_2788),zero_zero(U_2790)))
      | ~ ordered_ring(U_2790) ),
    inference(definitional_conversion,[status(esa)],[f_733_2]) ).

cnf(f_733_4,plain,
    ( hBOOL(hAPP(U_2790,bool,hAPP(U_2790,fun(U_2790,bool),ord_less_eq(U_2790),zero_zero(U_2790)),hAPP(U_2790,U_2790,hAPP(U_2790,fun(U_2790,U_2790),times_times(U_2790),U_2788),U_2789)))
    | ~ hBOOL(hAPP(U_2790,bool,hAPP(U_2790,fun(U_2790,bool),ord_less_eq(U_2790),U_2789),zero_zero(U_2790)))
    | ~ hBOOL(hAPP(U_2790,bool,hAPP(U_2790,fun(U_2790,bool),ord_less_eq(U_2790),U_2788),zero_zero(U_2790)))
    | ~ ordered_ring(U_2790) ),
    inference(clausify,[status(thm)],[f_733_3]) ).

fof(f_734_1,plain,
    ! [X_a] :
      ( ! [B,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),times_times(X_a),A_1),B)),zero_zero(X_a)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),zero_zero(X_a))) )
      | ~ ordere453448008miring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_663_mult__nonpos__nonneg]) ).

fof(f_734_2,plain,
    ! [U_2793] :
      ( ! [U_2792,U_2791] :
          ( hBOOL(hAPP(U_2793,bool,hAPP(U_2793,fun(U_2793,bool),ord_less_eq(U_2793),hAPP(U_2793,U_2793,hAPP(U_2793,fun(U_2793,U_2793),times_times(U_2793),U_2791),U_2792)),zero_zero(U_2793)))
          | ~ hBOOL(hAPP(U_2793,bool,hAPP(U_2793,fun(U_2793,bool),ord_less_eq(U_2793),zero_zero(U_2793)),U_2792))
          | ~ hBOOL(hAPP(U_2793,bool,hAPP(U_2793,fun(U_2793,bool),ord_less_eq(U_2793),U_2791),zero_zero(U_2793))) )
      | ~ ordere453448008miring(U_2793) ),
    inference(variable_rename,[status(thm)],[f_734_1]) ).

fof(f_734_3,plain,
    ! [U_2791,U_2793,U_2792] :
      ( hBOOL(hAPP(U_2793,bool,hAPP(U_2793,fun(U_2793,bool),ord_less_eq(U_2793),hAPP(U_2793,U_2793,hAPP(U_2793,fun(U_2793,U_2793),times_times(U_2793),U_2791),U_2792)),zero_zero(U_2793)))
      | ~ hBOOL(hAPP(U_2793,bool,hAPP(U_2793,fun(U_2793,bool),ord_less_eq(U_2793),zero_zero(U_2793)),U_2792))
      | ~ hBOOL(hAPP(U_2793,bool,hAPP(U_2793,fun(U_2793,bool),ord_less_eq(U_2793),U_2791),zero_zero(U_2793)))
      | ~ ordere453448008miring(U_2793) ),
    inference(definitional_conversion,[status(esa)],[f_734_2]) ).

cnf(f_734_4,plain,
    ( hBOOL(hAPP(U_2793,bool,hAPP(U_2793,fun(U_2793,bool),ord_less_eq(U_2793),hAPP(U_2793,U_2793,hAPP(U_2793,fun(U_2793,U_2793),times_times(U_2793),U_2791),U_2792)),zero_zero(U_2793)))
    | ~ hBOOL(hAPP(U_2793,bool,hAPP(U_2793,fun(U_2793,bool),ord_less_eq(U_2793),zero_zero(U_2793)),U_2792))
    | ~ hBOOL(hAPP(U_2793,bool,hAPP(U_2793,fun(U_2793,bool),ord_less_eq(U_2793),U_2791),zero_zero(U_2793)))
    | ~ ordere453448008miring(U_2793) ),
    inference(clausify,[status(thm)],[f_734_3]) ).

fof(f_735_1,plain,
    ! [X_a] :
      ( ! [B,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),times_times(X_a),B),A_1)),zero_zero(X_a)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),zero_zero(X_a)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) )
      | ~ ordere453448008miring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_664_mult__nonneg__nonpos2]) ).

fof(f_735_2,plain,
    ! [U_2796] :
      ( ! [U_2795,U_2794] :
          ( hBOOL(hAPP(U_2796,bool,hAPP(U_2796,fun(U_2796,bool),ord_less_eq(U_2796),hAPP(U_2796,U_2796,hAPP(U_2796,fun(U_2796,U_2796),times_times(U_2796),U_2795),U_2794)),zero_zero(U_2796)))
          | ~ hBOOL(hAPP(U_2796,bool,hAPP(U_2796,fun(U_2796,bool),ord_less_eq(U_2796),U_2795),zero_zero(U_2796)))
          | ~ hBOOL(hAPP(U_2796,bool,hAPP(U_2796,fun(U_2796,bool),ord_less_eq(U_2796),zero_zero(U_2796)),U_2794)) )
      | ~ ordere453448008miring(U_2796) ),
    inference(variable_rename,[status(thm)],[f_735_1]) ).

fof(f_735_3,plain,
    ! [U_2794,U_2796,U_2795] :
      ( hBOOL(hAPP(U_2796,bool,hAPP(U_2796,fun(U_2796,bool),ord_less_eq(U_2796),hAPP(U_2796,U_2796,hAPP(U_2796,fun(U_2796,U_2796),times_times(U_2796),U_2795),U_2794)),zero_zero(U_2796)))
      | ~ hBOOL(hAPP(U_2796,bool,hAPP(U_2796,fun(U_2796,bool),ord_less_eq(U_2796),U_2795),zero_zero(U_2796)))
      | ~ hBOOL(hAPP(U_2796,bool,hAPP(U_2796,fun(U_2796,bool),ord_less_eq(U_2796),zero_zero(U_2796)),U_2794))
      | ~ ordere453448008miring(U_2796) ),
    inference(definitional_conversion,[status(esa)],[f_735_2]) ).

cnf(f_735_4,plain,
    ( hBOOL(hAPP(U_2796,bool,hAPP(U_2796,fun(U_2796,bool),ord_less_eq(U_2796),hAPP(U_2796,U_2796,hAPP(U_2796,fun(U_2796,U_2796),times_times(U_2796),U_2795),U_2794)),zero_zero(U_2796)))
    | ~ hBOOL(hAPP(U_2796,bool,hAPP(U_2796,fun(U_2796,bool),ord_less_eq(U_2796),U_2795),zero_zero(U_2796)))
    | ~ hBOOL(hAPP(U_2796,bool,hAPP(U_2796,fun(U_2796,bool),ord_less_eq(U_2796),zero_zero(U_2796)),U_2794))
    | ~ ordere453448008miring(U_2796) ),
    inference(clausify,[status(thm)],[f_735_3]) ).

fof(f_736_1,plain,
    ! [X_a] :
      ( ! [B,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),times_times(X_a),A_1),B)),zero_zero(X_a)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),zero_zero(X_a)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) )
      | ~ ordere453448008miring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_665_mult__nonneg__nonpos]) ).

fof(f_736_2,plain,
    ! [U_2799] :
      ( ! [U_2798,U_2797] :
          ( hBOOL(hAPP(U_2799,bool,hAPP(U_2799,fun(U_2799,bool),ord_less_eq(U_2799),hAPP(U_2799,U_2799,hAPP(U_2799,fun(U_2799,U_2799),times_times(U_2799),U_2797),U_2798)),zero_zero(U_2799)))
          | ~ hBOOL(hAPP(U_2799,bool,hAPP(U_2799,fun(U_2799,bool),ord_less_eq(U_2799),U_2798),zero_zero(U_2799)))
          | ~ hBOOL(hAPP(U_2799,bool,hAPP(U_2799,fun(U_2799,bool),ord_less_eq(U_2799),zero_zero(U_2799)),U_2797)) )
      | ~ ordere453448008miring(U_2799) ),
    inference(variable_rename,[status(thm)],[f_736_1]) ).

fof(f_736_3,plain,
    ! [U_2799,U_2798,U_2797] :
      ( hBOOL(hAPP(U_2799,bool,hAPP(U_2799,fun(U_2799,bool),ord_less_eq(U_2799),hAPP(U_2799,U_2799,hAPP(U_2799,fun(U_2799,U_2799),times_times(U_2799),U_2797),U_2798)),zero_zero(U_2799)))
      | ~ hBOOL(hAPP(U_2799,bool,hAPP(U_2799,fun(U_2799,bool),ord_less_eq(U_2799),U_2798),zero_zero(U_2799)))
      | ~ hBOOL(hAPP(U_2799,bool,hAPP(U_2799,fun(U_2799,bool),ord_less_eq(U_2799),zero_zero(U_2799)),U_2797))
      | ~ ordere453448008miring(U_2799) ),
    inference(definitional_conversion,[status(esa)],[f_736_2]) ).

cnf(f_736_4,plain,
    ( hBOOL(hAPP(U_2799,bool,hAPP(U_2799,fun(U_2799,bool),ord_less_eq(U_2799),hAPP(U_2799,U_2799,hAPP(U_2799,fun(U_2799,U_2799),times_times(U_2799),U_2797),U_2798)),zero_zero(U_2799)))
    | ~ hBOOL(hAPP(U_2799,bool,hAPP(U_2799,fun(U_2799,bool),ord_less_eq(U_2799),U_2798),zero_zero(U_2799)))
    | ~ hBOOL(hAPP(U_2799,bool,hAPP(U_2799,fun(U_2799,bool),ord_less_eq(U_2799),zero_zero(U_2799)),U_2797))
    | ~ ordere453448008miring(U_2799) ),
    inference(clausify,[status(thm)],[f_736_3]) ).

fof(f_737_1,plain,
    ! [X_a] :
      ( ! [B,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),times_times(X_a),A_1),B)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) )
      | ~ ordere453448008miring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_666_mult__nonneg__nonneg]) ).

fof(f_737_2,plain,
    ! [U_2802] :
      ( ! [U_2801,U_2800] :
          ( hBOOL(hAPP(U_2802,bool,hAPP(U_2802,fun(U_2802,bool),ord_less_eq(U_2802),zero_zero(U_2802)),hAPP(U_2802,U_2802,hAPP(U_2802,fun(U_2802,U_2802),times_times(U_2802),U_2800),U_2801)))
          | ~ hBOOL(hAPP(U_2802,bool,hAPP(U_2802,fun(U_2802,bool),ord_less_eq(U_2802),zero_zero(U_2802)),U_2801))
          | ~ hBOOL(hAPP(U_2802,bool,hAPP(U_2802,fun(U_2802,bool),ord_less_eq(U_2802),zero_zero(U_2802)),U_2800)) )
      | ~ ordere453448008miring(U_2802) ),
    inference(variable_rename,[status(thm)],[f_737_1]) ).

fof(f_737_3,plain,
    ! [U_2801,U_2800,U_2802] :
      ( hBOOL(hAPP(U_2802,bool,hAPP(U_2802,fun(U_2802,bool),ord_less_eq(U_2802),zero_zero(U_2802)),hAPP(U_2802,U_2802,hAPP(U_2802,fun(U_2802,U_2802),times_times(U_2802),U_2800),U_2801)))
      | ~ hBOOL(hAPP(U_2802,bool,hAPP(U_2802,fun(U_2802,bool),ord_less_eq(U_2802),zero_zero(U_2802)),U_2801))
      | ~ hBOOL(hAPP(U_2802,bool,hAPP(U_2802,fun(U_2802,bool),ord_less_eq(U_2802),zero_zero(U_2802)),U_2800))
      | ~ ordere453448008miring(U_2802) ),
    inference(definitional_conversion,[status(esa)],[f_737_2]) ).

cnf(f_737_4,plain,
    ( hBOOL(hAPP(U_2802,bool,hAPP(U_2802,fun(U_2802,bool),ord_less_eq(U_2802),zero_zero(U_2802)),hAPP(U_2802,U_2802,hAPP(U_2802,fun(U_2802,U_2802),times_times(U_2802),U_2800),U_2801)))
    | ~ hBOOL(hAPP(U_2802,bool,hAPP(U_2802,fun(U_2802,bool),ord_less_eq(U_2802),zero_zero(U_2802)),U_2801))
    | ~ hBOOL(hAPP(U_2802,bool,hAPP(U_2802,fun(U_2802,bool),ord_less_eq(U_2802),zero_zero(U_2802)),U_2800))
    | ~ ordere453448008miring(U_2802) ),
    inference(clausify,[status(thm)],[f_737_3]) ).

fof(f_738_1,plain,
    ! [X_b] :
      ( ! [A_2,B_3] :
          ( ( 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),times_times(X_b),A_2),B_3)),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)),B_3))
                | ~ 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),B_3),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)),A_2)) ) ) )
          & ( ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),B_3))
              & 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),B_3),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)),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),times_times(X_b),A_2),B_3)),zero_zero(X_b))) ) )
      | ~ linord581940658strict(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_667_mult__le__0__iff]) ).

fof(f_738_2,plain,
    ! [U_2805] :
      ( ! [U_2804,U_2803] :
          ( ( hBOOL(hAPP(U_2805,bool,hAPP(U_2805,fun(U_2805,bool),ord_less_eq(U_2805),hAPP(U_2805,U_2805,hAPP(U_2805,fun(U_2805,U_2805),times_times(U_2805),U_2804),U_2803)),zero_zero(U_2805)))
            | ( ( ~ hBOOL(hAPP(U_2805,bool,hAPP(U_2805,fun(U_2805,bool),ord_less_eq(U_2805),zero_zero(U_2805)),U_2803))
                | ~ hBOOL(hAPP(U_2805,bool,hAPP(U_2805,fun(U_2805,bool),ord_less_eq(U_2805),U_2804),zero_zero(U_2805))) )
              & ( ~ hBOOL(hAPP(U_2805,bool,hAPP(U_2805,fun(U_2805,bool),ord_less_eq(U_2805),U_2803),zero_zero(U_2805)))
                | ~ hBOOL(hAPP(U_2805,bool,hAPP(U_2805,fun(U_2805,bool),ord_less_eq(U_2805),zero_zero(U_2805)),U_2804)) ) ) )
          & ( ( hBOOL(hAPP(U_2805,bool,hAPP(U_2805,fun(U_2805,bool),ord_less_eq(U_2805),zero_zero(U_2805)),U_2803))
              & hBOOL(hAPP(U_2805,bool,hAPP(U_2805,fun(U_2805,bool),ord_less_eq(U_2805),U_2804),zero_zero(U_2805))) )
            | ( hBOOL(hAPP(U_2805,bool,hAPP(U_2805,fun(U_2805,bool),ord_less_eq(U_2805),U_2803),zero_zero(U_2805)))
              & hBOOL(hAPP(U_2805,bool,hAPP(U_2805,fun(U_2805,bool),ord_less_eq(U_2805),zero_zero(U_2805)),U_2804)) )
            | ~ hBOOL(hAPP(U_2805,bool,hAPP(U_2805,fun(U_2805,bool),ord_less_eq(U_2805),hAPP(U_2805,U_2805,hAPP(U_2805,fun(U_2805,U_2805),times_times(U_2805),U_2804),U_2803)),zero_zero(U_2805))) ) )
      | ~ linord581940658strict(U_2805) ),
    inference(variable_rename,[status(thm)],[f_738_1]) ).

fof(f_738_3,plain,
    ! [U_2805] :
      ( ( ! [U_2809,U_2807] :
            ( hBOOL(hAPP(U_2805,bool,hAPP(U_2805,fun(U_2805,bool),ord_less_eq(U_2805),hAPP(U_2805,U_2805,hAPP(U_2805,fun(U_2805,U_2805),times_times(U_2805),U_2809),U_2807)),zero_zero(U_2805)))
            | ( ( ~ hBOOL(hAPP(U_2805,bool,hAPP(U_2805,fun(U_2805,bool),ord_less_eq(U_2805),zero_zero(U_2805)),U_2807))
                | ~ hBOOL(hAPP(U_2805,bool,hAPP(U_2805,fun(U_2805,bool),ord_less_eq(U_2805),U_2809),zero_zero(U_2805))) )
              & ( ~ hBOOL(hAPP(U_2805,bool,hAPP(U_2805,fun(U_2805,bool),ord_less_eq(U_2805),U_2807),zero_zero(U_2805)))
                | ~ hBOOL(hAPP(U_2805,bool,hAPP(U_2805,fun(U_2805,bool),ord_less_eq(U_2805),zero_zero(U_2805)),U_2809)) ) ) )
        & ! [U_2808,U_2806] :
            ( ( hBOOL(hAPP(U_2805,bool,hAPP(U_2805,fun(U_2805,bool),ord_less_eq(U_2805),zero_zero(U_2805)),U_2806))
              & hBOOL(hAPP(U_2805,bool,hAPP(U_2805,fun(U_2805,bool),ord_less_eq(U_2805),U_2808),zero_zero(U_2805))) )
            | ( hBOOL(hAPP(U_2805,bool,hAPP(U_2805,fun(U_2805,bool),ord_less_eq(U_2805),U_2806),zero_zero(U_2805)))
              & hBOOL(hAPP(U_2805,bool,hAPP(U_2805,fun(U_2805,bool),ord_less_eq(U_2805),zero_zero(U_2805)),U_2808)) )
            | ~ hBOOL(hAPP(U_2805,bool,hAPP(U_2805,fun(U_2805,bool),ord_less_eq(U_2805),hAPP(U_2805,U_2805,hAPP(U_2805,fun(U_2805,U_2805),times_times(U_2805),U_2808),U_2806)),zero_zero(U_2805))) ) )
      | ~ linord581940658strict(U_2805) ),
    inference(miniscope,[status(thm)],[f_738_2]) ).

fof(f_738_4,plain,
    ( ! [U_2809,U_2805,U_2807] :
        ( ~ hBOOL(hAPP(U_2805,bool,hAPP(U_2805,fun(U_2805,bool),ord_less_eq(U_2805),zero_zero(U_2805)),U_2807))
        | ~ hBOOL(hAPP(U_2805,bool,hAPP(U_2805,fun(U_2805,bool),ord_less_eq(U_2805),U_2809),zero_zero(U_2805)))
        | ~ sP190(U_2809,U_2805,U_2807) )
    & ! [U_2809,U_2805,U_2807] :
        ( ~ hBOOL(hAPP(U_2805,bool,hAPP(U_2805,fun(U_2805,bool),ord_less_eq(U_2805),U_2807),zero_zero(U_2805)))
        | ~ hBOOL(hAPP(U_2805,bool,hAPP(U_2805,fun(U_2805,bool),ord_less_eq(U_2805),zero_zero(U_2805)),U_2809))
        | ~ sP190(U_2809,U_2805,U_2807) )
    & ! [U_2805,U_2808,U_2806] :
        ( hBOOL(hAPP(U_2805,bool,hAPP(U_2805,fun(U_2805,bool),ord_less_eq(U_2805),zero_zero(U_2805)),U_2806))
        | ~ sP189(U_2805,U_2808,U_2806) )
    & ! [U_2805,U_2808,U_2806] :
        ( hBOOL(hAPP(U_2805,bool,hAPP(U_2805,fun(U_2805,bool),ord_less_eq(U_2805),U_2808),zero_zero(U_2805)))
        | ~ sP189(U_2805,U_2808,U_2806) )
    & ! [U_2805,U_2808,U_2806] :
        ( hBOOL(hAPP(U_2805,bool,hAPP(U_2805,fun(U_2805,bool),ord_less_eq(U_2805),U_2806),zero_zero(U_2805)))
        | ~ sP188(U_2805,U_2808,U_2806) )
    & ! [U_2805,U_2808,U_2806] :
        ( hBOOL(hAPP(U_2805,bool,hAPP(U_2805,fun(U_2805,bool),ord_less_eq(U_2805),zero_zero(U_2805)),U_2808))
        | ~ sP188(U_2805,U_2808,U_2806) )
    & ! [U_2809,U_2805,U_2808,U_2807,U_2806] :
        ( hBOOL(hAPP(U_2805,bool,hAPP(U_2805,fun(U_2805,bool),ord_less_eq(U_2805),hAPP(U_2805,U_2805,hAPP(U_2805,fun(U_2805,U_2805),times_times(U_2805),U_2809),U_2807)),zero_zero(U_2805)))
        | sP190(U_2809,U_2805,U_2807)
        | ~ sP191(U_2809,U_2805,U_2808,U_2807,U_2806) )
    & ! [U_2809,U_2805,U_2808,U_2807,U_2806] :
        ( sP189(U_2805,U_2808,U_2806)
        | sP188(U_2805,U_2808,U_2806)
        | ~ hBOOL(hAPP(U_2805,bool,hAPP(U_2805,fun(U_2805,bool),ord_less_eq(U_2805),hAPP(U_2805,U_2805,hAPP(U_2805,fun(U_2805,U_2805),times_times(U_2805),U_2808),U_2806)),zero_zero(U_2805)))
        | ~ sP191(U_2809,U_2805,U_2808,U_2807,U_2806) )
    & ! [U_2809,U_2805,U_2808,U_2807,U_2806] :
        ( sP191(U_2809,U_2805,U_2808,U_2807,U_2806)
        | ~ linord581940658strict(U_2805) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP188,sP189,sP190,sP191])],[f_738_3]) ).

cnf(f_738_5,plain,
    ( sP191(U_2809,U_2805,U_2808,U_2807,U_2806)
    | ~ linord581940658strict(U_2805) ),
    inference(clausify,[status(thm)],[f_738_4]) ).

cnf(f_738_6,plain,
    ( sP189(U_2805,U_2808,U_2806)
    | sP188(U_2805,U_2808,U_2806)
    | ~ hBOOL(hAPP(U_2805,bool,hAPP(U_2805,fun(U_2805,bool),ord_less_eq(U_2805),hAPP(U_2805,U_2805,hAPP(U_2805,fun(U_2805,U_2805),times_times(U_2805),U_2808),U_2806)),zero_zero(U_2805)))
    | ~ sP191(U_2809,U_2805,U_2808,U_2807,U_2806) ),
    inference(clausify,[status(thm)],[f_738_4]) ).

cnf(f_738_7,plain,
    ( hBOOL(hAPP(U_2805,bool,hAPP(U_2805,fun(U_2805,bool),ord_less_eq(U_2805),hAPP(U_2805,U_2805,hAPP(U_2805,fun(U_2805,U_2805),times_times(U_2805),U_2809),U_2807)),zero_zero(U_2805)))
    | sP190(U_2809,U_2805,U_2807)
    | ~ sP191(U_2809,U_2805,U_2808,U_2807,U_2806) ),
    inference(clausify,[status(thm)],[f_738_4]) ).

cnf(f_738_8,plain,
    ( hBOOL(hAPP(U_2805,bool,hAPP(U_2805,fun(U_2805,bool),ord_less_eq(U_2805),zero_zero(U_2805)),U_2808))
    | ~ sP188(U_2805,U_2808,U_2806) ),
    inference(clausify,[status(thm)],[f_738_4]) ).

cnf(f_738_9,plain,
    ( hBOOL(hAPP(U_2805,bool,hAPP(U_2805,fun(U_2805,bool),ord_less_eq(U_2805),U_2806),zero_zero(U_2805)))
    | ~ sP188(U_2805,U_2808,U_2806) ),
    inference(clausify,[status(thm)],[f_738_4]) ).

cnf(f_738_10,plain,
    ( hBOOL(hAPP(U_2805,bool,hAPP(U_2805,fun(U_2805,bool),ord_less_eq(U_2805),U_2808),zero_zero(U_2805)))
    | ~ sP189(U_2805,U_2808,U_2806) ),
    inference(clausify,[status(thm)],[f_738_4]) ).

cnf(f_738_11,plain,
    ( hBOOL(hAPP(U_2805,bool,hAPP(U_2805,fun(U_2805,bool),ord_less_eq(U_2805),zero_zero(U_2805)),U_2806))
    | ~ sP189(U_2805,U_2808,U_2806) ),
    inference(clausify,[status(thm)],[f_738_4]) ).

cnf(f_738_12,plain,
    ( ~ hBOOL(hAPP(U_2805,bool,hAPP(U_2805,fun(U_2805,bool),ord_less_eq(U_2805),U_2807),zero_zero(U_2805)))
    | ~ hBOOL(hAPP(U_2805,bool,hAPP(U_2805,fun(U_2805,bool),ord_less_eq(U_2805),zero_zero(U_2805)),U_2809))
    | ~ sP190(U_2809,U_2805,U_2807) ),
    inference(clausify,[status(thm)],[f_738_4]) ).

cnf(f_738_13,plain,
    ( ~ hBOOL(hAPP(U_2805,bool,hAPP(U_2805,fun(U_2805,bool),ord_less_eq(U_2805),zero_zero(U_2805)),U_2807))
    | ~ hBOOL(hAPP(U_2805,bool,hAPP(U_2805,fun(U_2805,bool),ord_less_eq(U_2805),U_2809),zero_zero(U_2805)))
    | ~ sP190(U_2809,U_2805,U_2807) ),
    inference(clausify,[status(thm)],[f_738_4]) ).

fof(f_739_1,plain,
    ! [X_b] :
      ( ! [A_2,B_3] :
          ( ( 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),times_times(X_b),A_2),B_3)))
            | ( ( ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),B_3),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),zero_zero(X_b)),B_3))
                | ~ 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),B_3),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),zero_zero(X_b)),B_3))
              & 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),times_times(X_b),A_2),B_3))) ) )
      | ~ linord581940658strict(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_668_zero__le__mult__iff]) ).

fof(f_739_2,plain,
    ! [U_2812] :
      ( ! [U_2811,U_2810] :
          ( ( hBOOL(hAPP(U_2812,bool,hAPP(U_2812,fun(U_2812,bool),ord_less_eq(U_2812),zero_zero(U_2812)),hAPP(U_2812,U_2812,hAPP(U_2812,fun(U_2812,U_2812),times_times(U_2812),U_2811),U_2810)))
            | ( ( ~ hBOOL(hAPP(U_2812,bool,hAPP(U_2812,fun(U_2812,bool),ord_less_eq(U_2812),U_2810),zero_zero(U_2812)))
                | ~ hBOOL(hAPP(U_2812,bool,hAPP(U_2812,fun(U_2812,bool),ord_less_eq(U_2812),U_2811),zero_zero(U_2812))) )
              & ( ~ hBOOL(hAPP(U_2812,bool,hAPP(U_2812,fun(U_2812,bool),ord_less_eq(U_2812),zero_zero(U_2812)),U_2810))
                | ~ hBOOL(hAPP(U_2812,bool,hAPP(U_2812,fun(U_2812,bool),ord_less_eq(U_2812),zero_zero(U_2812)),U_2811)) ) ) )
          & ( ( hBOOL(hAPP(U_2812,bool,hAPP(U_2812,fun(U_2812,bool),ord_less_eq(U_2812),U_2810),zero_zero(U_2812)))
              & hBOOL(hAPP(U_2812,bool,hAPP(U_2812,fun(U_2812,bool),ord_less_eq(U_2812),U_2811),zero_zero(U_2812))) )
            | ( hBOOL(hAPP(U_2812,bool,hAPP(U_2812,fun(U_2812,bool),ord_less_eq(U_2812),zero_zero(U_2812)),U_2810))
              & hBOOL(hAPP(U_2812,bool,hAPP(U_2812,fun(U_2812,bool),ord_less_eq(U_2812),zero_zero(U_2812)),U_2811)) )
            | ~ hBOOL(hAPP(U_2812,bool,hAPP(U_2812,fun(U_2812,bool),ord_less_eq(U_2812),zero_zero(U_2812)),hAPP(U_2812,U_2812,hAPP(U_2812,fun(U_2812,U_2812),times_times(U_2812),U_2811),U_2810))) ) )
      | ~ linord581940658strict(U_2812) ),
    inference(variable_rename,[status(thm)],[f_739_1]) ).

fof(f_739_3,plain,
    ! [U_2812] :
      ( ( ! [U_2816,U_2814] :
            ( hBOOL(hAPP(U_2812,bool,hAPP(U_2812,fun(U_2812,bool),ord_less_eq(U_2812),zero_zero(U_2812)),hAPP(U_2812,U_2812,hAPP(U_2812,fun(U_2812,U_2812),times_times(U_2812),U_2816),U_2814)))
            | ( ( ~ hBOOL(hAPP(U_2812,bool,hAPP(U_2812,fun(U_2812,bool),ord_less_eq(U_2812),U_2814),zero_zero(U_2812)))
                | ~ hBOOL(hAPP(U_2812,bool,hAPP(U_2812,fun(U_2812,bool),ord_less_eq(U_2812),U_2816),zero_zero(U_2812))) )
              & ( ~ hBOOL(hAPP(U_2812,bool,hAPP(U_2812,fun(U_2812,bool),ord_less_eq(U_2812),zero_zero(U_2812)),U_2814))
                | ~ hBOOL(hAPP(U_2812,bool,hAPP(U_2812,fun(U_2812,bool),ord_less_eq(U_2812),zero_zero(U_2812)),U_2816)) ) ) )
        & ! [U_2815,U_2813] :
            ( ( hBOOL(hAPP(U_2812,bool,hAPP(U_2812,fun(U_2812,bool),ord_less_eq(U_2812),U_2813),zero_zero(U_2812)))
              & hBOOL(hAPP(U_2812,bool,hAPP(U_2812,fun(U_2812,bool),ord_less_eq(U_2812),U_2815),zero_zero(U_2812))) )
            | ( hBOOL(hAPP(U_2812,bool,hAPP(U_2812,fun(U_2812,bool),ord_less_eq(U_2812),zero_zero(U_2812)),U_2813))
              & hBOOL(hAPP(U_2812,bool,hAPP(U_2812,fun(U_2812,bool),ord_less_eq(U_2812),zero_zero(U_2812)),U_2815)) )
            | ~ hBOOL(hAPP(U_2812,bool,hAPP(U_2812,fun(U_2812,bool),ord_less_eq(U_2812),zero_zero(U_2812)),hAPP(U_2812,U_2812,hAPP(U_2812,fun(U_2812,U_2812),times_times(U_2812),U_2815),U_2813))) ) )
      | ~ linord581940658strict(U_2812) ),
    inference(miniscope,[status(thm)],[f_739_2]) ).

fof(f_739_4,plain,
    ( ! [U_2812,U_2814,U_2816] :
        ( ~ hBOOL(hAPP(U_2812,bool,hAPP(U_2812,fun(U_2812,bool),ord_less_eq(U_2812),U_2814),zero_zero(U_2812)))
        | ~ hBOOL(hAPP(U_2812,bool,hAPP(U_2812,fun(U_2812,bool),ord_less_eq(U_2812),U_2816),zero_zero(U_2812)))
        | ~ sP194(U_2812,U_2814,U_2816) )
    & ! [U_2812,U_2814,U_2816] :
        ( ~ hBOOL(hAPP(U_2812,bool,hAPP(U_2812,fun(U_2812,bool),ord_less_eq(U_2812),zero_zero(U_2812)),U_2814))
        | ~ hBOOL(hAPP(U_2812,bool,hAPP(U_2812,fun(U_2812,bool),ord_less_eq(U_2812),zero_zero(U_2812)),U_2816))
        | ~ sP194(U_2812,U_2814,U_2816) )
    & ! [U_2813,U_2812,U_2815] :
        ( hBOOL(hAPP(U_2812,bool,hAPP(U_2812,fun(U_2812,bool),ord_less_eq(U_2812),U_2813),zero_zero(U_2812)))
        | ~ sP193(U_2813,U_2812,U_2815) )
    & ! [U_2813,U_2812,U_2815] :
        ( hBOOL(hAPP(U_2812,bool,hAPP(U_2812,fun(U_2812,bool),ord_less_eq(U_2812),U_2815),zero_zero(U_2812)))
        | ~ sP193(U_2813,U_2812,U_2815) )
    & ! [U_2813,U_2812,U_2815] :
        ( hBOOL(hAPP(U_2812,bool,hAPP(U_2812,fun(U_2812,bool),ord_less_eq(U_2812),zero_zero(U_2812)),U_2813))
        | ~ sP192(U_2813,U_2812,U_2815) )
    & ! [U_2813,U_2812,U_2815] :
        ( hBOOL(hAPP(U_2812,bool,hAPP(U_2812,fun(U_2812,bool),ord_less_eq(U_2812),zero_zero(U_2812)),U_2815))
        | ~ sP192(U_2813,U_2812,U_2815) )
    & ! [U_2813,U_2812,U_2814,U_2815,U_2816] :
        ( hBOOL(hAPP(U_2812,bool,hAPP(U_2812,fun(U_2812,bool),ord_less_eq(U_2812),zero_zero(U_2812)),hAPP(U_2812,U_2812,hAPP(U_2812,fun(U_2812,U_2812),times_times(U_2812),U_2816),U_2814)))
        | sP194(U_2812,U_2814,U_2816)
        | ~ sP195(U_2813,U_2812,U_2814,U_2815,U_2816) )
    & ! [U_2813,U_2812,U_2814,U_2815,U_2816] :
        ( sP193(U_2813,U_2812,U_2815)
        | sP192(U_2813,U_2812,U_2815)
        | ~ hBOOL(hAPP(U_2812,bool,hAPP(U_2812,fun(U_2812,bool),ord_less_eq(U_2812),zero_zero(U_2812)),hAPP(U_2812,U_2812,hAPP(U_2812,fun(U_2812,U_2812),times_times(U_2812),U_2815),U_2813)))
        | ~ sP195(U_2813,U_2812,U_2814,U_2815,U_2816) )
    & ! [U_2813,U_2812,U_2814,U_2815,U_2816] :
        ( sP195(U_2813,U_2812,U_2814,U_2815,U_2816)
        | ~ linord581940658strict(U_2812) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP192,sP193,sP194,sP195])],[f_739_3]) ).

cnf(f_739_5,plain,
    ( sP195(U_2813,U_2812,U_2814,U_2815,U_2816)
    | ~ linord581940658strict(U_2812) ),
    inference(clausify,[status(thm)],[f_739_4]) ).

cnf(f_739_6,plain,
    ( sP193(U_2813,U_2812,U_2815)
    | sP192(U_2813,U_2812,U_2815)
    | ~ hBOOL(hAPP(U_2812,bool,hAPP(U_2812,fun(U_2812,bool),ord_less_eq(U_2812),zero_zero(U_2812)),hAPP(U_2812,U_2812,hAPP(U_2812,fun(U_2812,U_2812),times_times(U_2812),U_2815),U_2813)))
    | ~ sP195(U_2813,U_2812,U_2814,U_2815,U_2816) ),
    inference(clausify,[status(thm)],[f_739_4]) ).

cnf(f_739_7,plain,
    ( hBOOL(hAPP(U_2812,bool,hAPP(U_2812,fun(U_2812,bool),ord_less_eq(U_2812),zero_zero(U_2812)),hAPP(U_2812,U_2812,hAPP(U_2812,fun(U_2812,U_2812),times_times(U_2812),U_2816),U_2814)))
    | sP194(U_2812,U_2814,U_2816)
    | ~ sP195(U_2813,U_2812,U_2814,U_2815,U_2816) ),
    inference(clausify,[status(thm)],[f_739_4]) ).

cnf(f_739_8,plain,
    ( hBOOL(hAPP(U_2812,bool,hAPP(U_2812,fun(U_2812,bool),ord_less_eq(U_2812),zero_zero(U_2812)),U_2815))
    | ~ sP192(U_2813,U_2812,U_2815) ),
    inference(clausify,[status(thm)],[f_739_4]) ).

cnf(f_739_9,plain,
    ( hBOOL(hAPP(U_2812,bool,hAPP(U_2812,fun(U_2812,bool),ord_less_eq(U_2812),zero_zero(U_2812)),U_2813))
    | ~ sP192(U_2813,U_2812,U_2815) ),
    inference(clausify,[status(thm)],[f_739_4]) ).

cnf(f_739_10,plain,
    ( hBOOL(hAPP(U_2812,bool,hAPP(U_2812,fun(U_2812,bool),ord_less_eq(U_2812),U_2815),zero_zero(U_2812)))
    | ~ sP193(U_2813,U_2812,U_2815) ),
    inference(clausify,[status(thm)],[f_739_4]) ).

cnf(f_739_11,plain,
    ( hBOOL(hAPP(U_2812,bool,hAPP(U_2812,fun(U_2812,bool),ord_less_eq(U_2812),U_2813),zero_zero(U_2812)))
    | ~ sP193(U_2813,U_2812,U_2815) ),
    inference(clausify,[status(thm)],[f_739_4]) ).

cnf(f_739_12,plain,
    ( ~ hBOOL(hAPP(U_2812,bool,hAPP(U_2812,fun(U_2812,bool),ord_less_eq(U_2812),zero_zero(U_2812)),U_2814))
    | ~ hBOOL(hAPP(U_2812,bool,hAPP(U_2812,fun(U_2812,bool),ord_less_eq(U_2812),zero_zero(U_2812)),U_2816))
    | ~ sP194(U_2812,U_2814,U_2816) ),
    inference(clausify,[status(thm)],[f_739_4]) ).

cnf(f_739_13,plain,
    ( ~ hBOOL(hAPP(U_2812,bool,hAPP(U_2812,fun(U_2812,bool),ord_less_eq(U_2812),U_2814),zero_zero(U_2812)))
    | ~ hBOOL(hAPP(U_2812,bool,hAPP(U_2812,fun(U_2812,bool),ord_less_eq(U_2812),U_2816),zero_zero(U_2812)))
    | ~ sP194(U_2812,U_2814,U_2816) ),
    inference(clausify,[status(thm)],[f_739_4]) ).

fof(f_740_1,plain,
    ! [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)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),A_1)))
      | ~ linordered_ring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_669_zero__le__square]) ).

fof(f_740_2,plain,
    ! [U_2818] :
      ( ! [U_2817] : hBOOL(hAPP(U_2818,bool,hAPP(U_2818,fun(U_2818,bool),ord_less_eq(U_2818),zero_zero(U_2818)),hAPP(U_2818,U_2818,hAPP(U_2818,fun(U_2818,U_2818),times_times(U_2818),U_2817),U_2817)))
      | ~ linordered_ring(U_2818) ),
    inference(variable_rename,[status(thm)],[f_740_1]) ).

fof(f_740_3,plain,
    ! [U_2817,U_2818] :
      ( hBOOL(hAPP(U_2818,bool,hAPP(U_2818,fun(U_2818,bool),ord_less_eq(U_2818),zero_zero(U_2818)),hAPP(U_2818,U_2818,hAPP(U_2818,fun(U_2818,U_2818),times_times(U_2818),U_2817),U_2817)))
      | ~ linordered_ring(U_2818) ),
    inference(definitional_conversion,[status(esa)],[f_740_2]) ).

cnf(f_740_4,plain,
    ( hBOOL(hAPP(U_2818,bool,hAPP(U_2818,fun(U_2818,bool),ord_less_eq(U_2818),zero_zero(U_2818)),hAPP(U_2818,U_2818,hAPP(U_2818,fun(U_2818,U_2818),times_times(U_2818),U_2817),U_2817)))
    | ~ linordered_ring(U_2818) ),
    inference(clausify,[status(thm)],[f_740_3]) ).

fof(f_741_1,plain,
    ! [X_a] :
      ( ! [A_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),times_times(X_a),A_1),A_1)),zero_zero(X_a)))
      | ~ linordered_ring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_670_not__square__less__zero]) ).

fof(f_741_2,plain,
    ! [U_2820] :
      ( ! [U_2819] : ~ hBOOL(hAPP(U_2820,bool,hAPP(U_2820,fun(U_2820,bool),ord_less(U_2820),hAPP(U_2820,U_2820,hAPP(U_2820,fun(U_2820,U_2820),times_times(U_2820),U_2819),U_2819)),zero_zero(U_2820)))
      | ~ linordered_ring(U_2820) ),
    inference(variable_rename,[status(thm)],[f_741_1]) ).

fof(f_741_3,plain,
    ! [U_2820,U_2819] :
      ( ~ hBOOL(hAPP(U_2820,bool,hAPP(U_2820,fun(U_2820,bool),ord_less(U_2820),hAPP(U_2820,U_2820,hAPP(U_2820,fun(U_2820,U_2820),times_times(U_2820),U_2819),U_2819)),zero_zero(U_2820)))
      | ~ linordered_ring(U_2820) ),
    inference(definitional_conversion,[status(esa)],[f_741_2]) ).

cnf(f_741_4,plain,
    ( ~ hBOOL(hAPP(U_2820,bool,hAPP(U_2820,fun(U_2820,bool),ord_less(U_2820),hAPP(U_2820,U_2820,hAPP(U_2820,fun(U_2820,U_2820),times_times(U_2820),U_2819),U_2819)),zero_zero(U_2820)))
    | ~ linordered_ring(U_2820) ),
    inference(clausify,[status(thm)],[f_741_3]) ).

fof(f_742_1,plain,
    ! [X_b] :
      ( ! [A_2,C_1,B_3] :
          ( ( 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),times_times(X_b),A_2),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),C_1)))
            | ( ( ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),B_3),A_2))
                | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),zero_zero(X_b))) )
              & ( ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_3))
                | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),C_1)) ) ) )
          & ( ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),B_3),A_2))
              & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),zero_zero(X_b))) )
            | ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_3))
              & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),C_1)) )
            | ~ 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),times_times(X_b),A_2),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),C_1))) ) )
      | ~ linord581940658strict(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_671_mult__less__cancel__right__disj]) ).

fof(f_742_2,plain,
    ! [U_2824] :
      ( ! [U_2823,U_2822,U_2821] :
          ( ( hBOOL(hAPP(U_2824,bool,hAPP(U_2824,fun(U_2824,bool),ord_less(U_2824),hAPP(U_2824,U_2824,hAPP(U_2824,fun(U_2824,U_2824),times_times(U_2824),U_2823),U_2822)),hAPP(U_2824,U_2824,hAPP(U_2824,fun(U_2824,U_2824),times_times(U_2824),U_2821),U_2822)))
            | ( ( ~ hBOOL(hAPP(U_2824,bool,hAPP(U_2824,fun(U_2824,bool),ord_less(U_2824),U_2821),U_2823))
                | ~ hBOOL(hAPP(U_2824,bool,hAPP(U_2824,fun(U_2824,bool),ord_less(U_2824),U_2822),zero_zero(U_2824))) )
              & ( ~ hBOOL(hAPP(U_2824,bool,hAPP(U_2824,fun(U_2824,bool),ord_less(U_2824),U_2823),U_2821))
                | ~ hBOOL(hAPP(U_2824,bool,hAPP(U_2824,fun(U_2824,bool),ord_less(U_2824),zero_zero(U_2824)),U_2822)) ) ) )
          & ( ( hBOOL(hAPP(U_2824,bool,hAPP(U_2824,fun(U_2824,bool),ord_less(U_2824),U_2821),U_2823))
              & hBOOL(hAPP(U_2824,bool,hAPP(U_2824,fun(U_2824,bool),ord_less(U_2824),U_2822),zero_zero(U_2824))) )
            | ( hBOOL(hAPP(U_2824,bool,hAPP(U_2824,fun(U_2824,bool),ord_less(U_2824),U_2823),U_2821))
              & hBOOL(hAPP(U_2824,bool,hAPP(U_2824,fun(U_2824,bool),ord_less(U_2824),zero_zero(U_2824)),U_2822)) )
            | ~ hBOOL(hAPP(U_2824,bool,hAPP(U_2824,fun(U_2824,bool),ord_less(U_2824),hAPP(U_2824,U_2824,hAPP(U_2824,fun(U_2824,U_2824),times_times(U_2824),U_2823),U_2822)),hAPP(U_2824,U_2824,hAPP(U_2824,fun(U_2824,U_2824),times_times(U_2824),U_2821),U_2822))) ) )
      | ~ linord581940658strict(U_2824) ),
    inference(variable_rename,[status(thm)],[f_742_1]) ).

fof(f_742_3,plain,
    ! [U_2824] :
      ( ( ! [U_2830,U_2828,U_2826] :
            ( hBOOL(hAPP(U_2824,bool,hAPP(U_2824,fun(U_2824,bool),ord_less(U_2824),hAPP(U_2824,U_2824,hAPP(U_2824,fun(U_2824,U_2824),times_times(U_2824),U_2830),U_2828)),hAPP(U_2824,U_2824,hAPP(U_2824,fun(U_2824,U_2824),times_times(U_2824),U_2826),U_2828)))
            | ( ( ~ hBOOL(hAPP(U_2824,bool,hAPP(U_2824,fun(U_2824,bool),ord_less(U_2824),U_2826),U_2830))
                | ~ hBOOL(hAPP(U_2824,bool,hAPP(U_2824,fun(U_2824,bool),ord_less(U_2824),U_2828),zero_zero(U_2824))) )
              & ( ~ hBOOL(hAPP(U_2824,bool,hAPP(U_2824,fun(U_2824,bool),ord_less(U_2824),U_2830),U_2826))
                | ~ hBOOL(hAPP(U_2824,bool,hAPP(U_2824,fun(U_2824,bool),ord_less(U_2824),zero_zero(U_2824)),U_2828)) ) ) )
        & ! [U_2829,U_2827,U_2825] :
            ( ( hBOOL(hAPP(U_2824,bool,hAPP(U_2824,fun(U_2824,bool),ord_less(U_2824),U_2825),U_2829))
              & hBOOL(hAPP(U_2824,bool,hAPP(U_2824,fun(U_2824,bool),ord_less(U_2824),U_2827),zero_zero(U_2824))) )
            | ( hBOOL(hAPP(U_2824,bool,hAPP(U_2824,fun(U_2824,bool),ord_less(U_2824),U_2829),U_2825))
              & hBOOL(hAPP(U_2824,bool,hAPP(U_2824,fun(U_2824,bool),ord_less(U_2824),zero_zero(U_2824)),U_2827)) )
            | ~ hBOOL(hAPP(U_2824,bool,hAPP(U_2824,fun(U_2824,bool),ord_less(U_2824),hAPP(U_2824,U_2824,hAPP(U_2824,fun(U_2824,U_2824),times_times(U_2824),U_2829),U_2827)),hAPP(U_2824,U_2824,hAPP(U_2824,fun(U_2824,U_2824),times_times(U_2824),U_2825),U_2827))) ) )
      | ~ linord581940658strict(U_2824) ),
    inference(miniscope,[status(thm)],[f_742_2]) ).

fof(f_742_4,plain,
    ( ! [U_2824,U_2828,U_2826,U_2830] :
        ( ~ hBOOL(hAPP(U_2824,bool,hAPP(U_2824,fun(U_2824,bool),ord_less(U_2824),U_2826),U_2830))
        | ~ hBOOL(hAPP(U_2824,bool,hAPP(U_2824,fun(U_2824,bool),ord_less(U_2824),U_2828),zero_zero(U_2824)))
        | ~ sP198(U_2824,U_2828,U_2826,U_2830) )
    & ! [U_2824,U_2828,U_2826,U_2830] :
        ( ~ hBOOL(hAPP(U_2824,bool,hAPP(U_2824,fun(U_2824,bool),ord_less(U_2824),U_2830),U_2826))
        | ~ hBOOL(hAPP(U_2824,bool,hAPP(U_2824,fun(U_2824,bool),ord_less(U_2824),zero_zero(U_2824)),U_2828))
        | ~ sP198(U_2824,U_2828,U_2826,U_2830) )
    & ! [U_2825,U_2827,U_2824,U_2829] :
        ( hBOOL(hAPP(U_2824,bool,hAPP(U_2824,fun(U_2824,bool),ord_less(U_2824),U_2825),U_2829))
        | ~ sP197(U_2825,U_2827,U_2824,U_2829) )
    & ! [U_2825,U_2827,U_2824,U_2829] :
        ( hBOOL(hAPP(U_2824,bool,hAPP(U_2824,fun(U_2824,bool),ord_less(U_2824),U_2827),zero_zero(U_2824)))
        | ~ sP197(U_2825,U_2827,U_2824,U_2829) )
    & ! [U_2825,U_2827,U_2824,U_2829] :
        ( hBOOL(hAPP(U_2824,bool,hAPP(U_2824,fun(U_2824,bool),ord_less(U_2824),U_2829),U_2825))
        | ~ sP196(U_2825,U_2827,U_2824,U_2829) )
    & ! [U_2825,U_2827,U_2824,U_2829] :
        ( hBOOL(hAPP(U_2824,bool,hAPP(U_2824,fun(U_2824,bool),ord_less(U_2824),zero_zero(U_2824)),U_2827))
        | ~ sP196(U_2825,U_2827,U_2824,U_2829) )
    & ! [U_2825,U_2827,U_2824,U_2828,U_2829,U_2826,U_2830] :
        ( hBOOL(hAPP(U_2824,bool,hAPP(U_2824,fun(U_2824,bool),ord_less(U_2824),hAPP(U_2824,U_2824,hAPP(U_2824,fun(U_2824,U_2824),times_times(U_2824),U_2830),U_2828)),hAPP(U_2824,U_2824,hAPP(U_2824,fun(U_2824,U_2824),times_times(U_2824),U_2826),U_2828)))
        | sP198(U_2824,U_2828,U_2826,U_2830)
        | ~ sP199(U_2825,U_2827,U_2824,U_2828,U_2829,U_2826,U_2830) )
    & ! [U_2825,U_2827,U_2824,U_2828,U_2829,U_2826,U_2830] :
        ( sP197(U_2825,U_2827,U_2824,U_2829)
        | sP196(U_2825,U_2827,U_2824,U_2829)
        | ~ hBOOL(hAPP(U_2824,bool,hAPP(U_2824,fun(U_2824,bool),ord_less(U_2824),hAPP(U_2824,U_2824,hAPP(U_2824,fun(U_2824,U_2824),times_times(U_2824),U_2829),U_2827)),hAPP(U_2824,U_2824,hAPP(U_2824,fun(U_2824,U_2824),times_times(U_2824),U_2825),U_2827)))
        | ~ sP199(U_2825,U_2827,U_2824,U_2828,U_2829,U_2826,U_2830) )
    & ! [U_2825,U_2827,U_2824,U_2828,U_2829,U_2826,U_2830] :
        ( sP199(U_2825,U_2827,U_2824,U_2828,U_2829,U_2826,U_2830)
        | ~ linord581940658strict(U_2824) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP196,sP197,sP198,sP199])],[f_742_3]) ).

cnf(f_742_5,plain,
    ( sP199(U_2825,U_2827,U_2824,U_2828,U_2829,U_2826,U_2830)
    | ~ linord581940658strict(U_2824) ),
    inference(clausify,[status(thm)],[f_742_4]) ).

cnf(f_742_6,plain,
    ( sP197(U_2825,U_2827,U_2824,U_2829)
    | sP196(U_2825,U_2827,U_2824,U_2829)
    | ~ hBOOL(hAPP(U_2824,bool,hAPP(U_2824,fun(U_2824,bool),ord_less(U_2824),hAPP(U_2824,U_2824,hAPP(U_2824,fun(U_2824,U_2824),times_times(U_2824),U_2829),U_2827)),hAPP(U_2824,U_2824,hAPP(U_2824,fun(U_2824,U_2824),times_times(U_2824),U_2825),U_2827)))
    | ~ sP199(U_2825,U_2827,U_2824,U_2828,U_2829,U_2826,U_2830) ),
    inference(clausify,[status(thm)],[f_742_4]) ).

cnf(f_742_7,plain,
    ( hBOOL(hAPP(U_2824,bool,hAPP(U_2824,fun(U_2824,bool),ord_less(U_2824),hAPP(U_2824,U_2824,hAPP(U_2824,fun(U_2824,U_2824),times_times(U_2824),U_2830),U_2828)),hAPP(U_2824,U_2824,hAPP(U_2824,fun(U_2824,U_2824),times_times(U_2824),U_2826),U_2828)))
    | sP198(U_2824,U_2828,U_2826,U_2830)
    | ~ sP199(U_2825,U_2827,U_2824,U_2828,U_2829,U_2826,U_2830) ),
    inference(clausify,[status(thm)],[f_742_4]) ).

cnf(f_742_8,plain,
    ( hBOOL(hAPP(U_2824,bool,hAPP(U_2824,fun(U_2824,bool),ord_less(U_2824),zero_zero(U_2824)),U_2827))
    | ~ sP196(U_2825,U_2827,U_2824,U_2829) ),
    inference(clausify,[status(thm)],[f_742_4]) ).

cnf(f_742_9,plain,
    ( hBOOL(hAPP(U_2824,bool,hAPP(U_2824,fun(U_2824,bool),ord_less(U_2824),U_2829),U_2825))
    | ~ sP196(U_2825,U_2827,U_2824,U_2829) ),
    inference(clausify,[status(thm)],[f_742_4]) ).

cnf(f_742_10,plain,
    ( hBOOL(hAPP(U_2824,bool,hAPP(U_2824,fun(U_2824,bool),ord_less(U_2824),U_2827),zero_zero(U_2824)))
    | ~ sP197(U_2825,U_2827,U_2824,U_2829) ),
    inference(clausify,[status(thm)],[f_742_4]) ).

cnf(f_742_11,plain,
    ( hBOOL(hAPP(U_2824,bool,hAPP(U_2824,fun(U_2824,bool),ord_less(U_2824),U_2825),U_2829))
    | ~ sP197(U_2825,U_2827,U_2824,U_2829) ),
    inference(clausify,[status(thm)],[f_742_4]) ).

cnf(f_742_12,plain,
    ( ~ hBOOL(hAPP(U_2824,bool,hAPP(U_2824,fun(U_2824,bool),ord_less(U_2824),U_2830),U_2826))
    | ~ hBOOL(hAPP(U_2824,bool,hAPP(U_2824,fun(U_2824,bool),ord_less(U_2824),zero_zero(U_2824)),U_2828))
    | ~ sP198(U_2824,U_2828,U_2826,U_2830) ),
    inference(clausify,[status(thm)],[f_742_4]) ).

cnf(f_742_13,plain,
    ( ~ hBOOL(hAPP(U_2824,bool,hAPP(U_2824,fun(U_2824,bool),ord_less(U_2824),U_2826),U_2830))
    | ~ hBOOL(hAPP(U_2824,bool,hAPP(U_2824,fun(U_2824,bool),ord_less(U_2824),U_2828),zero_zero(U_2824)))
    | ~ sP198(U_2824,U_2828,U_2826,U_2830) ),
    inference(clausify,[status(thm)],[f_742_4]) ).

fof(f_743_1,plain,
    ! [X_b] :
      ( ! [C_1,A_2,B_3] :
          ( ( 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),times_times(X_b),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),B_3)))
            | ( ( ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),B_3),A_2))
                | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),zero_zero(X_b))) )
              & ( ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_3))
                | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),C_1)) ) ) )
          & ( ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),B_3),A_2))
              & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),zero_zero(X_b))) )
            | ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_3))
              & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),C_1)) )
            | ~ 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),times_times(X_b),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),B_3))) ) )
      | ~ linord581940658strict(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_672_mult__less__cancel__left__disj]) ).

fof(f_743_2,plain,
    ! [U_2834] :
      ( ! [U_2833,U_2832,U_2831] :
          ( ( hBOOL(hAPP(U_2834,bool,hAPP(U_2834,fun(U_2834,bool),ord_less(U_2834),hAPP(U_2834,U_2834,hAPP(U_2834,fun(U_2834,U_2834),times_times(U_2834),U_2833),U_2832)),hAPP(U_2834,U_2834,hAPP(U_2834,fun(U_2834,U_2834),times_times(U_2834),U_2833),U_2831)))
            | ( ( ~ hBOOL(hAPP(U_2834,bool,hAPP(U_2834,fun(U_2834,bool),ord_less(U_2834),U_2831),U_2832))
                | ~ hBOOL(hAPP(U_2834,bool,hAPP(U_2834,fun(U_2834,bool),ord_less(U_2834),U_2833),zero_zero(U_2834))) )
              & ( ~ hBOOL(hAPP(U_2834,bool,hAPP(U_2834,fun(U_2834,bool),ord_less(U_2834),U_2832),U_2831))
                | ~ hBOOL(hAPP(U_2834,bool,hAPP(U_2834,fun(U_2834,bool),ord_less(U_2834),zero_zero(U_2834)),U_2833)) ) ) )
          & ( ( hBOOL(hAPP(U_2834,bool,hAPP(U_2834,fun(U_2834,bool),ord_less(U_2834),U_2831),U_2832))
              & hBOOL(hAPP(U_2834,bool,hAPP(U_2834,fun(U_2834,bool),ord_less(U_2834),U_2833),zero_zero(U_2834))) )
            | ( hBOOL(hAPP(U_2834,bool,hAPP(U_2834,fun(U_2834,bool),ord_less(U_2834),U_2832),U_2831))
              & hBOOL(hAPP(U_2834,bool,hAPP(U_2834,fun(U_2834,bool),ord_less(U_2834),zero_zero(U_2834)),U_2833)) )
            | ~ hBOOL(hAPP(U_2834,bool,hAPP(U_2834,fun(U_2834,bool),ord_less(U_2834),hAPP(U_2834,U_2834,hAPP(U_2834,fun(U_2834,U_2834),times_times(U_2834),U_2833),U_2832)),hAPP(U_2834,U_2834,hAPP(U_2834,fun(U_2834,U_2834),times_times(U_2834),U_2833),U_2831))) ) )
      | ~ linord581940658strict(U_2834) ),
    inference(variable_rename,[status(thm)],[f_743_1]) ).

fof(f_743_3,plain,
    ! [U_2834] :
      ( ( ! [U_2840,U_2838,U_2836] :
            ( hBOOL(hAPP(U_2834,bool,hAPP(U_2834,fun(U_2834,bool),ord_less(U_2834),hAPP(U_2834,U_2834,hAPP(U_2834,fun(U_2834,U_2834),times_times(U_2834),U_2840),U_2838)),hAPP(U_2834,U_2834,hAPP(U_2834,fun(U_2834,U_2834),times_times(U_2834),U_2840),U_2836)))
            | ( ( ~ hBOOL(hAPP(U_2834,bool,hAPP(U_2834,fun(U_2834,bool),ord_less(U_2834),U_2836),U_2838))
                | ~ hBOOL(hAPP(U_2834,bool,hAPP(U_2834,fun(U_2834,bool),ord_less(U_2834),U_2840),zero_zero(U_2834))) )
              & ( ~ hBOOL(hAPP(U_2834,bool,hAPP(U_2834,fun(U_2834,bool),ord_less(U_2834),U_2838),U_2836))
                | ~ hBOOL(hAPP(U_2834,bool,hAPP(U_2834,fun(U_2834,bool),ord_less(U_2834),zero_zero(U_2834)),U_2840)) ) ) )
        & ! [U_2839,U_2837,U_2835] :
            ( ( hBOOL(hAPP(U_2834,bool,hAPP(U_2834,fun(U_2834,bool),ord_less(U_2834),U_2835),U_2837))
              & hBOOL(hAPP(U_2834,bool,hAPP(U_2834,fun(U_2834,bool),ord_less(U_2834),U_2839),zero_zero(U_2834))) )
            | ( hBOOL(hAPP(U_2834,bool,hAPP(U_2834,fun(U_2834,bool),ord_less(U_2834),U_2837),U_2835))
              & hBOOL(hAPP(U_2834,bool,hAPP(U_2834,fun(U_2834,bool),ord_less(U_2834),zero_zero(U_2834)),U_2839)) )
            | ~ hBOOL(hAPP(U_2834,bool,hAPP(U_2834,fun(U_2834,bool),ord_less(U_2834),hAPP(U_2834,U_2834,hAPP(U_2834,fun(U_2834,U_2834),times_times(U_2834),U_2839),U_2837)),hAPP(U_2834,U_2834,hAPP(U_2834,fun(U_2834,U_2834),times_times(U_2834),U_2839),U_2835))) ) )
      | ~ linord581940658strict(U_2834) ),
    inference(miniscope,[status(thm)],[f_743_2]) ).

fof(f_743_4,plain,
    ( ! [U_2834,U_2836,U_2840,U_2838] :
        ( ~ hBOOL(hAPP(U_2834,bool,hAPP(U_2834,fun(U_2834,bool),ord_less(U_2834),U_2836),U_2838))
        | ~ hBOOL(hAPP(U_2834,bool,hAPP(U_2834,fun(U_2834,bool),ord_less(U_2834),U_2840),zero_zero(U_2834)))
        | ~ sP202(U_2834,U_2836,U_2840,U_2838) )
    & ! [U_2834,U_2836,U_2840,U_2838] :
        ( ~ hBOOL(hAPP(U_2834,bool,hAPP(U_2834,fun(U_2834,bool),ord_less(U_2834),U_2838),U_2836))
        | ~ hBOOL(hAPP(U_2834,bool,hAPP(U_2834,fun(U_2834,bool),ord_less(U_2834),zero_zero(U_2834)),U_2840))
        | ~ sP202(U_2834,U_2836,U_2840,U_2838) )
    & ! [U_2835,U_2834,U_2839,U_2837] :
        ( hBOOL(hAPP(U_2834,bool,hAPP(U_2834,fun(U_2834,bool),ord_less(U_2834),U_2835),U_2837))
        | ~ sP201(U_2835,U_2834,U_2839,U_2837) )
    & ! [U_2835,U_2834,U_2839,U_2837] :
        ( hBOOL(hAPP(U_2834,bool,hAPP(U_2834,fun(U_2834,bool),ord_less(U_2834),U_2839),zero_zero(U_2834)))
        | ~ sP201(U_2835,U_2834,U_2839,U_2837) )
    & ! [U_2835,U_2834,U_2839,U_2837] :
        ( hBOOL(hAPP(U_2834,bool,hAPP(U_2834,fun(U_2834,bool),ord_less(U_2834),U_2837),U_2835))
        | ~ sP200(U_2835,U_2834,U_2839,U_2837) )
    & ! [U_2835,U_2834,U_2839,U_2837] :
        ( hBOOL(hAPP(U_2834,bool,hAPP(U_2834,fun(U_2834,bool),ord_less(U_2834),zero_zero(U_2834)),U_2839))
        | ~ sP200(U_2835,U_2834,U_2839,U_2837) )
    & ! [U_2835,U_2834,U_2839,U_2836,U_2840,U_2838,U_2837] :
        ( hBOOL(hAPP(U_2834,bool,hAPP(U_2834,fun(U_2834,bool),ord_less(U_2834),hAPP(U_2834,U_2834,hAPP(U_2834,fun(U_2834,U_2834),times_times(U_2834),U_2840),U_2838)),hAPP(U_2834,U_2834,hAPP(U_2834,fun(U_2834,U_2834),times_times(U_2834),U_2840),U_2836)))
        | sP202(U_2834,U_2836,U_2840,U_2838)
        | ~ sP203(U_2835,U_2834,U_2839,U_2836,U_2840,U_2838,U_2837) )
    & ! [U_2835,U_2834,U_2839,U_2836,U_2840,U_2838,U_2837] :
        ( sP201(U_2835,U_2834,U_2839,U_2837)
        | sP200(U_2835,U_2834,U_2839,U_2837)
        | ~ hBOOL(hAPP(U_2834,bool,hAPP(U_2834,fun(U_2834,bool),ord_less(U_2834),hAPP(U_2834,U_2834,hAPP(U_2834,fun(U_2834,U_2834),times_times(U_2834),U_2839),U_2837)),hAPP(U_2834,U_2834,hAPP(U_2834,fun(U_2834,U_2834),times_times(U_2834),U_2839),U_2835)))
        | ~ sP203(U_2835,U_2834,U_2839,U_2836,U_2840,U_2838,U_2837) )
    & ! [U_2835,U_2834,U_2839,U_2836,U_2840,U_2838,U_2837] :
        ( sP203(U_2835,U_2834,U_2839,U_2836,U_2840,U_2838,U_2837)
        | ~ linord581940658strict(U_2834) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP200,sP201,sP202,sP203])],[f_743_3]) ).

cnf(f_743_5,plain,
    ( sP203(U_2835,U_2834,U_2839,U_2836,U_2840,U_2838,U_2837)
    | ~ linord581940658strict(U_2834) ),
    inference(clausify,[status(thm)],[f_743_4]) ).

cnf(f_743_6,plain,
    ( sP201(U_2835,U_2834,U_2839,U_2837)
    | sP200(U_2835,U_2834,U_2839,U_2837)
    | ~ hBOOL(hAPP(U_2834,bool,hAPP(U_2834,fun(U_2834,bool),ord_less(U_2834),hAPP(U_2834,U_2834,hAPP(U_2834,fun(U_2834,U_2834),times_times(U_2834),U_2839),U_2837)),hAPP(U_2834,U_2834,hAPP(U_2834,fun(U_2834,U_2834),times_times(U_2834),U_2839),U_2835)))
    | ~ sP203(U_2835,U_2834,U_2839,U_2836,U_2840,U_2838,U_2837) ),
    inference(clausify,[status(thm)],[f_743_4]) ).

cnf(f_743_7,plain,
    ( hBOOL(hAPP(U_2834,bool,hAPP(U_2834,fun(U_2834,bool),ord_less(U_2834),hAPP(U_2834,U_2834,hAPP(U_2834,fun(U_2834,U_2834),times_times(U_2834),U_2840),U_2838)),hAPP(U_2834,U_2834,hAPP(U_2834,fun(U_2834,U_2834),times_times(U_2834),U_2840),U_2836)))
    | sP202(U_2834,U_2836,U_2840,U_2838)
    | ~ sP203(U_2835,U_2834,U_2839,U_2836,U_2840,U_2838,U_2837) ),
    inference(clausify,[status(thm)],[f_743_4]) ).

cnf(f_743_8,plain,
    ( hBOOL(hAPP(U_2834,bool,hAPP(U_2834,fun(U_2834,bool),ord_less(U_2834),zero_zero(U_2834)),U_2839))
    | ~ sP200(U_2835,U_2834,U_2839,U_2837) ),
    inference(clausify,[status(thm)],[f_743_4]) ).

cnf(f_743_9,plain,
    ( hBOOL(hAPP(U_2834,bool,hAPP(U_2834,fun(U_2834,bool),ord_less(U_2834),U_2837),U_2835))
    | ~ sP200(U_2835,U_2834,U_2839,U_2837) ),
    inference(clausify,[status(thm)],[f_743_4]) ).

cnf(f_743_10,plain,
    ( hBOOL(hAPP(U_2834,bool,hAPP(U_2834,fun(U_2834,bool),ord_less(U_2834),U_2839),zero_zero(U_2834)))
    | ~ sP201(U_2835,U_2834,U_2839,U_2837) ),
    inference(clausify,[status(thm)],[f_743_4]) ).

cnf(f_743_11,plain,
    ( hBOOL(hAPP(U_2834,bool,hAPP(U_2834,fun(U_2834,bool),ord_less(U_2834),U_2835),U_2837))
    | ~ sP201(U_2835,U_2834,U_2839,U_2837) ),
    inference(clausify,[status(thm)],[f_743_4]) ).

cnf(f_743_12,plain,
    ( ~ hBOOL(hAPP(U_2834,bool,hAPP(U_2834,fun(U_2834,bool),ord_less(U_2834),U_2838),U_2836))
    | ~ hBOOL(hAPP(U_2834,bool,hAPP(U_2834,fun(U_2834,bool),ord_less(U_2834),zero_zero(U_2834)),U_2840))
    | ~ sP202(U_2834,U_2836,U_2840,U_2838) ),
    inference(clausify,[status(thm)],[f_743_4]) ).

cnf(f_743_13,plain,
    ( ~ hBOOL(hAPP(U_2834,bool,hAPP(U_2834,fun(U_2834,bool),ord_less(U_2834),U_2836),U_2838))
    | ~ hBOOL(hAPP(U_2834,bool,hAPP(U_2834,fun(U_2834,bool),ord_less(U_2834),U_2840),zero_zero(U_2834)))
    | ~ sP202(U_2834,U_2836,U_2840,U_2838) ),
    inference(clausify,[status(thm)],[f_743_4]) ).

fof(f_744_1,plain,
    ! [X_b] :
      ( ! [A_2,B_3,C_1] :
          ( ( ( 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),times_times(X_b),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),B_3)))
              | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_3)) )
            & ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_3))
              | ~ 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),times_times(X_b),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),B_3))) ) )
          | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),C_1)) )
      | ~ linord581940658strict(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_673_mult__less__cancel__left__pos]) ).

fof(f_744_2,plain,
    ! [U_2844] :
      ( ! [U_2843,U_2842,U_2841] :
          ( ( ( hBOOL(hAPP(U_2844,bool,hAPP(U_2844,fun(U_2844,bool),ord_less(U_2844),hAPP(U_2844,U_2844,hAPP(U_2844,fun(U_2844,U_2844),times_times(U_2844),U_2841),U_2843)),hAPP(U_2844,U_2844,hAPP(U_2844,fun(U_2844,U_2844),times_times(U_2844),U_2841),U_2842)))
              | ~ hBOOL(hAPP(U_2844,bool,hAPP(U_2844,fun(U_2844,bool),ord_less(U_2844),U_2843),U_2842)) )
            & ( hBOOL(hAPP(U_2844,bool,hAPP(U_2844,fun(U_2844,bool),ord_less(U_2844),U_2843),U_2842))
              | ~ hBOOL(hAPP(U_2844,bool,hAPP(U_2844,fun(U_2844,bool),ord_less(U_2844),hAPP(U_2844,U_2844,hAPP(U_2844,fun(U_2844,U_2844),times_times(U_2844),U_2841),U_2843)),hAPP(U_2844,U_2844,hAPP(U_2844,fun(U_2844,U_2844),times_times(U_2844),U_2841),U_2842))) ) )
          | ~ hBOOL(hAPP(U_2844,bool,hAPP(U_2844,fun(U_2844,bool),ord_less(U_2844),zero_zero(U_2844)),U_2841)) )
      | ~ linord581940658strict(U_2844) ),
    inference(variable_rename,[status(thm)],[f_744_1]) ).

fof(f_744_3,plain,
    ( ! [U_2843,U_2842,U_2844,U_2841] :
        ( hBOOL(hAPP(U_2844,bool,hAPP(U_2844,fun(U_2844,bool),ord_less(U_2844),hAPP(U_2844,U_2844,hAPP(U_2844,fun(U_2844,U_2844),times_times(U_2844),U_2841),U_2843)),hAPP(U_2844,U_2844,hAPP(U_2844,fun(U_2844,U_2844),times_times(U_2844),U_2841),U_2842)))
        | ~ hBOOL(hAPP(U_2844,bool,hAPP(U_2844,fun(U_2844,bool),ord_less(U_2844),U_2843),U_2842))
        | ~ sP204(U_2843,U_2842,U_2844,U_2841) )
    & ! [U_2843,U_2842,U_2844,U_2841] :
        ( hBOOL(hAPP(U_2844,bool,hAPP(U_2844,fun(U_2844,bool),ord_less(U_2844),U_2843),U_2842))
        | ~ hBOOL(hAPP(U_2844,bool,hAPP(U_2844,fun(U_2844,bool),ord_less(U_2844),hAPP(U_2844,U_2844,hAPP(U_2844,fun(U_2844,U_2844),times_times(U_2844),U_2841),U_2843)),hAPP(U_2844,U_2844,hAPP(U_2844,fun(U_2844,U_2844),times_times(U_2844),U_2841),U_2842)))
        | ~ sP204(U_2843,U_2842,U_2844,U_2841) )
    & ! [U_2843,U_2842,U_2844,U_2841] :
        ( sP204(U_2843,U_2842,U_2844,U_2841)
        | ~ hBOOL(hAPP(U_2844,bool,hAPP(U_2844,fun(U_2844,bool),ord_less(U_2844),zero_zero(U_2844)),U_2841))
        | ~ linord581940658strict(U_2844) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP204])],[f_744_2]) ).

cnf(f_744_4,plain,
    ( sP204(U_2843,U_2842,U_2844,U_2841)
    | ~ hBOOL(hAPP(U_2844,bool,hAPP(U_2844,fun(U_2844,bool),ord_less(U_2844),zero_zero(U_2844)),U_2841))
    | ~ linord581940658strict(U_2844) ),
    inference(clausify,[status(thm)],[f_744_3]) ).

cnf(f_744_5,plain,
    ( hBOOL(hAPP(U_2844,bool,hAPP(U_2844,fun(U_2844,bool),ord_less(U_2844),U_2843),U_2842))
    | ~ hBOOL(hAPP(U_2844,bool,hAPP(U_2844,fun(U_2844,bool),ord_less(U_2844),hAPP(U_2844,U_2844,hAPP(U_2844,fun(U_2844,U_2844),times_times(U_2844),U_2841),U_2843)),hAPP(U_2844,U_2844,hAPP(U_2844,fun(U_2844,U_2844),times_times(U_2844),U_2841),U_2842)))
    | ~ sP204(U_2843,U_2842,U_2844,U_2841) ),
    inference(clausify,[status(thm)],[f_744_3]) ).

cnf(f_744_6,plain,
    ( hBOOL(hAPP(U_2844,bool,hAPP(U_2844,fun(U_2844,bool),ord_less(U_2844),hAPP(U_2844,U_2844,hAPP(U_2844,fun(U_2844,U_2844),times_times(U_2844),U_2841),U_2843)),hAPP(U_2844,U_2844,hAPP(U_2844,fun(U_2844,U_2844),times_times(U_2844),U_2841),U_2842)))
    | ~ hBOOL(hAPP(U_2844,bool,hAPP(U_2844,fun(U_2844,bool),ord_less(U_2844),U_2843),U_2842))
    | ~ sP204(U_2843,U_2842,U_2844,U_2841) ),
    inference(clausify,[status(thm)],[f_744_3]) ).

fof(f_745_1,plain,
    ! [X_a] :
      ( ! [B,A_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) )
      | ~ linord20386208strict(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_674_mult__pos__pos]) ).

fof(f_745_2,plain,
    ! [U_2847] :
      ( ! [U_2846,U_2845] :
          ( hBOOL(hAPP(U_2847,bool,hAPP(U_2847,fun(U_2847,bool),ord_less(U_2847),zero_zero(U_2847)),hAPP(U_2847,U_2847,hAPP(U_2847,fun(U_2847,U_2847),times_times(U_2847),U_2845),U_2846)))
          | ~ hBOOL(hAPP(U_2847,bool,hAPP(U_2847,fun(U_2847,bool),ord_less(U_2847),zero_zero(U_2847)),U_2846))
          | ~ hBOOL(hAPP(U_2847,bool,hAPP(U_2847,fun(U_2847,bool),ord_less(U_2847),zero_zero(U_2847)),U_2845)) )
      | ~ linord20386208strict(U_2847) ),
    inference(variable_rename,[status(thm)],[f_745_1]) ).

fof(f_745_3,plain,
    ! [U_2847,U_2845,U_2846] :
      ( hBOOL(hAPP(U_2847,bool,hAPP(U_2847,fun(U_2847,bool),ord_less(U_2847),zero_zero(U_2847)),hAPP(U_2847,U_2847,hAPP(U_2847,fun(U_2847,U_2847),times_times(U_2847),U_2845),U_2846)))
      | ~ hBOOL(hAPP(U_2847,bool,hAPP(U_2847,fun(U_2847,bool),ord_less(U_2847),zero_zero(U_2847)),U_2846))
      | ~ hBOOL(hAPP(U_2847,bool,hAPP(U_2847,fun(U_2847,bool),ord_less(U_2847),zero_zero(U_2847)),U_2845))
      | ~ linord20386208strict(U_2847) ),
    inference(definitional_conversion,[status(esa)],[f_745_2]) ).

cnf(f_745_4,plain,
    ( hBOOL(hAPP(U_2847,bool,hAPP(U_2847,fun(U_2847,bool),ord_less(U_2847),zero_zero(U_2847)),hAPP(U_2847,U_2847,hAPP(U_2847,fun(U_2847,U_2847),times_times(U_2847),U_2845),U_2846)))
    | ~ hBOOL(hAPP(U_2847,bool,hAPP(U_2847,fun(U_2847,bool),ord_less(U_2847),zero_zero(U_2847)),U_2846))
    | ~ hBOOL(hAPP(U_2847,bool,hAPP(U_2847,fun(U_2847,bool),ord_less(U_2847),zero_zero(U_2847)),U_2845))
    | ~ linord20386208strict(U_2847) ),
    inference(clausify,[status(thm)],[f_745_3]) ).

fof(f_746_1,plain,
    ! [X_a] :
      ( ! [B,A_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),times_times(X_a),A_1),B)),zero_zero(X_a)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) )
      | ~ linord20386208strict(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_675_mult__pos__neg]) ).

fof(f_746_2,plain,
    ! [U_2850] :
      ( ! [U_2849,U_2848] :
          ( hBOOL(hAPP(U_2850,bool,hAPP(U_2850,fun(U_2850,bool),ord_less(U_2850),hAPP(U_2850,U_2850,hAPP(U_2850,fun(U_2850,U_2850),times_times(U_2850),U_2848),U_2849)),zero_zero(U_2850)))
          | ~ hBOOL(hAPP(U_2850,bool,hAPP(U_2850,fun(U_2850,bool),ord_less(U_2850),U_2849),zero_zero(U_2850)))
          | ~ hBOOL(hAPP(U_2850,bool,hAPP(U_2850,fun(U_2850,bool),ord_less(U_2850),zero_zero(U_2850)),U_2848)) )
      | ~ linord20386208strict(U_2850) ),
    inference(variable_rename,[status(thm)],[f_746_1]) ).

fof(f_746_3,plain,
    ! [U_2848,U_2850,U_2849] :
      ( hBOOL(hAPP(U_2850,bool,hAPP(U_2850,fun(U_2850,bool),ord_less(U_2850),hAPP(U_2850,U_2850,hAPP(U_2850,fun(U_2850,U_2850),times_times(U_2850),U_2848),U_2849)),zero_zero(U_2850)))
      | ~ hBOOL(hAPP(U_2850,bool,hAPP(U_2850,fun(U_2850,bool),ord_less(U_2850),U_2849),zero_zero(U_2850)))
      | ~ hBOOL(hAPP(U_2850,bool,hAPP(U_2850,fun(U_2850,bool),ord_less(U_2850),zero_zero(U_2850)),U_2848))
      | ~ linord20386208strict(U_2850) ),
    inference(definitional_conversion,[status(esa)],[f_746_2]) ).

cnf(f_746_4,plain,
    ( hBOOL(hAPP(U_2850,bool,hAPP(U_2850,fun(U_2850,bool),ord_less(U_2850),hAPP(U_2850,U_2850,hAPP(U_2850,fun(U_2850,U_2850),times_times(U_2850),U_2848),U_2849)),zero_zero(U_2850)))
    | ~ hBOOL(hAPP(U_2850,bool,hAPP(U_2850,fun(U_2850,bool),ord_less(U_2850),U_2849),zero_zero(U_2850)))
    | ~ hBOOL(hAPP(U_2850,bool,hAPP(U_2850,fun(U_2850,bool),ord_less(U_2850),zero_zero(U_2850)),U_2848))
    | ~ linord20386208strict(U_2850) ),
    inference(clausify,[status(thm)],[f_746_3]) ).

fof(f_747_1,plain,
    ! [X_a] :
      ( ! [B,A_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),times_times(X_a),B),A_1)),zero_zero(X_a)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) )
      | ~ linord20386208strict(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_676_mult__pos__neg2]) ).

fof(f_747_2,plain,
    ! [U_2853] :
      ( ! [U_2852,U_2851] :
          ( hBOOL(hAPP(U_2853,bool,hAPP(U_2853,fun(U_2853,bool),ord_less(U_2853),hAPP(U_2853,U_2853,hAPP(U_2853,fun(U_2853,U_2853),times_times(U_2853),U_2852),U_2851)),zero_zero(U_2853)))
          | ~ hBOOL(hAPP(U_2853,bool,hAPP(U_2853,fun(U_2853,bool),ord_less(U_2853),U_2852),zero_zero(U_2853)))
          | ~ hBOOL(hAPP(U_2853,bool,hAPP(U_2853,fun(U_2853,bool),ord_less(U_2853),zero_zero(U_2853)),U_2851)) )
      | ~ linord20386208strict(U_2853) ),
    inference(variable_rename,[status(thm)],[f_747_1]) ).

fof(f_747_3,plain,
    ! [U_2853,U_2852,U_2851] :
      ( hBOOL(hAPP(U_2853,bool,hAPP(U_2853,fun(U_2853,bool),ord_less(U_2853),hAPP(U_2853,U_2853,hAPP(U_2853,fun(U_2853,U_2853),times_times(U_2853),U_2852),U_2851)),zero_zero(U_2853)))
      | ~ hBOOL(hAPP(U_2853,bool,hAPP(U_2853,fun(U_2853,bool),ord_less(U_2853),U_2852),zero_zero(U_2853)))
      | ~ hBOOL(hAPP(U_2853,bool,hAPP(U_2853,fun(U_2853,bool),ord_less(U_2853),zero_zero(U_2853)),U_2851))
      | ~ linord20386208strict(U_2853) ),
    inference(definitional_conversion,[status(esa)],[f_747_2]) ).

cnf(f_747_4,plain,
    ( hBOOL(hAPP(U_2853,bool,hAPP(U_2853,fun(U_2853,bool),ord_less(U_2853),hAPP(U_2853,U_2853,hAPP(U_2853,fun(U_2853,U_2853),times_times(U_2853),U_2852),U_2851)),zero_zero(U_2853)))
    | ~ hBOOL(hAPP(U_2853,bool,hAPP(U_2853,fun(U_2853,bool),ord_less(U_2853),U_2852),zero_zero(U_2853)))
    | ~ hBOOL(hAPP(U_2853,bool,hAPP(U_2853,fun(U_2853,bool),ord_less(U_2853),zero_zero(U_2853)),U_2851))
    | ~ linord20386208strict(U_2853) ),
    inference(clausify,[status(thm)],[f_747_3]) ).

fof(f_748_1,plain,
    ! [X_a] :
      ( ! [A_1,B] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B))
          | ~ 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),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))) )
      | ~ linord20386208strict(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_677_zero__less__mult__pos]) ).

fof(f_748_2,plain,
    ! [U_2856] :
      ( ! [U_2855,U_2854] :
          ( hBOOL(hAPP(U_2856,bool,hAPP(U_2856,fun(U_2856,bool),ord_less(U_2856),zero_zero(U_2856)),U_2854))
          | ~ hBOOL(hAPP(U_2856,bool,hAPP(U_2856,fun(U_2856,bool),ord_less(U_2856),zero_zero(U_2856)),U_2855))
          | ~ hBOOL(hAPP(U_2856,bool,hAPP(U_2856,fun(U_2856,bool),ord_less(U_2856),zero_zero(U_2856)),hAPP(U_2856,U_2856,hAPP(U_2856,fun(U_2856,U_2856),times_times(U_2856),U_2855),U_2854))) )
      | ~ linord20386208strict(U_2856) ),
    inference(variable_rename,[status(thm)],[f_748_1]) ).

fof(f_748_3,plain,
    ! [U_2856,U_2855,U_2854] :
      ( hBOOL(hAPP(U_2856,bool,hAPP(U_2856,fun(U_2856,bool),ord_less(U_2856),zero_zero(U_2856)),U_2854))
      | ~ hBOOL(hAPP(U_2856,bool,hAPP(U_2856,fun(U_2856,bool),ord_less(U_2856),zero_zero(U_2856)),U_2855))
      | ~ hBOOL(hAPP(U_2856,bool,hAPP(U_2856,fun(U_2856,bool),ord_less(U_2856),zero_zero(U_2856)),hAPP(U_2856,U_2856,hAPP(U_2856,fun(U_2856,U_2856),times_times(U_2856),U_2855),U_2854)))
      | ~ linord20386208strict(U_2856) ),
    inference(definitional_conversion,[status(esa)],[f_748_2]) ).

cnf(f_748_4,plain,
    ( hBOOL(hAPP(U_2856,bool,hAPP(U_2856,fun(U_2856,bool),ord_less(U_2856),zero_zero(U_2856)),U_2854))
    | ~ hBOOL(hAPP(U_2856,bool,hAPP(U_2856,fun(U_2856,bool),ord_less(U_2856),zero_zero(U_2856)),U_2855))
    | ~ hBOOL(hAPP(U_2856,bool,hAPP(U_2856,fun(U_2856,bool),ord_less(U_2856),zero_zero(U_2856)),hAPP(U_2856,U_2856,hAPP(U_2856,fun(U_2856,U_2856),times_times(U_2856),U_2855),U_2854)))
    | ~ linord20386208strict(U_2856) ),
    inference(clausify,[status(thm)],[f_748_3]) ).

fof(f_749_1,plain,
    ! [X_a] :
      ( ! [B,A_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B))
          | ~ 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),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),A_1))) )
      | ~ linord20386208strict(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_678_zero__less__mult__pos2]) ).

fof(f_749_2,plain,
    ! [U_2859] :
      ( ! [U_2858,U_2857] :
          ( hBOOL(hAPP(U_2859,bool,hAPP(U_2859,fun(U_2859,bool),ord_less(U_2859),zero_zero(U_2859)),U_2858))
          | ~ hBOOL(hAPP(U_2859,bool,hAPP(U_2859,fun(U_2859,bool),ord_less(U_2859),zero_zero(U_2859)),U_2857))
          | ~ hBOOL(hAPP(U_2859,bool,hAPP(U_2859,fun(U_2859,bool),ord_less(U_2859),zero_zero(U_2859)),hAPP(U_2859,U_2859,hAPP(U_2859,fun(U_2859,U_2859),times_times(U_2859),U_2858),U_2857))) )
      | ~ linord20386208strict(U_2859) ),
    inference(variable_rename,[status(thm)],[f_749_1]) ).

fof(f_749_3,plain,
    ! [U_2857,U_2858,U_2859] :
      ( hBOOL(hAPP(U_2859,bool,hAPP(U_2859,fun(U_2859,bool),ord_less(U_2859),zero_zero(U_2859)),U_2858))
      | ~ hBOOL(hAPP(U_2859,bool,hAPP(U_2859,fun(U_2859,bool),ord_less(U_2859),zero_zero(U_2859)),U_2857))
      | ~ hBOOL(hAPP(U_2859,bool,hAPP(U_2859,fun(U_2859,bool),ord_less(U_2859),zero_zero(U_2859)),hAPP(U_2859,U_2859,hAPP(U_2859,fun(U_2859,U_2859),times_times(U_2859),U_2858),U_2857)))
      | ~ linord20386208strict(U_2859) ),
    inference(definitional_conversion,[status(esa)],[f_749_2]) ).

cnf(f_749_4,plain,
    ( hBOOL(hAPP(U_2859,bool,hAPP(U_2859,fun(U_2859,bool),ord_less(U_2859),zero_zero(U_2859)),U_2858))
    | ~ hBOOL(hAPP(U_2859,bool,hAPP(U_2859,fun(U_2859,bool),ord_less(U_2859),zero_zero(U_2859)),U_2857))
    | ~ hBOOL(hAPP(U_2859,bool,hAPP(U_2859,fun(U_2859,bool),ord_less(U_2859),zero_zero(U_2859)),hAPP(U_2859,U_2859,hAPP(U_2859,fun(U_2859,U_2859),times_times(U_2859),U_2858),U_2857)))
    | ~ linord20386208strict(U_2859) ),
    inference(clausify,[status(thm)],[f_749_3]) ).

fof(f_750_1,plain,
    ! [X_b] :
      ( ! [A_2,B_3,C_1] :
          ( ( ( 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),times_times(X_b),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),B_3)))
              | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),B_3),A_2)) )
            & ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),B_3),A_2))
              | ~ 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),times_times(X_b),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),B_3))) ) )
          | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),zero_zero(X_b))) )
      | ~ linord581940658strict(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_679_mult__less__cancel__left__neg]) ).

fof(f_750_2,plain,
    ! [U_2863] :
      ( ! [U_2862,U_2861,U_2860] :
          ( ( ( hBOOL(hAPP(U_2863,bool,hAPP(U_2863,fun(U_2863,bool),ord_less(U_2863),hAPP(U_2863,U_2863,hAPP(U_2863,fun(U_2863,U_2863),times_times(U_2863),U_2860),U_2862)),hAPP(U_2863,U_2863,hAPP(U_2863,fun(U_2863,U_2863),times_times(U_2863),U_2860),U_2861)))
              | ~ hBOOL(hAPP(U_2863,bool,hAPP(U_2863,fun(U_2863,bool),ord_less(U_2863),U_2861),U_2862)) )
            & ( hBOOL(hAPP(U_2863,bool,hAPP(U_2863,fun(U_2863,bool),ord_less(U_2863),U_2861),U_2862))
              | ~ hBOOL(hAPP(U_2863,bool,hAPP(U_2863,fun(U_2863,bool),ord_less(U_2863),hAPP(U_2863,U_2863,hAPP(U_2863,fun(U_2863,U_2863),times_times(U_2863),U_2860),U_2862)),hAPP(U_2863,U_2863,hAPP(U_2863,fun(U_2863,U_2863),times_times(U_2863),U_2860),U_2861))) ) )
          | ~ hBOOL(hAPP(U_2863,bool,hAPP(U_2863,fun(U_2863,bool),ord_less(U_2863),U_2860),zero_zero(U_2863))) )
      | ~ linord581940658strict(U_2863) ),
    inference(variable_rename,[status(thm)],[f_750_1]) ).

fof(f_750_3,plain,
    ( ! [U_2863,U_2860,U_2861,U_2862] :
        ( hBOOL(hAPP(U_2863,bool,hAPP(U_2863,fun(U_2863,bool),ord_less(U_2863),hAPP(U_2863,U_2863,hAPP(U_2863,fun(U_2863,U_2863),times_times(U_2863),U_2860),U_2862)),hAPP(U_2863,U_2863,hAPP(U_2863,fun(U_2863,U_2863),times_times(U_2863),U_2860),U_2861)))
        | ~ hBOOL(hAPP(U_2863,bool,hAPP(U_2863,fun(U_2863,bool),ord_less(U_2863),U_2861),U_2862))
        | ~ sP205(U_2863,U_2860,U_2861,U_2862) )
    & ! [U_2863,U_2860,U_2861,U_2862] :
        ( hBOOL(hAPP(U_2863,bool,hAPP(U_2863,fun(U_2863,bool),ord_less(U_2863),U_2861),U_2862))
        | ~ hBOOL(hAPP(U_2863,bool,hAPP(U_2863,fun(U_2863,bool),ord_less(U_2863),hAPP(U_2863,U_2863,hAPP(U_2863,fun(U_2863,U_2863),times_times(U_2863),U_2860),U_2862)),hAPP(U_2863,U_2863,hAPP(U_2863,fun(U_2863,U_2863),times_times(U_2863),U_2860),U_2861)))
        | ~ sP205(U_2863,U_2860,U_2861,U_2862) )
    & ! [U_2863,U_2860,U_2861,U_2862] :
        ( sP205(U_2863,U_2860,U_2861,U_2862)
        | ~ hBOOL(hAPP(U_2863,bool,hAPP(U_2863,fun(U_2863,bool),ord_less(U_2863),U_2860),zero_zero(U_2863)))
        | ~ linord581940658strict(U_2863) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP205])],[f_750_2]) ).

cnf(f_750_4,plain,
    ( sP205(U_2863,U_2860,U_2861,U_2862)
    | ~ hBOOL(hAPP(U_2863,bool,hAPP(U_2863,fun(U_2863,bool),ord_less(U_2863),U_2860),zero_zero(U_2863)))
    | ~ linord581940658strict(U_2863) ),
    inference(clausify,[status(thm)],[f_750_3]) ).

cnf(f_750_5,plain,
    ( hBOOL(hAPP(U_2863,bool,hAPP(U_2863,fun(U_2863,bool),ord_less(U_2863),U_2861),U_2862))
    | ~ hBOOL(hAPP(U_2863,bool,hAPP(U_2863,fun(U_2863,bool),ord_less(U_2863),hAPP(U_2863,U_2863,hAPP(U_2863,fun(U_2863,U_2863),times_times(U_2863),U_2860),U_2862)),hAPP(U_2863,U_2863,hAPP(U_2863,fun(U_2863,U_2863),times_times(U_2863),U_2860),U_2861)))
    | ~ sP205(U_2863,U_2860,U_2861,U_2862) ),
    inference(clausify,[status(thm)],[f_750_3]) ).

cnf(f_750_6,plain,
    ( hBOOL(hAPP(U_2863,bool,hAPP(U_2863,fun(U_2863,bool),ord_less(U_2863),hAPP(U_2863,U_2863,hAPP(U_2863,fun(U_2863,U_2863),times_times(U_2863),U_2860),U_2862)),hAPP(U_2863,U_2863,hAPP(U_2863,fun(U_2863,U_2863),times_times(U_2863),U_2860),U_2861)))
    | ~ hBOOL(hAPP(U_2863,bool,hAPP(U_2863,fun(U_2863,bool),ord_less(U_2863),U_2861),U_2862))
    | ~ sP205(U_2863,U_2860,U_2861,U_2862) ),
    inference(clausify,[status(thm)],[f_750_3]) ).

fof(f_751_1,plain,
    ! [X_a] :
      ( ! [B,A_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),times_times(X_a),A_1),B)),zero_zero(X_a)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a))) )
      | ~ linord20386208strict(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_680_mult__neg__pos]) ).

fof(f_751_2,plain,
    ! [U_2866] :
      ( ! [U_2865,U_2864] :
          ( hBOOL(hAPP(U_2866,bool,hAPP(U_2866,fun(U_2866,bool),ord_less(U_2866),hAPP(U_2866,U_2866,hAPP(U_2866,fun(U_2866,U_2866),times_times(U_2866),U_2864),U_2865)),zero_zero(U_2866)))
          | ~ hBOOL(hAPP(U_2866,bool,hAPP(U_2866,fun(U_2866,bool),ord_less(U_2866),zero_zero(U_2866)),U_2865))
          | ~ hBOOL(hAPP(U_2866,bool,hAPP(U_2866,fun(U_2866,bool),ord_less(U_2866),U_2864),zero_zero(U_2866))) )
      | ~ linord20386208strict(U_2866) ),
    inference(variable_rename,[status(thm)],[f_751_1]) ).

fof(f_751_3,plain,
    ! [U_2866,U_2864,U_2865] :
      ( hBOOL(hAPP(U_2866,bool,hAPP(U_2866,fun(U_2866,bool),ord_less(U_2866),hAPP(U_2866,U_2866,hAPP(U_2866,fun(U_2866,U_2866),times_times(U_2866),U_2864),U_2865)),zero_zero(U_2866)))
      | ~ hBOOL(hAPP(U_2866,bool,hAPP(U_2866,fun(U_2866,bool),ord_less(U_2866),zero_zero(U_2866)),U_2865))
      | ~ hBOOL(hAPP(U_2866,bool,hAPP(U_2866,fun(U_2866,bool),ord_less(U_2866),U_2864),zero_zero(U_2866)))
      | ~ linord20386208strict(U_2866) ),
    inference(definitional_conversion,[status(esa)],[f_751_2]) ).

cnf(f_751_4,plain,
    ( hBOOL(hAPP(U_2866,bool,hAPP(U_2866,fun(U_2866,bool),ord_less(U_2866),hAPP(U_2866,U_2866,hAPP(U_2866,fun(U_2866,U_2866),times_times(U_2866),U_2864),U_2865)),zero_zero(U_2866)))
    | ~ hBOOL(hAPP(U_2866,bool,hAPP(U_2866,fun(U_2866,bool),ord_less(U_2866),zero_zero(U_2866)),U_2865))
    | ~ hBOOL(hAPP(U_2866,bool,hAPP(U_2866,fun(U_2866,bool),ord_less(U_2866),U_2864),zero_zero(U_2866)))
    | ~ linord20386208strict(U_2866) ),
    inference(clausify,[status(thm)],[f_751_3]) ).

fof(f_752_1,plain,
    ! [X_a] :
      ( ! [B,A_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a))) )
      | ~ linord581940658strict(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_681_mult__neg__neg]) ).

fof(f_752_2,plain,
    ! [U_2869] :
      ( ! [U_2868,U_2867] :
          ( hBOOL(hAPP(U_2869,bool,hAPP(U_2869,fun(U_2869,bool),ord_less(U_2869),zero_zero(U_2869)),hAPP(U_2869,U_2869,hAPP(U_2869,fun(U_2869,U_2869),times_times(U_2869),U_2867),U_2868)))
          | ~ hBOOL(hAPP(U_2869,bool,hAPP(U_2869,fun(U_2869,bool),ord_less(U_2869),U_2868),zero_zero(U_2869)))
          | ~ hBOOL(hAPP(U_2869,bool,hAPP(U_2869,fun(U_2869,bool),ord_less(U_2869),U_2867),zero_zero(U_2869))) )
      | ~ linord581940658strict(U_2869) ),
    inference(variable_rename,[status(thm)],[f_752_1]) ).

fof(f_752_3,plain,
    ! [U_2868,U_2867,U_2869] :
      ( hBOOL(hAPP(U_2869,bool,hAPP(U_2869,fun(U_2869,bool),ord_less(U_2869),zero_zero(U_2869)),hAPP(U_2869,U_2869,hAPP(U_2869,fun(U_2869,U_2869),times_times(U_2869),U_2867),U_2868)))
      | ~ hBOOL(hAPP(U_2869,bool,hAPP(U_2869,fun(U_2869,bool),ord_less(U_2869),U_2868),zero_zero(U_2869)))
      | ~ hBOOL(hAPP(U_2869,bool,hAPP(U_2869,fun(U_2869,bool),ord_less(U_2869),U_2867),zero_zero(U_2869)))
      | ~ linord581940658strict(U_2869) ),
    inference(definitional_conversion,[status(esa)],[f_752_2]) ).

cnf(f_752_4,plain,
    ( hBOOL(hAPP(U_2869,bool,hAPP(U_2869,fun(U_2869,bool),ord_less(U_2869),zero_zero(U_2869)),hAPP(U_2869,U_2869,hAPP(U_2869,fun(U_2869,U_2869),times_times(U_2869),U_2867),U_2868)))
    | ~ hBOOL(hAPP(U_2869,bool,hAPP(U_2869,fun(U_2869,bool),ord_less(U_2869),U_2868),zero_zero(U_2869)))
    | ~ hBOOL(hAPP(U_2869,bool,hAPP(U_2869,fun(U_2869,bool),ord_less(U_2869),U_2867),zero_zero(U_2869)))
    | ~ linord581940658strict(U_2869) ),
    inference(clausify,[status(thm)],[f_752_3]) ).

fof(f_753_1,plain,
    ! [X_a] :
      ( ! [C,A_1,B] :
          ( 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),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) )
      | ~ linord20386208strict(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_682_mult__strict__right__mono]) ).

fof(f_753_2,plain,
    ! [U_2873] :
      ( ! [U_2872,U_2871,U_2870] :
          ( hBOOL(hAPP(U_2873,bool,hAPP(U_2873,fun(U_2873,bool),ord_less(U_2873),hAPP(U_2873,U_2873,hAPP(U_2873,fun(U_2873,U_2873),times_times(U_2873),U_2871),U_2872)),hAPP(U_2873,U_2873,hAPP(U_2873,fun(U_2873,U_2873),times_times(U_2873),U_2870),U_2872)))
          | ~ hBOOL(hAPP(U_2873,bool,hAPP(U_2873,fun(U_2873,bool),ord_less(U_2873),zero_zero(U_2873)),U_2872))
          | ~ hBOOL(hAPP(U_2873,bool,hAPP(U_2873,fun(U_2873,bool),ord_less(U_2873),U_2871),U_2870)) )
      | ~ linord20386208strict(U_2873) ),
    inference(variable_rename,[status(thm)],[f_753_1]) ).

fof(f_753_3,plain,
    ! [U_2871,U_2873,U_2870,U_2872] :
      ( hBOOL(hAPP(U_2873,bool,hAPP(U_2873,fun(U_2873,bool),ord_less(U_2873),hAPP(U_2873,U_2873,hAPP(U_2873,fun(U_2873,U_2873),times_times(U_2873),U_2871),U_2872)),hAPP(U_2873,U_2873,hAPP(U_2873,fun(U_2873,U_2873),times_times(U_2873),U_2870),U_2872)))
      | ~ hBOOL(hAPP(U_2873,bool,hAPP(U_2873,fun(U_2873,bool),ord_less(U_2873),zero_zero(U_2873)),U_2872))
      | ~ hBOOL(hAPP(U_2873,bool,hAPP(U_2873,fun(U_2873,bool),ord_less(U_2873),U_2871),U_2870))
      | ~ linord20386208strict(U_2873) ),
    inference(definitional_conversion,[status(esa)],[f_753_2]) ).

cnf(f_753_4,plain,
    ( hBOOL(hAPP(U_2873,bool,hAPP(U_2873,fun(U_2873,bool),ord_less(U_2873),hAPP(U_2873,U_2873,hAPP(U_2873,fun(U_2873,U_2873),times_times(U_2873),U_2871),U_2872)),hAPP(U_2873,U_2873,hAPP(U_2873,fun(U_2873,U_2873),times_times(U_2873),U_2870),U_2872)))
    | ~ hBOOL(hAPP(U_2873,bool,hAPP(U_2873,fun(U_2873,bool),ord_less(U_2873),zero_zero(U_2873)),U_2872))
    | ~ hBOOL(hAPP(U_2873,bool,hAPP(U_2873,fun(U_2873,bool),ord_less(U_2873),U_2871),U_2870))
    | ~ linord20386208strict(U_2873) ),
    inference(clausify,[status(thm)],[f_753_3]) ).

fof(f_754_1,plain,
    ! [X_a] :
      ( ! [C,A_1,B] :
          ( 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),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) )
      | ~ linord20386208strict(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_683_mult__strict__left__mono]) ).

fof(f_754_2,plain,
    ! [U_2877] :
      ( ! [U_2876,U_2875,U_2874] :
          ( hBOOL(hAPP(U_2877,bool,hAPP(U_2877,fun(U_2877,bool),ord_less(U_2877),hAPP(U_2877,U_2877,hAPP(U_2877,fun(U_2877,U_2877),times_times(U_2877),U_2876),U_2875)),hAPP(U_2877,U_2877,hAPP(U_2877,fun(U_2877,U_2877),times_times(U_2877),U_2876),U_2874)))
          | ~ hBOOL(hAPP(U_2877,bool,hAPP(U_2877,fun(U_2877,bool),ord_less(U_2877),zero_zero(U_2877)),U_2876))
          | ~ hBOOL(hAPP(U_2877,bool,hAPP(U_2877,fun(U_2877,bool),ord_less(U_2877),U_2875),U_2874)) )
      | ~ linord20386208strict(U_2877) ),
    inference(variable_rename,[status(thm)],[f_754_1]) ).

fof(f_754_3,plain,
    ! [U_2876,U_2877,U_2874,U_2875] :
      ( hBOOL(hAPP(U_2877,bool,hAPP(U_2877,fun(U_2877,bool),ord_less(U_2877),hAPP(U_2877,U_2877,hAPP(U_2877,fun(U_2877,U_2877),times_times(U_2877),U_2876),U_2875)),hAPP(U_2877,U_2877,hAPP(U_2877,fun(U_2877,U_2877),times_times(U_2877),U_2876),U_2874)))
      | ~ hBOOL(hAPP(U_2877,bool,hAPP(U_2877,fun(U_2877,bool),ord_less(U_2877),zero_zero(U_2877)),U_2876))
      | ~ hBOOL(hAPP(U_2877,bool,hAPP(U_2877,fun(U_2877,bool),ord_less(U_2877),U_2875),U_2874))
      | ~ linord20386208strict(U_2877) ),
    inference(definitional_conversion,[status(esa)],[f_754_2]) ).

cnf(f_754_4,plain,
    ( hBOOL(hAPP(U_2877,bool,hAPP(U_2877,fun(U_2877,bool),ord_less(U_2877),hAPP(U_2877,U_2877,hAPP(U_2877,fun(U_2877,U_2877),times_times(U_2877),U_2876),U_2875)),hAPP(U_2877,U_2877,hAPP(U_2877,fun(U_2877,U_2877),times_times(U_2877),U_2876),U_2874)))
    | ~ hBOOL(hAPP(U_2877,bool,hAPP(U_2877,fun(U_2877,bool),ord_less(U_2877),zero_zero(U_2877)),U_2876))
    | ~ hBOOL(hAPP(U_2877,bool,hAPP(U_2877,fun(U_2877,bool),ord_less(U_2877),U_2875),U_2874))
    | ~ linord20386208strict(U_2877) ),
    inference(clausify,[status(thm)],[f_754_3]) ).

fof(f_755_1,plain,
    ! [X_a] :
      ( ! [C,A_1,B] :
          ( 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),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) )
      | ~ linord893533164strict(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_684_comm__mult__strict__left__mono]) ).

fof(f_755_2,plain,
    ! [U_2881] :
      ( ! [U_2880,U_2879,U_2878] :
          ( hBOOL(hAPP(U_2881,bool,hAPP(U_2881,fun(U_2881,bool),ord_less(U_2881),hAPP(U_2881,U_2881,hAPP(U_2881,fun(U_2881,U_2881),times_times(U_2881),U_2880),U_2879)),hAPP(U_2881,U_2881,hAPP(U_2881,fun(U_2881,U_2881),times_times(U_2881),U_2880),U_2878)))
          | ~ hBOOL(hAPP(U_2881,bool,hAPP(U_2881,fun(U_2881,bool),ord_less(U_2881),zero_zero(U_2881)),U_2880))
          | ~ hBOOL(hAPP(U_2881,bool,hAPP(U_2881,fun(U_2881,bool),ord_less(U_2881),U_2879),U_2878)) )
      | ~ linord893533164strict(U_2881) ),
    inference(variable_rename,[status(thm)],[f_755_1]) ).

fof(f_755_3,plain,
    ! [U_2879,U_2878,U_2881,U_2880] :
      ( hBOOL(hAPP(U_2881,bool,hAPP(U_2881,fun(U_2881,bool),ord_less(U_2881),hAPP(U_2881,U_2881,hAPP(U_2881,fun(U_2881,U_2881),times_times(U_2881),U_2880),U_2879)),hAPP(U_2881,U_2881,hAPP(U_2881,fun(U_2881,U_2881),times_times(U_2881),U_2880),U_2878)))
      | ~ hBOOL(hAPP(U_2881,bool,hAPP(U_2881,fun(U_2881,bool),ord_less(U_2881),zero_zero(U_2881)),U_2880))
      | ~ hBOOL(hAPP(U_2881,bool,hAPP(U_2881,fun(U_2881,bool),ord_less(U_2881),U_2879),U_2878))
      | ~ linord893533164strict(U_2881) ),
    inference(definitional_conversion,[status(esa)],[f_755_2]) ).

cnf(f_755_4,plain,
    ( hBOOL(hAPP(U_2881,bool,hAPP(U_2881,fun(U_2881,bool),ord_less(U_2881),hAPP(U_2881,U_2881,hAPP(U_2881,fun(U_2881,U_2881),times_times(U_2881),U_2880),U_2879)),hAPP(U_2881,U_2881,hAPP(U_2881,fun(U_2881,U_2881),times_times(U_2881),U_2880),U_2878)))
    | ~ hBOOL(hAPP(U_2881,bool,hAPP(U_2881,fun(U_2881,bool),ord_less(U_2881),zero_zero(U_2881)),U_2880))
    | ~ hBOOL(hAPP(U_2881,bool,hAPP(U_2881,fun(U_2881,bool),ord_less(U_2881),U_2879),U_2878))
    | ~ linord893533164strict(U_2881) ),
    inference(clausify,[status(thm)],[f_755_3]) ).

fof(f_756_1,plain,
    ! [X_a] :
      ( ! [C,B,A_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),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),zero_zero(X_a)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)) )
      | ~ linord581940658strict(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_685_mult__strict__right__mono__neg]) ).

fof(f_756_2,plain,
    ! [U_2885] :
      ( ! [U_2884,U_2883,U_2882] :
          ( hBOOL(hAPP(U_2885,bool,hAPP(U_2885,fun(U_2885,bool),ord_less(U_2885),hAPP(U_2885,U_2885,hAPP(U_2885,fun(U_2885,U_2885),times_times(U_2885),U_2882),U_2884)),hAPP(U_2885,U_2885,hAPP(U_2885,fun(U_2885,U_2885),times_times(U_2885),U_2883),U_2884)))
          | ~ hBOOL(hAPP(U_2885,bool,hAPP(U_2885,fun(U_2885,bool),ord_less(U_2885),U_2884),zero_zero(U_2885)))
          | ~ hBOOL(hAPP(U_2885,bool,hAPP(U_2885,fun(U_2885,bool),ord_less(U_2885),U_2883),U_2882)) )
      | ~ linord581940658strict(U_2885) ),
    inference(variable_rename,[status(thm)],[f_756_1]) ).

fof(f_756_3,plain,
    ! [U_2884,U_2883,U_2885,U_2882] :
      ( hBOOL(hAPP(U_2885,bool,hAPP(U_2885,fun(U_2885,bool),ord_less(U_2885),hAPP(U_2885,U_2885,hAPP(U_2885,fun(U_2885,U_2885),times_times(U_2885),U_2882),U_2884)),hAPP(U_2885,U_2885,hAPP(U_2885,fun(U_2885,U_2885),times_times(U_2885),U_2883),U_2884)))
      | ~ hBOOL(hAPP(U_2885,bool,hAPP(U_2885,fun(U_2885,bool),ord_less(U_2885),U_2884),zero_zero(U_2885)))
      | ~ hBOOL(hAPP(U_2885,bool,hAPP(U_2885,fun(U_2885,bool),ord_less(U_2885),U_2883),U_2882))
      | ~ linord581940658strict(U_2885) ),
    inference(definitional_conversion,[status(esa)],[f_756_2]) ).

cnf(f_756_4,plain,
    ( hBOOL(hAPP(U_2885,bool,hAPP(U_2885,fun(U_2885,bool),ord_less(U_2885),hAPP(U_2885,U_2885,hAPP(U_2885,fun(U_2885,U_2885),times_times(U_2885),U_2882),U_2884)),hAPP(U_2885,U_2885,hAPP(U_2885,fun(U_2885,U_2885),times_times(U_2885),U_2883),U_2884)))
    | ~ hBOOL(hAPP(U_2885,bool,hAPP(U_2885,fun(U_2885,bool),ord_less(U_2885),U_2884),zero_zero(U_2885)))
    | ~ hBOOL(hAPP(U_2885,bool,hAPP(U_2885,fun(U_2885,bool),ord_less(U_2885),U_2883),U_2882))
    | ~ linord581940658strict(U_2885) ),
    inference(clausify,[status(thm)],[f_756_3]) ).

fof(f_757_1,plain,
    ! [X_a] :
      ( ! [C,B,A_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),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),zero_zero(X_a)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)) )
      | ~ linord581940658strict(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_686_mult__strict__left__mono__neg]) ).

fof(f_757_2,plain,
    ! [U_2889] :
      ( ! [U_2888,U_2887,U_2886] :
          ( hBOOL(hAPP(U_2889,bool,hAPP(U_2889,fun(U_2889,bool),ord_less(U_2889),hAPP(U_2889,U_2889,hAPP(U_2889,fun(U_2889,U_2889),times_times(U_2889),U_2888),U_2886)),hAPP(U_2889,U_2889,hAPP(U_2889,fun(U_2889,U_2889),times_times(U_2889),U_2888),U_2887)))
          | ~ hBOOL(hAPP(U_2889,bool,hAPP(U_2889,fun(U_2889,bool),ord_less(U_2889),U_2888),zero_zero(U_2889)))
          | ~ hBOOL(hAPP(U_2889,bool,hAPP(U_2889,fun(U_2889,bool),ord_less(U_2889),U_2887),U_2886)) )
      | ~ linord581940658strict(U_2889) ),
    inference(variable_rename,[status(thm)],[f_757_1]) ).

fof(f_757_3,plain,
    ! [U_2888,U_2889,U_2887,U_2886] :
      ( hBOOL(hAPP(U_2889,bool,hAPP(U_2889,fun(U_2889,bool),ord_less(U_2889),hAPP(U_2889,U_2889,hAPP(U_2889,fun(U_2889,U_2889),times_times(U_2889),U_2888),U_2886)),hAPP(U_2889,U_2889,hAPP(U_2889,fun(U_2889,U_2889),times_times(U_2889),U_2888),U_2887)))
      | ~ hBOOL(hAPP(U_2889,bool,hAPP(U_2889,fun(U_2889,bool),ord_less(U_2889),U_2888),zero_zero(U_2889)))
      | ~ hBOOL(hAPP(U_2889,bool,hAPP(U_2889,fun(U_2889,bool),ord_less(U_2889),U_2887),U_2886))
      | ~ linord581940658strict(U_2889) ),
    inference(definitional_conversion,[status(esa)],[f_757_2]) ).

cnf(f_757_4,plain,
    ( hBOOL(hAPP(U_2889,bool,hAPP(U_2889,fun(U_2889,bool),ord_less(U_2889),hAPP(U_2889,U_2889,hAPP(U_2889,fun(U_2889,U_2889),times_times(U_2889),U_2888),U_2886)),hAPP(U_2889,U_2889,hAPP(U_2889,fun(U_2889,U_2889),times_times(U_2889),U_2888),U_2887)))
    | ~ hBOOL(hAPP(U_2889,bool,hAPP(U_2889,fun(U_2889,bool),ord_less(U_2889),U_2888),zero_zero(U_2889)))
    | ~ hBOOL(hAPP(U_2889,bool,hAPP(U_2889,fun(U_2889,bool),ord_less(U_2889),U_2887),U_2886))
    | ~ linord581940658strict(U_2889) ),
    inference(clausify,[status(thm)],[f_757_3]) ).

fof(f_758_1,plain,
    ! [X_a] :
      ( ! [C,D,A_1,B,R_3] :
          ( 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),times_times(X_a),R_3),C)) != hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),R_3),D))
          | ti(X_a,C) = ti(X_a,D)
          | ti(X_a,A_1) != ti(X_a,B)
          | ti(X_a,R_3) = zero_zero(X_a) )
      | ~ semiri456707255roduct(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_687_add__scale__eq__noteq]) ).

fof(f_758_2,plain,
    ! [U_2895] :
      ( ! [U_2894,U_2893,U_2892,U_2891,U_2890] :
          ( hAPP(U_2895,U_2895,hAPP(U_2895,fun(U_2895,U_2895),plus_plus(U_2895),U_2892),hAPP(U_2895,U_2895,hAPP(U_2895,fun(U_2895,U_2895),times_times(U_2895),U_2890),U_2894)) != hAPP(U_2895,U_2895,hAPP(U_2895,fun(U_2895,U_2895),plus_plus(U_2895),U_2891),hAPP(U_2895,U_2895,hAPP(U_2895,fun(U_2895,U_2895),times_times(U_2895),U_2890),U_2893))
          | ti(U_2895,U_2894) = ti(U_2895,U_2893)
          | ti(U_2895,U_2892) != ti(U_2895,U_2891)
          | ti(U_2895,U_2890) = zero_zero(U_2895) )
      | ~ semiri456707255roduct(U_2895) ),
    inference(variable_rename,[status(thm)],[f_758_1]) ).

fof(f_758_3,plain,
    ! [U_2890,U_2892,U_2891,U_2893,U_2894,U_2895] :
      ( hAPP(U_2895,U_2895,hAPP(U_2895,fun(U_2895,U_2895),plus_plus(U_2895),U_2892),hAPP(U_2895,U_2895,hAPP(U_2895,fun(U_2895,U_2895),times_times(U_2895),U_2890),U_2894)) != hAPP(U_2895,U_2895,hAPP(U_2895,fun(U_2895,U_2895),plus_plus(U_2895),U_2891),hAPP(U_2895,U_2895,hAPP(U_2895,fun(U_2895,U_2895),times_times(U_2895),U_2890),U_2893))
      | ti(U_2895,U_2894) = ti(U_2895,U_2893)
      | ti(U_2895,U_2892) != ti(U_2895,U_2891)
      | ti(U_2895,U_2890) = zero_zero(U_2895)
      | ~ semiri456707255roduct(U_2895) ),
    inference(definitional_conversion,[status(esa)],[f_758_2]) ).

cnf(f_758_4,plain,
    ( hAPP(U_2895,U_2895,hAPP(U_2895,fun(U_2895,U_2895),plus_plus(U_2895),U_2892),hAPP(U_2895,U_2895,hAPP(U_2895,fun(U_2895,U_2895),times_times(U_2895),U_2890),U_2894)) != hAPP(U_2895,U_2895,hAPP(U_2895,fun(U_2895,U_2895),plus_plus(U_2895),U_2891),hAPP(U_2895,U_2895,hAPP(U_2895,fun(U_2895,U_2895),times_times(U_2895),U_2890),U_2893))
    | ti(U_2895,U_2894) = ti(U_2895,U_2893)
    | ti(U_2895,U_2892) != ti(U_2895,U_2891)
    | ti(U_2895,U_2890) = zero_zero(U_2895)
    | ~ semiri456707255roduct(U_2895) ),
    inference(clausify,[status(thm)],[f_758_3]) ).

fof(f_759_1,plain,
    ! [X_b] :
      ( ! [X_1,Y_2] :
          ( ( hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),X_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Y_2),Y_2)) = zero_zero(X_b)
            | ti(X_b,Y_2) != zero_zero(X_b)
            | ti(X_b,X_1) != zero_zero(X_b) )
          & ( ( ti(X_b,Y_2) = 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),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),X_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Y_2),Y_2)) != zero_zero(X_b) ) )
      | ~ linord581940658strict(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_688_sum__squares__eq__zero__iff]) ).

fof(f_759_2,plain,
    ! [U_2898] :
      ( ! [U_2897,U_2896] :
          ( ( hAPP(U_2898,U_2898,hAPP(U_2898,fun(U_2898,U_2898),plus_plus(U_2898),hAPP(U_2898,U_2898,hAPP(U_2898,fun(U_2898,U_2898),times_times(U_2898),U_2897),U_2897)),hAPP(U_2898,U_2898,hAPP(U_2898,fun(U_2898,U_2898),times_times(U_2898),U_2896),U_2896)) = zero_zero(U_2898)
            | ti(U_2898,U_2896) != zero_zero(U_2898)
            | ti(U_2898,U_2897) != zero_zero(U_2898) )
          & ( ( ti(U_2898,U_2896) = zero_zero(U_2898)
              & ti(U_2898,U_2897) = zero_zero(U_2898) )
            | hAPP(U_2898,U_2898,hAPP(U_2898,fun(U_2898,U_2898),plus_plus(U_2898),hAPP(U_2898,U_2898,hAPP(U_2898,fun(U_2898,U_2898),times_times(U_2898),U_2897),U_2897)),hAPP(U_2898,U_2898,hAPP(U_2898,fun(U_2898,U_2898),times_times(U_2898),U_2896),U_2896)) != zero_zero(U_2898) ) )
      | ~ linord581940658strict(U_2898) ),
    inference(variable_rename,[status(thm)],[f_759_1]) ).

fof(f_759_3,plain,
    ! [U_2898] :
      ( ( ! [U_2902,U_2900] :
            ( hAPP(U_2898,U_2898,hAPP(U_2898,fun(U_2898,U_2898),plus_plus(U_2898),hAPP(U_2898,U_2898,hAPP(U_2898,fun(U_2898,U_2898),times_times(U_2898),U_2902),U_2902)),hAPP(U_2898,U_2898,hAPP(U_2898,fun(U_2898,U_2898),times_times(U_2898),U_2900),U_2900)) = zero_zero(U_2898)
            | ti(U_2898,U_2900) != zero_zero(U_2898)
            | ti(U_2898,U_2902) != zero_zero(U_2898) )
        & ! [U_2901,U_2899] :
            ( ( ti(U_2898,U_2899) = zero_zero(U_2898)
              & ti(U_2898,U_2901) = zero_zero(U_2898) )
            | hAPP(U_2898,U_2898,hAPP(U_2898,fun(U_2898,U_2898),plus_plus(U_2898),hAPP(U_2898,U_2898,hAPP(U_2898,fun(U_2898,U_2898),times_times(U_2898),U_2901),U_2901)),hAPP(U_2898,U_2898,hAPP(U_2898,fun(U_2898,U_2898),times_times(U_2898),U_2899),U_2899)) != zero_zero(U_2898) ) )
      | ~ linord581940658strict(U_2898) ),
    inference(miniscope,[status(thm)],[f_759_2]) ).

fof(f_759_4,plain,
    ( ! [U_2898,U_2901,U_2899] :
        ( ti(U_2898,U_2899) = zero_zero(U_2898)
        | ~ sP206(U_2898,U_2901,U_2899) )
    & ! [U_2898,U_2901,U_2899] :
        ( ti(U_2898,U_2901) = zero_zero(U_2898)
        | ~ sP206(U_2898,U_2901,U_2899) )
    & ! [U_2898,U_2901,U_2899,U_2900,U_2902] :
        ( hAPP(U_2898,U_2898,hAPP(U_2898,fun(U_2898,U_2898),plus_plus(U_2898),hAPP(U_2898,U_2898,hAPP(U_2898,fun(U_2898,U_2898),times_times(U_2898),U_2902),U_2902)),hAPP(U_2898,U_2898,hAPP(U_2898,fun(U_2898,U_2898),times_times(U_2898),U_2900),U_2900)) = zero_zero(U_2898)
        | ti(U_2898,U_2900) != zero_zero(U_2898)
        | ti(U_2898,U_2902) != zero_zero(U_2898)
        | ~ sP207(U_2898,U_2901,U_2899,U_2900,U_2902) )
    & ! [U_2898,U_2901,U_2899,U_2900,U_2902] :
        ( sP206(U_2898,U_2901,U_2899)
        | hAPP(U_2898,U_2898,hAPP(U_2898,fun(U_2898,U_2898),plus_plus(U_2898),hAPP(U_2898,U_2898,hAPP(U_2898,fun(U_2898,U_2898),times_times(U_2898),U_2901),U_2901)),hAPP(U_2898,U_2898,hAPP(U_2898,fun(U_2898,U_2898),times_times(U_2898),U_2899),U_2899)) != zero_zero(U_2898)
        | ~ sP207(U_2898,U_2901,U_2899,U_2900,U_2902) )
    & ! [U_2898,U_2901,U_2899,U_2900,U_2902] :
        ( sP207(U_2898,U_2901,U_2899,U_2900,U_2902)
        | ~ linord581940658strict(U_2898) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP206,sP207])],[f_759_3]) ).

cnf(f_759_5,plain,
    ( sP207(U_2898,U_2901,U_2899,U_2900,U_2902)
    | ~ linord581940658strict(U_2898) ),
    inference(clausify,[status(thm)],[f_759_4]) ).

cnf(f_759_6,plain,
    ( sP206(U_2898,U_2901,U_2899)
    | hAPP(U_2898,U_2898,hAPP(U_2898,fun(U_2898,U_2898),plus_plus(U_2898),hAPP(U_2898,U_2898,hAPP(U_2898,fun(U_2898,U_2898),times_times(U_2898),U_2901),U_2901)),hAPP(U_2898,U_2898,hAPP(U_2898,fun(U_2898,U_2898),times_times(U_2898),U_2899),U_2899)) != zero_zero(U_2898)
    | ~ sP207(U_2898,U_2901,U_2899,U_2900,U_2902) ),
    inference(clausify,[status(thm)],[f_759_4]) ).

cnf(f_759_7,plain,
    ( hAPP(U_2898,U_2898,hAPP(U_2898,fun(U_2898,U_2898),plus_plus(U_2898),hAPP(U_2898,U_2898,hAPP(U_2898,fun(U_2898,U_2898),times_times(U_2898),U_2902),U_2902)),hAPP(U_2898,U_2898,hAPP(U_2898,fun(U_2898,U_2898),times_times(U_2898),U_2900),U_2900)) = zero_zero(U_2898)
    | ti(U_2898,U_2900) != zero_zero(U_2898)
    | ti(U_2898,U_2902) != zero_zero(U_2898)
    | ~ sP207(U_2898,U_2901,U_2899,U_2900,U_2902) ),
    inference(clausify,[status(thm)],[f_759_4]) ).

cnf(f_759_8,plain,
    ( ti(U_2898,U_2901) = zero_zero(U_2898)
    | ~ sP206(U_2898,U_2901,U_2899) ),
    inference(clausify,[status(thm)],[f_759_4]) ).

cnf(f_759_9,plain,
    ( ti(U_2898,U_2899) = zero_zero(U_2898)
    | ~ sP206(U_2898,U_2901,U_2899) ),
    inference(clausify,[status(thm)],[f_759_4]) ).

fof(f_760_1,plain,
    ! [X_a] :
      ( ! [N,M_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),M_1),N)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),N))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),M_1)) )
      | ~ linordered_semidom(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_689_less__1__mult]) ).

fof(f_760_2,plain,
    ! [U_2905] :
      ( ! [U_2904,U_2903] :
          ( hBOOL(hAPP(U_2905,bool,hAPP(U_2905,fun(U_2905,bool),ord_less(U_2905),one_one(U_2905)),hAPP(U_2905,U_2905,hAPP(U_2905,fun(U_2905,U_2905),times_times(U_2905),U_2903),U_2904)))
          | ~ hBOOL(hAPP(U_2905,bool,hAPP(U_2905,fun(U_2905,bool),ord_less(U_2905),one_one(U_2905)),U_2904))
          | ~ hBOOL(hAPP(U_2905,bool,hAPP(U_2905,fun(U_2905,bool),ord_less(U_2905),one_one(U_2905)),U_2903)) )
      | ~ linordered_semidom(U_2905) ),
    inference(variable_rename,[status(thm)],[f_760_1]) ).

fof(f_760_3,plain,
    ! [U_2904,U_2903,U_2905] :
      ( hBOOL(hAPP(U_2905,bool,hAPP(U_2905,fun(U_2905,bool),ord_less(U_2905),one_one(U_2905)),hAPP(U_2905,U_2905,hAPP(U_2905,fun(U_2905,U_2905),times_times(U_2905),U_2903),U_2904)))
      | ~ hBOOL(hAPP(U_2905,bool,hAPP(U_2905,fun(U_2905,bool),ord_less(U_2905),one_one(U_2905)),U_2904))
      | ~ hBOOL(hAPP(U_2905,bool,hAPP(U_2905,fun(U_2905,bool),ord_less(U_2905),one_one(U_2905)),U_2903))
      | ~ linordered_semidom(U_2905) ),
    inference(definitional_conversion,[status(esa)],[f_760_2]) ).

cnf(f_760_4,plain,
    ( hBOOL(hAPP(U_2905,bool,hAPP(U_2905,fun(U_2905,bool),ord_less(U_2905),one_one(U_2905)),hAPP(U_2905,U_2905,hAPP(U_2905,fun(U_2905,U_2905),times_times(U_2905),U_2903),U_2904)))
    | ~ hBOOL(hAPP(U_2905,bool,hAPP(U_2905,fun(U_2905,bool),ord_less(U_2905),one_one(U_2905)),U_2904))
    | ~ hBOOL(hAPP(U_2905,bool,hAPP(U_2905,fun(U_2905,bool),ord_less(U_2905),one_one(U_2905)),U_2903))
    | ~ linordered_semidom(U_2905) ),
    inference(clausify,[status(thm)],[f_760_3]) ).

fof(f_761_1,plain,
    ! [X_b] :
      ( ! [A_2,E,C_1,B_3,D_1] :
          ( ( hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),C_1) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),E)),D_1)
            | ti(X_b,C_1) != hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),B_3),A_2)),E)),D_1) )
          & ( ti(X_b,C_1) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),B_3),A_2)),E)),D_1)
            | hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),C_1) != hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),E)),D_1) ) )
      | ~ ring(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_690_eq__add__iff2]) ).

fof(f_761_2,plain,
    ! [U_2911] :
      ( ! [U_2910,U_2909,U_2908,U_2907,U_2906] :
          ( ( hAPP(U_2911,U_2911,hAPP(U_2911,fun(U_2911,U_2911),plus_plus(U_2911),hAPP(U_2911,U_2911,hAPP(U_2911,fun(U_2911,U_2911),times_times(U_2911),U_2910),U_2909)),U_2908) = hAPP(U_2911,U_2911,hAPP(U_2911,fun(U_2911,U_2911),plus_plus(U_2911),hAPP(U_2911,U_2911,hAPP(U_2911,fun(U_2911,U_2911),times_times(U_2911),U_2907),U_2909)),U_2906)
            | ti(U_2911,U_2908) != hAPP(U_2911,U_2911,hAPP(U_2911,fun(U_2911,U_2911),plus_plus(U_2911),hAPP(U_2911,U_2911,hAPP(U_2911,fun(U_2911,U_2911),times_times(U_2911),hAPP(U_2911,U_2911,hAPP(U_2911,fun(U_2911,U_2911),minus_minus(U_2911),U_2907),U_2910)),U_2909)),U_2906) )
          & ( ti(U_2911,U_2908) = hAPP(U_2911,U_2911,hAPP(U_2911,fun(U_2911,U_2911),plus_plus(U_2911),hAPP(U_2911,U_2911,hAPP(U_2911,fun(U_2911,U_2911),times_times(U_2911),hAPP(U_2911,U_2911,hAPP(U_2911,fun(U_2911,U_2911),minus_minus(U_2911),U_2907),U_2910)),U_2909)),U_2906)
            | hAPP(U_2911,U_2911,hAPP(U_2911,fun(U_2911,U_2911),plus_plus(U_2911),hAPP(U_2911,U_2911,hAPP(U_2911,fun(U_2911,U_2911),times_times(U_2911),U_2910),U_2909)),U_2908) != hAPP(U_2911,U_2911,hAPP(U_2911,fun(U_2911,U_2911),plus_plus(U_2911),hAPP(U_2911,U_2911,hAPP(U_2911,fun(U_2911,U_2911),times_times(U_2911),U_2907),U_2909)),U_2906) ) )
      | ~ ring(U_2911) ),
    inference(variable_rename,[status(thm)],[f_761_1]) ).

fof(f_761_3,plain,
    ! [U_2911] :
      ( ( ! [U_2921,U_2919,U_2917,U_2915,U_2913] :
            ( hAPP(U_2911,U_2911,hAPP(U_2911,fun(U_2911,U_2911),plus_plus(U_2911),hAPP(U_2911,U_2911,hAPP(U_2911,fun(U_2911,U_2911),times_times(U_2911),U_2921),U_2919)),U_2917) = hAPP(U_2911,U_2911,hAPP(U_2911,fun(U_2911,U_2911),plus_plus(U_2911),hAPP(U_2911,U_2911,hAPP(U_2911,fun(U_2911,U_2911),times_times(U_2911),U_2915),U_2919)),U_2913)
            | ti(U_2911,U_2917) != hAPP(U_2911,U_2911,hAPP(U_2911,fun(U_2911,U_2911),plus_plus(U_2911),hAPP(U_2911,U_2911,hAPP(U_2911,fun(U_2911,U_2911),times_times(U_2911),hAPP(U_2911,U_2911,hAPP(U_2911,fun(U_2911,U_2911),minus_minus(U_2911),U_2915),U_2921)),U_2919)),U_2913) )
        & ! [U_2920,U_2918,U_2916,U_2914,U_2912] :
            ( ti(U_2911,U_2916) = hAPP(U_2911,U_2911,hAPP(U_2911,fun(U_2911,U_2911),plus_plus(U_2911),hAPP(U_2911,U_2911,hAPP(U_2911,fun(U_2911,U_2911),times_times(U_2911),hAPP(U_2911,U_2911,hAPP(U_2911,fun(U_2911,U_2911),minus_minus(U_2911),U_2914),U_2920)),U_2918)),U_2912)
            | hAPP(U_2911,U_2911,hAPP(U_2911,fun(U_2911,U_2911),plus_plus(U_2911),hAPP(U_2911,U_2911,hAPP(U_2911,fun(U_2911,U_2911),times_times(U_2911),U_2920),U_2918)),U_2916) != hAPP(U_2911,U_2911,hAPP(U_2911,fun(U_2911,U_2911),plus_plus(U_2911),hAPP(U_2911,U_2911,hAPP(U_2911,fun(U_2911,U_2911),times_times(U_2911),U_2914),U_2918)),U_2912) ) )
      | ~ ring(U_2911) ),
    inference(miniscope,[status(thm)],[f_761_2]) ).

fof(f_761_4,plain,
    ( ! [U_2911,U_2914,U_2917,U_2913,U_2912,U_2916,U_2920,U_2915,U_2918,U_2919,U_2921] :
        ( hAPP(U_2911,U_2911,hAPP(U_2911,fun(U_2911,U_2911),plus_plus(U_2911),hAPP(U_2911,U_2911,hAPP(U_2911,fun(U_2911,U_2911),times_times(U_2911),U_2921),U_2919)),U_2917) = hAPP(U_2911,U_2911,hAPP(U_2911,fun(U_2911,U_2911),plus_plus(U_2911),hAPP(U_2911,U_2911,hAPP(U_2911,fun(U_2911,U_2911),times_times(U_2911),U_2915),U_2919)),U_2913)
        | ti(U_2911,U_2917) != hAPP(U_2911,U_2911,hAPP(U_2911,fun(U_2911,U_2911),plus_plus(U_2911),hAPP(U_2911,U_2911,hAPP(U_2911,fun(U_2911,U_2911),times_times(U_2911),hAPP(U_2911,U_2911,hAPP(U_2911,fun(U_2911,U_2911),minus_minus(U_2911),U_2915),U_2921)),U_2919)),U_2913)
        | ~ sP208(U_2911,U_2914,U_2917,U_2913,U_2912,U_2916,U_2920,U_2915,U_2918,U_2919,U_2921) )
    & ! [U_2911,U_2914,U_2917,U_2913,U_2912,U_2916,U_2920,U_2915,U_2918,U_2919,U_2921] :
        ( ti(U_2911,U_2916) = hAPP(U_2911,U_2911,hAPP(U_2911,fun(U_2911,U_2911),plus_plus(U_2911),hAPP(U_2911,U_2911,hAPP(U_2911,fun(U_2911,U_2911),times_times(U_2911),hAPP(U_2911,U_2911,hAPP(U_2911,fun(U_2911,U_2911),minus_minus(U_2911),U_2914),U_2920)),U_2918)),U_2912)
        | hAPP(U_2911,U_2911,hAPP(U_2911,fun(U_2911,U_2911),plus_plus(U_2911),hAPP(U_2911,U_2911,hAPP(U_2911,fun(U_2911,U_2911),times_times(U_2911),U_2920),U_2918)),U_2916) != hAPP(U_2911,U_2911,hAPP(U_2911,fun(U_2911,U_2911),plus_plus(U_2911),hAPP(U_2911,U_2911,hAPP(U_2911,fun(U_2911,U_2911),times_times(U_2911),U_2914),U_2918)),U_2912)
        | ~ sP208(U_2911,U_2914,U_2917,U_2913,U_2912,U_2916,U_2920,U_2915,U_2918,U_2919,U_2921) )
    & ! [U_2911,U_2914,U_2917,U_2913,U_2912,U_2916,U_2920,U_2915,U_2918,U_2919,U_2921] :
        ( sP208(U_2911,U_2914,U_2917,U_2913,U_2912,U_2916,U_2920,U_2915,U_2918,U_2919,U_2921)
        | ~ ring(U_2911) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP208])],[f_761_3]) ).

cnf(f_761_5,plain,
    ( sP208(U_2911,U_2914,U_2917,U_2913,U_2912,U_2916,U_2920,U_2915,U_2918,U_2919,U_2921)
    | ~ ring(U_2911) ),
    inference(clausify,[status(thm)],[f_761_4]) ).

cnf(f_761_6,plain,
    ( ti(U_2911,U_2916) = hAPP(U_2911,U_2911,hAPP(U_2911,fun(U_2911,U_2911),plus_plus(U_2911),hAPP(U_2911,U_2911,hAPP(U_2911,fun(U_2911,U_2911),times_times(U_2911),hAPP(U_2911,U_2911,hAPP(U_2911,fun(U_2911,U_2911),minus_minus(U_2911),U_2914),U_2920)),U_2918)),U_2912)
    | hAPP(U_2911,U_2911,hAPP(U_2911,fun(U_2911,U_2911),plus_plus(U_2911),hAPP(U_2911,U_2911,hAPP(U_2911,fun(U_2911,U_2911),times_times(U_2911),U_2920),U_2918)),U_2916) != hAPP(U_2911,U_2911,hAPP(U_2911,fun(U_2911,U_2911),plus_plus(U_2911),hAPP(U_2911,U_2911,hAPP(U_2911,fun(U_2911,U_2911),times_times(U_2911),U_2914),U_2918)),U_2912)
    | ~ sP208(U_2911,U_2914,U_2917,U_2913,U_2912,U_2916,U_2920,U_2915,U_2918,U_2919,U_2921) ),
    inference(clausify,[status(thm)],[f_761_4]) ).

cnf(f_761_7,plain,
    ( hAPP(U_2911,U_2911,hAPP(U_2911,fun(U_2911,U_2911),plus_plus(U_2911),hAPP(U_2911,U_2911,hAPP(U_2911,fun(U_2911,U_2911),times_times(U_2911),U_2921),U_2919)),U_2917) = hAPP(U_2911,U_2911,hAPP(U_2911,fun(U_2911,U_2911),plus_plus(U_2911),hAPP(U_2911,U_2911,hAPP(U_2911,fun(U_2911,U_2911),times_times(U_2911),U_2915),U_2919)),U_2913)
    | ti(U_2911,U_2917) != hAPP(U_2911,U_2911,hAPP(U_2911,fun(U_2911,U_2911),plus_plus(U_2911),hAPP(U_2911,U_2911,hAPP(U_2911,fun(U_2911,U_2911),times_times(U_2911),hAPP(U_2911,U_2911,hAPP(U_2911,fun(U_2911,U_2911),minus_minus(U_2911),U_2915),U_2921)),U_2919)),U_2913)
    | ~ sP208(U_2911,U_2914,U_2917,U_2913,U_2912,U_2916,U_2920,U_2915,U_2918,U_2919,U_2921) ),
    inference(clausify,[status(thm)],[f_761_4]) ).

fof(f_762_1,plain,
    ! [X_b] :
      ( ! [A_2,E,C_1,B_3,D_1] :
          ( ( hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),C_1) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),E)),D_1)
            | hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3)),E)),C_1) != ti(X_b,D_1) )
          & ( hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3)),E)),C_1) = ti(X_b,D_1)
            | hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),C_1) != hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),E)),D_1) ) )
      | ~ ring(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_691_eq__add__iff1]) ).

fof(f_762_2,plain,
    ! [U_2927] :
      ( ! [U_2926,U_2925,U_2924,U_2923,U_2922] :
          ( ( hAPP(U_2927,U_2927,hAPP(U_2927,fun(U_2927,U_2927),plus_plus(U_2927),hAPP(U_2927,U_2927,hAPP(U_2927,fun(U_2927,U_2927),times_times(U_2927),U_2926),U_2925)),U_2924) = hAPP(U_2927,U_2927,hAPP(U_2927,fun(U_2927,U_2927),plus_plus(U_2927),hAPP(U_2927,U_2927,hAPP(U_2927,fun(U_2927,U_2927),times_times(U_2927),U_2923),U_2925)),U_2922)
            | hAPP(U_2927,U_2927,hAPP(U_2927,fun(U_2927,U_2927),plus_plus(U_2927),hAPP(U_2927,U_2927,hAPP(U_2927,fun(U_2927,U_2927),times_times(U_2927),hAPP(U_2927,U_2927,hAPP(U_2927,fun(U_2927,U_2927),minus_minus(U_2927),U_2926),U_2923)),U_2925)),U_2924) != ti(U_2927,U_2922) )
          & ( hAPP(U_2927,U_2927,hAPP(U_2927,fun(U_2927,U_2927),plus_plus(U_2927),hAPP(U_2927,U_2927,hAPP(U_2927,fun(U_2927,U_2927),times_times(U_2927),hAPP(U_2927,U_2927,hAPP(U_2927,fun(U_2927,U_2927),minus_minus(U_2927),U_2926),U_2923)),U_2925)),U_2924) = ti(U_2927,U_2922)
            | hAPP(U_2927,U_2927,hAPP(U_2927,fun(U_2927,U_2927),plus_plus(U_2927),hAPP(U_2927,U_2927,hAPP(U_2927,fun(U_2927,U_2927),times_times(U_2927),U_2926),U_2925)),U_2924) != hAPP(U_2927,U_2927,hAPP(U_2927,fun(U_2927,U_2927),plus_plus(U_2927),hAPP(U_2927,U_2927,hAPP(U_2927,fun(U_2927,U_2927),times_times(U_2927),U_2923),U_2925)),U_2922) ) )
      | ~ ring(U_2927) ),
    inference(variable_rename,[status(thm)],[f_762_1]) ).

fof(f_762_3,plain,
    ! [U_2927] :
      ( ( ! [U_2937,U_2935,U_2933,U_2931,U_2929] :
            ( hAPP(U_2927,U_2927,hAPP(U_2927,fun(U_2927,U_2927),plus_plus(U_2927),hAPP(U_2927,U_2927,hAPP(U_2927,fun(U_2927,U_2927),times_times(U_2927),U_2937),U_2935)),U_2933) = hAPP(U_2927,U_2927,hAPP(U_2927,fun(U_2927,U_2927),plus_plus(U_2927),hAPP(U_2927,U_2927,hAPP(U_2927,fun(U_2927,U_2927),times_times(U_2927),U_2931),U_2935)),U_2929)
            | hAPP(U_2927,U_2927,hAPP(U_2927,fun(U_2927,U_2927),plus_plus(U_2927),hAPP(U_2927,U_2927,hAPP(U_2927,fun(U_2927,U_2927),times_times(U_2927),hAPP(U_2927,U_2927,hAPP(U_2927,fun(U_2927,U_2927),minus_minus(U_2927),U_2937),U_2931)),U_2935)),U_2933) != ti(U_2927,U_2929) )
        & ! [U_2936,U_2934,U_2932,U_2930,U_2928] :
            ( hAPP(U_2927,U_2927,hAPP(U_2927,fun(U_2927,U_2927),plus_plus(U_2927),hAPP(U_2927,U_2927,hAPP(U_2927,fun(U_2927,U_2927),times_times(U_2927),hAPP(U_2927,U_2927,hAPP(U_2927,fun(U_2927,U_2927),minus_minus(U_2927),U_2936),U_2930)),U_2934)),U_2932) = ti(U_2927,U_2928)
            | hAPP(U_2927,U_2927,hAPP(U_2927,fun(U_2927,U_2927),plus_plus(U_2927),hAPP(U_2927,U_2927,hAPP(U_2927,fun(U_2927,U_2927),times_times(U_2927),U_2936),U_2934)),U_2932) != hAPP(U_2927,U_2927,hAPP(U_2927,fun(U_2927,U_2927),plus_plus(U_2927),hAPP(U_2927,U_2927,hAPP(U_2927,fun(U_2927,U_2927),times_times(U_2927),U_2930),U_2934)),U_2928) ) )
      | ~ ring(U_2927) ),
    inference(miniscope,[status(thm)],[f_762_2]) ).

fof(f_762_4,plain,
    ( ! [U_2927,U_2930,U_2929,U_2928,U_2932,U_2933,U_2936,U_2931,U_2934,U_2935,U_2937] :
        ( hAPP(U_2927,U_2927,hAPP(U_2927,fun(U_2927,U_2927),plus_plus(U_2927),hAPP(U_2927,U_2927,hAPP(U_2927,fun(U_2927,U_2927),times_times(U_2927),U_2937),U_2935)),U_2933) = hAPP(U_2927,U_2927,hAPP(U_2927,fun(U_2927,U_2927),plus_plus(U_2927),hAPP(U_2927,U_2927,hAPP(U_2927,fun(U_2927,U_2927),times_times(U_2927),U_2931),U_2935)),U_2929)
        | hAPP(U_2927,U_2927,hAPP(U_2927,fun(U_2927,U_2927),plus_plus(U_2927),hAPP(U_2927,U_2927,hAPP(U_2927,fun(U_2927,U_2927),times_times(U_2927),hAPP(U_2927,U_2927,hAPP(U_2927,fun(U_2927,U_2927),minus_minus(U_2927),U_2937),U_2931)),U_2935)),U_2933) != ti(U_2927,U_2929)
        | ~ sP209(U_2927,U_2930,U_2929,U_2928,U_2932,U_2933,U_2936,U_2931,U_2934,U_2935,U_2937) )
    & ! [U_2927,U_2930,U_2929,U_2928,U_2932,U_2933,U_2936,U_2931,U_2934,U_2935,U_2937] :
        ( hAPP(U_2927,U_2927,hAPP(U_2927,fun(U_2927,U_2927),plus_plus(U_2927),hAPP(U_2927,U_2927,hAPP(U_2927,fun(U_2927,U_2927),times_times(U_2927),hAPP(U_2927,U_2927,hAPP(U_2927,fun(U_2927,U_2927),minus_minus(U_2927),U_2936),U_2930)),U_2934)),U_2932) = ti(U_2927,U_2928)
        | hAPP(U_2927,U_2927,hAPP(U_2927,fun(U_2927,U_2927),plus_plus(U_2927),hAPP(U_2927,U_2927,hAPP(U_2927,fun(U_2927,U_2927),times_times(U_2927),U_2936),U_2934)),U_2932) != hAPP(U_2927,U_2927,hAPP(U_2927,fun(U_2927,U_2927),plus_plus(U_2927),hAPP(U_2927,U_2927,hAPP(U_2927,fun(U_2927,U_2927),times_times(U_2927),U_2930),U_2934)),U_2928)
        | ~ sP209(U_2927,U_2930,U_2929,U_2928,U_2932,U_2933,U_2936,U_2931,U_2934,U_2935,U_2937) )
    & ! [U_2927,U_2930,U_2929,U_2928,U_2932,U_2933,U_2936,U_2931,U_2934,U_2935,U_2937] :
        ( sP209(U_2927,U_2930,U_2929,U_2928,U_2932,U_2933,U_2936,U_2931,U_2934,U_2935,U_2937)
        | ~ ring(U_2927) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP209])],[f_762_3]) ).

cnf(f_762_5,plain,
    ( sP209(U_2927,U_2930,U_2929,U_2928,U_2932,U_2933,U_2936,U_2931,U_2934,U_2935,U_2937)
    | ~ ring(U_2927) ),
    inference(clausify,[status(thm)],[f_762_4]) ).

cnf(f_762_6,plain,
    ( hAPP(U_2927,U_2927,hAPP(U_2927,fun(U_2927,U_2927),plus_plus(U_2927),hAPP(U_2927,U_2927,hAPP(U_2927,fun(U_2927,U_2927),times_times(U_2927),hAPP(U_2927,U_2927,hAPP(U_2927,fun(U_2927,U_2927),minus_minus(U_2927),U_2936),U_2930)),U_2934)),U_2932) = ti(U_2927,U_2928)
    | hAPP(U_2927,U_2927,hAPP(U_2927,fun(U_2927,U_2927),plus_plus(U_2927),hAPP(U_2927,U_2927,hAPP(U_2927,fun(U_2927,U_2927),times_times(U_2927),U_2936),U_2934)),U_2932) != hAPP(U_2927,U_2927,hAPP(U_2927,fun(U_2927,U_2927),plus_plus(U_2927),hAPP(U_2927,U_2927,hAPP(U_2927,fun(U_2927,U_2927),times_times(U_2927),U_2930),U_2934)),U_2928)
    | ~ sP209(U_2927,U_2930,U_2929,U_2928,U_2932,U_2933,U_2936,U_2931,U_2934,U_2935,U_2937) ),
    inference(clausify,[status(thm)],[f_762_4]) ).

cnf(f_762_7,plain,
    ( hAPP(U_2927,U_2927,hAPP(U_2927,fun(U_2927,U_2927),plus_plus(U_2927),hAPP(U_2927,U_2927,hAPP(U_2927,fun(U_2927,U_2927),times_times(U_2927),U_2937),U_2935)),U_2933) = hAPP(U_2927,U_2927,hAPP(U_2927,fun(U_2927,U_2927),plus_plus(U_2927),hAPP(U_2927,U_2927,hAPP(U_2927,fun(U_2927,U_2927),times_times(U_2927),U_2931),U_2935)),U_2929)
    | hAPP(U_2927,U_2927,hAPP(U_2927,fun(U_2927,U_2927),plus_plus(U_2927),hAPP(U_2927,U_2927,hAPP(U_2927,fun(U_2927,U_2927),times_times(U_2927),hAPP(U_2927,U_2927,hAPP(U_2927,fun(U_2927,U_2927),minus_minus(U_2927),U_2937),U_2931)),U_2935)),U_2933) != ti(U_2927,U_2929)
    | ~ sP209(U_2927,U_2930,U_2929,U_2928,U_2932,U_2933,U_2936,U_2931,U_2934,U_2935,U_2937) ),
    inference(clausify,[status(thm)],[f_762_4]) ).

fof(f_763_1,plain,
    ! [X_a] :
      ( ! [A_1,M_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),times_times(X_a),A_1),M_1)),M_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),one_one(X_a))),M_1)
      | ~ comm_semiring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_692_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J]) ).

fof(f_763_2,plain,
    ! [U_2940] :
      ( ! [U_2939,U_2938] : hAPP(U_2940,U_2940,hAPP(U_2940,fun(U_2940,U_2940),plus_plus(U_2940),hAPP(U_2940,U_2940,hAPP(U_2940,fun(U_2940,U_2940),times_times(U_2940),U_2939),U_2938)),U_2938) = hAPP(U_2940,U_2940,hAPP(U_2940,fun(U_2940,U_2940),times_times(U_2940),hAPP(U_2940,U_2940,hAPP(U_2940,fun(U_2940,U_2940),plus_plus(U_2940),U_2939),one_one(U_2940))),U_2938)
      | ~ comm_semiring_1(U_2940) ),
    inference(variable_rename,[status(thm)],[f_763_1]) ).

fof(f_763_3,plain,
    ! [U_2939,U_2938,U_2940] :
      ( hAPP(U_2940,U_2940,hAPP(U_2940,fun(U_2940,U_2940),plus_plus(U_2940),hAPP(U_2940,U_2940,hAPP(U_2940,fun(U_2940,U_2940),times_times(U_2940),U_2939),U_2938)),U_2938) = hAPP(U_2940,U_2940,hAPP(U_2940,fun(U_2940,U_2940),times_times(U_2940),hAPP(U_2940,U_2940,hAPP(U_2940,fun(U_2940,U_2940),plus_plus(U_2940),U_2939),one_one(U_2940))),U_2938)
      | ~ comm_semiring_1(U_2940) ),
    inference(definitional_conversion,[status(esa)],[f_763_2]) ).

cnf(f_763_4,plain,
    ( hAPP(U_2940,U_2940,hAPP(U_2940,fun(U_2940,U_2940),plus_plus(U_2940),hAPP(U_2940,U_2940,hAPP(U_2940,fun(U_2940,U_2940),times_times(U_2940),U_2939),U_2938)),U_2938) = hAPP(U_2940,U_2940,hAPP(U_2940,fun(U_2940,U_2940),times_times(U_2940),hAPP(U_2940,U_2940,hAPP(U_2940,fun(U_2940,U_2940),plus_plus(U_2940),U_2939),one_one(U_2940))),U_2938)
    | ~ comm_semiring_1(U_2940) ),
    inference(clausify,[status(thm)],[f_763_3]) ).

fof(f_764_1,plain,
    ! [X_a] :
      ( ! [M_1,A_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),M_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),M_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),one_one(X_a))),M_1)
      | ~ comm_semiring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_693_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J]) ).

fof(f_764_2,plain,
    ! [U_2943] :
      ( ! [U_2942,U_2941] : hAPP(U_2943,U_2943,hAPP(U_2943,fun(U_2943,U_2943),plus_plus(U_2943),U_2942),hAPP(U_2943,U_2943,hAPP(U_2943,fun(U_2943,U_2943),times_times(U_2943),U_2941),U_2942)) = hAPP(U_2943,U_2943,hAPP(U_2943,fun(U_2943,U_2943),times_times(U_2943),hAPP(U_2943,U_2943,hAPP(U_2943,fun(U_2943,U_2943),plus_plus(U_2943),U_2941),one_one(U_2943))),U_2942)
      | ~ comm_semiring_1(U_2943) ),
    inference(variable_rename,[status(thm)],[f_764_1]) ).

fof(f_764_3,plain,
    ! [U_2942,U_2943,U_2941] :
      ( hAPP(U_2943,U_2943,hAPP(U_2943,fun(U_2943,U_2943),plus_plus(U_2943),U_2942),hAPP(U_2943,U_2943,hAPP(U_2943,fun(U_2943,U_2943),times_times(U_2943),U_2941),U_2942)) = hAPP(U_2943,U_2943,hAPP(U_2943,fun(U_2943,U_2943),times_times(U_2943),hAPP(U_2943,U_2943,hAPP(U_2943,fun(U_2943,U_2943),plus_plus(U_2943),U_2941),one_one(U_2943))),U_2942)
      | ~ comm_semiring_1(U_2943) ),
    inference(definitional_conversion,[status(esa)],[f_764_2]) ).

cnf(f_764_4,plain,
    ( hAPP(U_2943,U_2943,hAPP(U_2943,fun(U_2943,U_2943),plus_plus(U_2943),U_2942),hAPP(U_2943,U_2943,hAPP(U_2943,fun(U_2943,U_2943),times_times(U_2943),U_2941),U_2942)) = hAPP(U_2943,U_2943,hAPP(U_2943,fun(U_2943,U_2943),times_times(U_2943),hAPP(U_2943,U_2943,hAPP(U_2943,fun(U_2943,U_2943),plus_plus(U_2943),U_2941),one_one(U_2943))),U_2942)
    | ~ comm_semiring_1(U_2943) ),
    inference(clausify,[status(thm)],[f_764_3]) ).

fof(f_765_1,plain,
    ! [X_a] :
      ( ! [M_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),M_1),M_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),one_one(X_a))),M_1)
      | ~ comm_semiring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_694_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J]) ).

fof(f_765_2,plain,
    ! [U_2945] :
      ( ! [U_2944] : hAPP(U_2945,U_2945,hAPP(U_2945,fun(U_2945,U_2945),plus_plus(U_2945),U_2944),U_2944) = hAPP(U_2945,U_2945,hAPP(U_2945,fun(U_2945,U_2945),times_times(U_2945),hAPP(U_2945,U_2945,hAPP(U_2945,fun(U_2945,U_2945),plus_plus(U_2945),one_one(U_2945)),one_one(U_2945))),U_2944)
      | ~ comm_semiring_1(U_2945) ),
    inference(variable_rename,[status(thm)],[f_765_1]) ).

fof(f_765_3,plain,
    ! [U_2945,U_2944] :
      ( hAPP(U_2945,U_2945,hAPP(U_2945,fun(U_2945,U_2945),plus_plus(U_2945),U_2944),U_2944) = hAPP(U_2945,U_2945,hAPP(U_2945,fun(U_2945,U_2945),times_times(U_2945),hAPP(U_2945,U_2945,hAPP(U_2945,fun(U_2945,U_2945),plus_plus(U_2945),one_one(U_2945)),one_one(U_2945))),U_2944)
      | ~ comm_semiring_1(U_2945) ),
    inference(definitional_conversion,[status(esa)],[f_765_2]) ).

cnf(f_765_4,plain,
    ( hAPP(U_2945,U_2945,hAPP(U_2945,fun(U_2945,U_2945),plus_plus(U_2945),U_2944),U_2944) = hAPP(U_2945,U_2945,hAPP(U_2945,fun(U_2945,U_2945),times_times(U_2945),hAPP(U_2945,U_2945,hAPP(U_2945,fun(U_2945,U_2945),plus_plus(U_2945),one_one(U_2945)),one_one(U_2945))),U_2944)
    | ~ comm_semiring_1(U_2945) ),
    inference(clausify,[status(thm)],[f_765_3]) ).

fof(f_766_1,plain,
    ! [M,Na] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na) = hAPP(nat,nat,suc,zero_zero(nat))
        | Na != hAPP(nat,nat,suc,zero_zero(nat))
        | M != hAPP(nat,nat,suc,zero_zero(nat)) )
      & ( ( Na = hAPP(nat,nat,suc,zero_zero(nat))
          & M = hAPP(nat,nat,suc,zero_zero(nat)) )
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na) != hAPP(nat,nat,suc,zero_zero(nat)) ) ),
    inference(fof_nnf,[status(thm)],[fact_695_mult__eq__1__iff]) ).

fof(f_766_2,plain,
    ! [U_2947,U_2946] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2947),U_2946) = hAPP(nat,nat,suc,zero_zero(nat))
        | U_2946 != hAPP(nat,nat,suc,zero_zero(nat))
        | U_2947 != hAPP(nat,nat,suc,zero_zero(nat)) )
      & ( ( U_2946 = hAPP(nat,nat,suc,zero_zero(nat))
          & U_2947 = hAPP(nat,nat,suc,zero_zero(nat)) )
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2947),U_2946) != hAPP(nat,nat,suc,zero_zero(nat)) ) ),
    inference(variable_rename,[status(thm)],[f_766_1]) ).

fof(f_766_3,plain,
    ( ! [U_2951,U_2949] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2951),U_2949) = hAPP(nat,nat,suc,zero_zero(nat))
        | U_2949 != hAPP(nat,nat,suc,zero_zero(nat))
        | U_2951 != hAPP(nat,nat,suc,zero_zero(nat)) )
    & ! [U_2950,U_2948] :
        ( ( U_2948 = hAPP(nat,nat,suc,zero_zero(nat))
          & U_2950 = hAPP(nat,nat,suc,zero_zero(nat)) )
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2950),U_2948) != hAPP(nat,nat,suc,zero_zero(nat)) ) ),
    inference(miniscope,[status(thm)],[f_766_2]) ).

fof(f_766_4,plain,
    ( ! [U_2948,U_2950] :
        ( U_2948 = hAPP(nat,nat,suc,zero_zero(nat))
        | ~ sP210(U_2948,U_2950) )
    & ! [U_2948,U_2950] :
        ( U_2950 = hAPP(nat,nat,suc,zero_zero(nat))
        | ~ sP210(U_2948,U_2950) )
    & ! [U_2949,U_2951] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2951),U_2949) = hAPP(nat,nat,suc,zero_zero(nat))
        | U_2949 != hAPP(nat,nat,suc,zero_zero(nat))
        | U_2951 != hAPP(nat,nat,suc,zero_zero(nat)) )
    & ! [U_2948,U_2950] :
        ( sP210(U_2948,U_2950)
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2950),U_2948) != hAPP(nat,nat,suc,zero_zero(nat)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP210])],[f_766_3]) ).

cnf(f_766_5,plain,
    ( sP210(U_2948,U_2950)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2950),U_2948) != hAPP(nat,nat,suc,zero_zero(nat)) ),
    inference(clausify,[status(thm)],[f_766_4]) ).

cnf(f_766_6,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2951),U_2949) = hAPP(nat,nat,suc,zero_zero(nat))
    | U_2949 != hAPP(nat,nat,suc,zero_zero(nat))
    | U_2951 != hAPP(nat,nat,suc,zero_zero(nat)) ),
    inference(clausify,[status(thm)],[f_766_4]) ).

cnf(f_766_7,plain,
    ( U_2950 = hAPP(nat,nat,suc,zero_zero(nat))
    | ~ sP210(U_2948,U_2950) ),
    inference(clausify,[status(thm)],[f_766_4]) ).

cnf(f_766_8,plain,
    ( U_2948 = hAPP(nat,nat,suc,zero_zero(nat))
    | ~ sP210(U_2948,U_2950) ),
    inference(clausify,[status(thm)],[f_766_4]) ).

fof(f_767_1,plain,
    ! [K_1,I_2,J] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),I_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),J)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J)) ),
    inference(fof_nnf,[status(thm)],[fact_696_mult__less__mono2]) ).

fof(f_767_2,plain,
    ! [U_2954,U_2953,U_2952] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2954),U_2953)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2954),U_2952)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2954))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2953),U_2952)) ),
    inference(variable_rename,[status(thm)],[f_767_1]) ).

fof(f_767_3,plain,
    ! [U_2954,U_2953,U_2952] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2954),U_2953)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2954),U_2952)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2954))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2953),U_2952)) ),
    inference(definitional_conversion,[status(esa)],[f_767_2]) ).

cnf(f_767_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2954),U_2953)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2954),U_2952)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2954))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2953),U_2952)) ),
    inference(clausify,[status(thm)],[f_767_3]) ).

fof(f_768_1,plain,
    ! [K_1,I_2,J] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_2),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),K_1)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J)) ),
    inference(fof_nnf,[status(thm)],[fact_697_mult__less__mono1]) ).

fof(f_768_2,plain,
    ! [U_2957,U_2956,U_2955] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2956),U_2957)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2955),U_2957)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2957))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2956),U_2955)) ),
    inference(variable_rename,[status(thm)],[f_768_1]) ).

fof(f_768_3,plain,
    ! [U_2955,U_2956,U_2957] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2956),U_2957)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2955),U_2957)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2957))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2956),U_2955)) ),
    inference(definitional_conversion,[status(esa)],[f_768_2]) ).

cnf(f_768_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2956),U_2957)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2955),U_2957)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2957))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2956),U_2955)) ),
    inference(clausify,[status(thm)],[f_768_3]) ).

fof(f_769_1,plain,
    ! [M,K,Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Na),K)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) )
      & ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) )
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Na),K))) ) ),
    inference(fof_nnf,[status(thm)],[fact_698_mult__less__cancel2]) ).

fof(f_769_2,plain,
    ! [U_2960,U_2959,U_2958] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2960),U_2959)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2958),U_2959)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2960),U_2958))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2959)) )
      & ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2960),U_2958))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2959)) )
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2960),U_2959)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2958),U_2959))) ) ),
    inference(variable_rename,[status(thm)],[f_769_1]) ).

fof(f_769_3,plain,
    ( ! [U_2966,U_2964,U_2962] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2966),U_2964)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2962),U_2964)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2966),U_2962))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2964)) )
    & ! [U_2965,U_2963,U_2961] :
        ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2965),U_2961))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2963)) )
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2965),U_2963)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2961),U_2963))) ) ),
    inference(miniscope,[status(thm)],[f_769_2]) ).

fof(f_769_4,plain,
    ( ! [U_2963,U_2961,U_2965] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2965),U_2961))
        | ~ sP211(U_2963,U_2961,U_2965) )
    & ! [U_2963,U_2961,U_2965] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2963))
        | ~ sP211(U_2963,U_2961,U_2965) )
    & ! [U_2962,U_2964,U_2966] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2966),U_2964)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2962),U_2964)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2966),U_2962))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2964)) )
    & ! [U_2963,U_2961,U_2965] :
        ( sP211(U_2963,U_2961,U_2965)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2965),U_2963)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2961),U_2963))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP211])],[f_769_3]) ).

cnf(f_769_5,plain,
    ( sP211(U_2963,U_2961,U_2965)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2965),U_2963)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2961),U_2963))) ),
    inference(clausify,[status(thm)],[f_769_4]) ).

cnf(f_769_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2966),U_2964)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2962),U_2964)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2966),U_2962))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2964)) ),
    inference(clausify,[status(thm)],[f_769_4]) ).

cnf(f_769_7,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2963))
    | ~ sP211(U_2963,U_2961,U_2965) ),
    inference(clausify,[status(thm)],[f_769_4]) ).

cnf(f_769_8,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2965),U_2961))
    | ~ sP211(U_2963,U_2961,U_2965) ),
    inference(clausify,[status(thm)],[f_769_4]) ).

fof(f_770_1,plain,
    ! [K,M,Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) )
      & ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) )
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_699_mult__less__cancel1]) ).

fof(f_770_2,plain,
    ! [U_2969,U_2968,U_2967] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2969),U_2968)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2969),U_2967)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2968),U_2967))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2969)) )
      & ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2968),U_2967))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2969)) )
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2969),U_2968)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2969),U_2967))) ) ),
    inference(variable_rename,[status(thm)],[f_770_1]) ).

fof(f_770_3,plain,
    ( ! [U_2975,U_2973,U_2971] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2975),U_2973)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2975),U_2971)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2973),U_2971))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2975)) )
    & ! [U_2974,U_2972,U_2970] :
        ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2972),U_2970))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2974)) )
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2974),U_2972)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2974),U_2970))) ) ),
    inference(miniscope,[status(thm)],[f_770_2]) ).

fof(f_770_4,plain,
    ( ! [U_2970,U_2972,U_2974] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2972),U_2970))
        | ~ sP212(U_2970,U_2972,U_2974) )
    & ! [U_2970,U_2972,U_2974] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2974))
        | ~ sP212(U_2970,U_2972,U_2974) )
    & ! [U_2971,U_2973,U_2975] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2975),U_2973)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2975),U_2971)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2973),U_2971))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2975)) )
    & ! [U_2970,U_2972,U_2974] :
        ( sP212(U_2970,U_2972,U_2974)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2974),U_2972)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2974),U_2970))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP212])],[f_770_3]) ).

cnf(f_770_5,plain,
    ( sP212(U_2970,U_2972,U_2974)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2974),U_2972)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2974),U_2970))) ),
    inference(clausify,[status(thm)],[f_770_4]) ).

cnf(f_770_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2975),U_2973)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2975),U_2971)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2973),U_2971))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2975)) ),
    inference(clausify,[status(thm)],[f_770_4]) ).

cnf(f_770_7,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2974))
    | ~ sP212(U_2970,U_2972,U_2974) ),
    inference(clausify,[status(thm)],[f_770_4]) ).

cnf(f_770_8,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2972),U_2970))
    | ~ sP212(U_2970,U_2972,U_2974) ),
    inference(clausify,[status(thm)],[f_770_4]) ).

fof(f_771_1,plain,
    ! [M,Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M)) )
      & ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M)) )
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_700_nat__0__less__mult__iff]) ).

fof(f_771_2,plain,
    ! [U_2977,U_2976] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2977),U_2976)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2976))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2977)) )
      & ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2976))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2977)) )
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2977),U_2976))) ) ),
    inference(variable_rename,[status(thm)],[f_771_1]) ).

fof(f_771_3,plain,
    ( ! [U_2981,U_2979] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2981),U_2979)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2979))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2981)) )
    & ! [U_2980,U_2978] :
        ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2978))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2980)) )
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2980),U_2978))) ) ),
    inference(miniscope,[status(thm)],[f_771_2]) ).

fof(f_771_4,plain,
    ( ! [U_2978,U_2980] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2978))
        | ~ sP213(U_2978,U_2980) )
    & ! [U_2978,U_2980] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2980))
        | ~ sP213(U_2978,U_2980) )
    & ! [U_2981,U_2979] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2981),U_2979)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2979))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2981)) )
    & ! [U_2978,U_2980] :
        ( sP213(U_2978,U_2980)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2980),U_2978))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP213])],[f_771_3]) ).

cnf(f_771_5,plain,
    ( sP213(U_2978,U_2980)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2980),U_2978))) ),
    inference(clausify,[status(thm)],[f_771_4]) ).

cnf(f_771_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2981),U_2979)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2979))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2981)) ),
    inference(clausify,[status(thm)],[f_771_4]) ).

cnf(f_771_7,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2980))
    | ~ sP213(U_2978,U_2980) ),
    inference(clausify,[status(thm)],[f_771_4]) ).

cnf(f_771_8,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2978))
    | ~ sP213(U_2978,U_2980) ),
    inference(clausify,[status(thm)],[f_771_4]) ).

fof(f_772_1,plain,
    ! [K,M,Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),Na)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_701_Suc__mult__less__cancel1]) ).

fof(f_772_2,plain,
    ! [U_2984,U_2983,U_2982] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2984)),U_2983)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2984)),U_2982)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2983),U_2982)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2983),U_2982))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2984)),U_2983)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2984)),U_2982))) ) ),
    inference(variable_rename,[status(thm)],[f_772_1]) ).

fof(f_772_3,plain,
    ( ! [U_2990,U_2988,U_2986] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2990)),U_2988)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2990)),U_2986)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2988),U_2986)) )
    & ! [U_2989,U_2987,U_2985] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2987),U_2985))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2989)),U_2987)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2989)),U_2985))) ) ),
    inference(miniscope,[status(thm)],[f_772_2]) ).

fof(f_772_4,plain,
    ( ! [U_2986,U_2988,U_2990] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2990)),U_2988)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2990)),U_2986)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2988),U_2986)) )
    & ! [U_2989,U_2987,U_2985] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2987),U_2985))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2989)),U_2987)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2989)),U_2985))) ) ),
    inference(definitional_conversion,[status(esa)],[f_772_3]) ).

cnf(f_772_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2987),U_2985))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2989)),U_2987)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2989)),U_2985))) ),
    inference(clausify,[status(thm)],[f_772_4]) ).

cnf(f_772_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2990)),U_2988)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2990)),U_2986)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2988),U_2986)) ),
    inference(clausify,[status(thm)],[f_772_4]) ).

fof(f_773_1,plain,
    ! [M_1,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),hAPP(nat,nat,suc,N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N)),
    inference(fof_nnf,[status(thm)],[fact_702_mult__Suc__right]) ).

fof(f_773_2,plain,
    ! [U_2992,U_2991] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2992),hAPP(nat,nat,suc,U_2991)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2992),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2992),U_2991)),
    inference(variable_rename,[status(thm)],[f_773_1]) ).

fof(f_773_3,plain,
    ! [U_2992,U_2991] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2992),hAPP(nat,nat,suc,U_2991)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2992),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2992),U_2991)),
    inference(definitional_conversion,[status(esa)],[f_773_2]) ).

cnf(f_773_4,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2992),hAPP(nat,nat,suc,U_2991)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2992),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2992),U_2991)),
    inference(clausify,[status(thm)],[f_773_3]) ).

fof(f_774_1,plain,
    ! [M_1,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,M_1)),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N)),
    inference(fof_nnf,[status(thm)],[fact_703_mult__Suc]) ).

fof(f_774_2,plain,
    ! [U_2994,U_2993] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2994)),U_2993) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2993),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2994),U_2993)),
    inference(variable_rename,[status(thm)],[f_774_1]) ).

fof(f_774_3,plain,
    ! [U_2993,U_2994] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2994)),U_2993) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2993),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2994),U_2993)),
    inference(definitional_conversion,[status(esa)],[f_774_2]) ).

cnf(f_774_4,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2994)),U_2993) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2993),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2994),U_2993)),
    inference(clausify,[status(thm)],[f_774_3]) ).

fof(f_775_1,plain,
    ! [K,M,Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),Na)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_704_Suc__mult__le__cancel1]) ).

fof(f_775_2,plain,
    ! [U_2997,U_2996,U_2995] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2997)),U_2996)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2997)),U_2995)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2996),U_2995)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2996),U_2995))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2997)),U_2996)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2997)),U_2995))) ) ),
    inference(variable_rename,[status(thm)],[f_775_1]) ).

fof(f_775_3,plain,
    ( ! [U_3003,U_3001,U_2999] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_3003)),U_3001)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_3003)),U_2999)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3001),U_2999)) )
    & ! [U_3002,U_3000,U_2998] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3000),U_2998))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_3002)),U_3000)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_3002)),U_2998))) ) ),
    inference(miniscope,[status(thm)],[f_775_2]) ).

fof(f_775_4,plain,
    ( ! [U_2999,U_3001,U_3003] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_3003)),U_3001)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_3003)),U_2999)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3001),U_2999)) )
    & ! [U_3002,U_3000,U_2998] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3000),U_2998))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_3002)),U_3000)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_3002)),U_2998))) ) ),
    inference(definitional_conversion,[status(esa)],[f_775_3]) ).

cnf(f_775_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3000),U_2998))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_3002)),U_3000)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_3002)),U_2998))) ),
    inference(clausify,[status(thm)],[f_775_4]) ).

cnf(f_775_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_3003)),U_3001)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_3003)),U_2999)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3001),U_2999)) ),
    inference(clausify,[status(thm)],[f_775_4]) ).

fof(f_776_1,plain,
    ! [M_1,N] :
      ( M_1 = zero_zero(nat)
      | N = one_one(nat)
      | M_1 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N) ),
    inference(fof_nnf,[status(thm)],[fact_705_mult__eq__self__implies__10]) ).

fof(f_776_2,plain,
    ! [U_3005,U_3004] :
      ( U_3005 = zero_zero(nat)
      | U_3004 = one_one(nat)
      | U_3005 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3005),U_3004) ),
    inference(variable_rename,[status(thm)],[f_776_1]) ).

fof(f_776_3,plain,
    ! [U_3004,U_3005] :
      ( U_3005 = zero_zero(nat)
      | U_3004 = one_one(nat)
      | U_3005 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3005),U_3004) ),
    inference(definitional_conversion,[status(esa)],[f_776_2]) ).

cnf(f_776_4,plain,
    ( U_3005 = zero_zero(nat)
    | U_3004 = one_one(nat)
    | U_3005 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3005),U_3004) ),
    inference(clausify,[status(thm)],[f_776_3]) ).

fof(f_777_1,plain,
    ! [X_b] :
      ( ! [A_2] :
          ( ( ( 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)
              | ti(X_b,A_2) != zero_zero(X_b) )
            & ( ti(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) != zero_zero(X_b) ) )
          | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),ring_1_Ints(X_b))) )
      | ~ ring_char_0(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_706_Ints__double__eq__0__iff]) ).

fof(f_777_2,plain,
    ! [U_3007] :
      ( ! [U_3006] :
          ( ( ( hAPP(U_3007,U_3007,hAPP(U_3007,fun(U_3007,U_3007),plus_plus(U_3007),U_3006),U_3006) = zero_zero(U_3007)
              | ti(U_3007,U_3006) != zero_zero(U_3007) )
            & ( ti(U_3007,U_3006) = zero_zero(U_3007)
              | hAPP(U_3007,U_3007,hAPP(U_3007,fun(U_3007,U_3007),plus_plus(U_3007),U_3006),U_3006) != zero_zero(U_3007) ) )
          | ~ hBOOL(hAPP(fun(U_3007,bool),bool,hAPP(U_3007,fun(fun(U_3007,bool),bool),member(U_3007),U_3006),ring_1_Ints(U_3007))) )
      | ~ ring_char_0(U_3007) ),
    inference(variable_rename,[status(thm)],[f_777_1]) ).

fof(f_777_3,plain,
    ( ! [U_3007,U_3006] :
        ( hAPP(U_3007,U_3007,hAPP(U_3007,fun(U_3007,U_3007),plus_plus(U_3007),U_3006),U_3006) = zero_zero(U_3007)
        | ti(U_3007,U_3006) != zero_zero(U_3007)
        | ~ sP214(U_3007,U_3006) )
    & ! [U_3007,U_3006] :
        ( ti(U_3007,U_3006) = zero_zero(U_3007)
        | hAPP(U_3007,U_3007,hAPP(U_3007,fun(U_3007,U_3007),plus_plus(U_3007),U_3006),U_3006) != zero_zero(U_3007)
        | ~ sP214(U_3007,U_3006) )
    & ! [U_3007,U_3006] :
        ( sP214(U_3007,U_3006)
        | ~ hBOOL(hAPP(fun(U_3007,bool),bool,hAPP(U_3007,fun(fun(U_3007,bool),bool),member(U_3007),U_3006),ring_1_Ints(U_3007)))
        | ~ ring_char_0(U_3007) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP214])],[f_777_2]) ).

cnf(f_777_4,plain,
    ( sP214(U_3007,U_3006)
    | ~ hBOOL(hAPP(fun(U_3007,bool),bool,hAPP(U_3007,fun(fun(U_3007,bool),bool),member(U_3007),U_3006),ring_1_Ints(U_3007)))
    | ~ ring_char_0(U_3007) ),
    inference(clausify,[status(thm)],[f_777_3]) ).

cnf(f_777_5,plain,
    ( ti(U_3007,U_3006) = zero_zero(U_3007)
    | hAPP(U_3007,U_3007,hAPP(U_3007,fun(U_3007,U_3007),plus_plus(U_3007),U_3006),U_3006) != zero_zero(U_3007)
    | ~ sP214(U_3007,U_3006) ),
    inference(clausify,[status(thm)],[f_777_3]) ).

cnf(f_777_6,plain,
    ( hAPP(U_3007,U_3007,hAPP(U_3007,fun(U_3007,U_3007),plus_plus(U_3007),U_3006),U_3006) = zero_zero(U_3007)
    | ti(U_3007,U_3006) != zero_zero(U_3007)
    | ~ sP214(U_3007,U_3006) ),
    inference(clausify,[status(thm)],[f_777_3]) ).

fof(f_778_1,plain,
    ! [X_a] :
      ( ! [C,A_1,B] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C))
          | ~ 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),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B))) )
      | ~ linord20386208strict(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_707_mult__left__le__imp__le]) ).

fof(f_778_2,plain,
    ! [U_3011] :
      ( ! [U_3010,U_3009,U_3008] :
          ( hBOOL(hAPP(U_3011,bool,hAPP(U_3011,fun(U_3011,bool),ord_less_eq(U_3011),U_3009),U_3008))
          | ~ hBOOL(hAPP(U_3011,bool,hAPP(U_3011,fun(U_3011,bool),ord_less(U_3011),zero_zero(U_3011)),U_3010))
          | ~ hBOOL(hAPP(U_3011,bool,hAPP(U_3011,fun(U_3011,bool),ord_less_eq(U_3011),hAPP(U_3011,U_3011,hAPP(U_3011,fun(U_3011,U_3011),times_times(U_3011),U_3010),U_3009)),hAPP(U_3011,U_3011,hAPP(U_3011,fun(U_3011,U_3011),times_times(U_3011),U_3010),U_3008))) )
      | ~ linord20386208strict(U_3011) ),
    inference(variable_rename,[status(thm)],[f_778_1]) ).

fof(f_778_3,plain,
    ! [U_3008,U_3009,U_3011,U_3010] :
      ( hBOOL(hAPP(U_3011,bool,hAPP(U_3011,fun(U_3011,bool),ord_less_eq(U_3011),U_3009),U_3008))
      | ~ hBOOL(hAPP(U_3011,bool,hAPP(U_3011,fun(U_3011,bool),ord_less(U_3011),zero_zero(U_3011)),U_3010))
      | ~ hBOOL(hAPP(U_3011,bool,hAPP(U_3011,fun(U_3011,bool),ord_less_eq(U_3011),hAPP(U_3011,U_3011,hAPP(U_3011,fun(U_3011,U_3011),times_times(U_3011),U_3010),U_3009)),hAPP(U_3011,U_3011,hAPP(U_3011,fun(U_3011,U_3011),times_times(U_3011),U_3010),U_3008)))
      | ~ linord20386208strict(U_3011) ),
    inference(definitional_conversion,[status(esa)],[f_778_2]) ).

cnf(f_778_4,plain,
    ( hBOOL(hAPP(U_3011,bool,hAPP(U_3011,fun(U_3011,bool),ord_less_eq(U_3011),U_3009),U_3008))
    | ~ hBOOL(hAPP(U_3011,bool,hAPP(U_3011,fun(U_3011,bool),ord_less(U_3011),zero_zero(U_3011)),U_3010))
    | ~ hBOOL(hAPP(U_3011,bool,hAPP(U_3011,fun(U_3011,bool),ord_less_eq(U_3011),hAPP(U_3011,U_3011,hAPP(U_3011,fun(U_3011,U_3011),times_times(U_3011),U_3010),U_3009)),hAPP(U_3011,U_3011,hAPP(U_3011,fun(U_3011,U_3011),times_times(U_3011),U_3010),U_3008)))
    | ~ linord20386208strict(U_3011) ),
    inference(clausify,[status(thm)],[f_778_3]) ).

fof(f_779_1,plain,
    ! [X_a] :
      ( ! [A_1,C,B] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C))
          | ~ 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),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C))) )
      | ~ linord20386208strict(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_708_mult__right__le__imp__le]) ).

fof(f_779_2,plain,
    ! [U_3015] :
      ( ! [U_3014,U_3013,U_3012] :
          ( hBOOL(hAPP(U_3015,bool,hAPP(U_3015,fun(U_3015,bool),ord_less_eq(U_3015),U_3014),U_3012))
          | ~ hBOOL(hAPP(U_3015,bool,hAPP(U_3015,fun(U_3015,bool),ord_less(U_3015),zero_zero(U_3015)),U_3013))
          | ~ hBOOL(hAPP(U_3015,bool,hAPP(U_3015,fun(U_3015,bool),ord_less_eq(U_3015),hAPP(U_3015,U_3015,hAPP(U_3015,fun(U_3015,U_3015),times_times(U_3015),U_3014),U_3013)),hAPP(U_3015,U_3015,hAPP(U_3015,fun(U_3015,U_3015),times_times(U_3015),U_3012),U_3013))) )
      | ~ linord20386208strict(U_3015) ),
    inference(variable_rename,[status(thm)],[f_779_1]) ).

fof(f_779_3,plain,
    ! [U_3012,U_3013,U_3015,U_3014] :
      ( hBOOL(hAPP(U_3015,bool,hAPP(U_3015,fun(U_3015,bool),ord_less_eq(U_3015),U_3014),U_3012))
      | ~ hBOOL(hAPP(U_3015,bool,hAPP(U_3015,fun(U_3015,bool),ord_less(U_3015),zero_zero(U_3015)),U_3013))
      | ~ hBOOL(hAPP(U_3015,bool,hAPP(U_3015,fun(U_3015,bool),ord_less_eq(U_3015),hAPP(U_3015,U_3015,hAPP(U_3015,fun(U_3015,U_3015),times_times(U_3015),U_3014),U_3013)),hAPP(U_3015,U_3015,hAPP(U_3015,fun(U_3015,U_3015),times_times(U_3015),U_3012),U_3013)))
      | ~ linord20386208strict(U_3015) ),
    inference(definitional_conversion,[status(esa)],[f_779_2]) ).

cnf(f_779_4,plain,
    ( hBOOL(hAPP(U_3015,bool,hAPP(U_3015,fun(U_3015,bool),ord_less_eq(U_3015),U_3014),U_3012))
    | ~ hBOOL(hAPP(U_3015,bool,hAPP(U_3015,fun(U_3015,bool),ord_less(U_3015),zero_zero(U_3015)),U_3013))
    | ~ hBOOL(hAPP(U_3015,bool,hAPP(U_3015,fun(U_3015,bool),ord_less_eq(U_3015),hAPP(U_3015,U_3015,hAPP(U_3015,fun(U_3015,U_3015),times_times(U_3015),U_3014),U_3013)),hAPP(U_3015,U_3015,hAPP(U_3015,fun(U_3015,U_3015),times_times(U_3015),U_3012),U_3013)))
    | ~ linord20386208strict(U_3015) ),
    inference(clausify,[status(thm)],[f_779_3]) ).

fof(f_780_1,plain,
    ! [X_a] :
      ( ! [C,A_1,B] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))
          | ~ 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(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B))) )
      | ~ linord20386208strict(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_709_mult__less__imp__less__left]) ).

fof(f_780_2,plain,
    ! [U_3019] :
      ( ! [U_3018,U_3017,U_3016] :
          ( hBOOL(hAPP(U_3019,bool,hAPP(U_3019,fun(U_3019,bool),ord_less(U_3019),U_3017),U_3016))
          | ~ hBOOL(hAPP(U_3019,bool,hAPP(U_3019,fun(U_3019,bool),ord_less_eq(U_3019),zero_zero(U_3019)),U_3018))
          | ~ hBOOL(hAPP(U_3019,bool,hAPP(U_3019,fun(U_3019,bool),ord_less(U_3019),hAPP(U_3019,U_3019,hAPP(U_3019,fun(U_3019,U_3019),times_times(U_3019),U_3018),U_3017)),hAPP(U_3019,U_3019,hAPP(U_3019,fun(U_3019,U_3019),times_times(U_3019),U_3018),U_3016))) )
      | ~ linord20386208strict(U_3019) ),
    inference(variable_rename,[status(thm)],[f_780_1]) ).

fof(f_780_3,plain,
    ! [U_3018,U_3017,U_3016,U_3019] :
      ( hBOOL(hAPP(U_3019,bool,hAPP(U_3019,fun(U_3019,bool),ord_less(U_3019),U_3017),U_3016))
      | ~ hBOOL(hAPP(U_3019,bool,hAPP(U_3019,fun(U_3019,bool),ord_less_eq(U_3019),zero_zero(U_3019)),U_3018))
      | ~ hBOOL(hAPP(U_3019,bool,hAPP(U_3019,fun(U_3019,bool),ord_less(U_3019),hAPP(U_3019,U_3019,hAPP(U_3019,fun(U_3019,U_3019),times_times(U_3019),U_3018),U_3017)),hAPP(U_3019,U_3019,hAPP(U_3019,fun(U_3019,U_3019),times_times(U_3019),U_3018),U_3016)))
      | ~ linord20386208strict(U_3019) ),
    inference(definitional_conversion,[status(esa)],[f_780_2]) ).

cnf(f_780_4,plain,
    ( hBOOL(hAPP(U_3019,bool,hAPP(U_3019,fun(U_3019,bool),ord_less(U_3019),U_3017),U_3016))
    | ~ hBOOL(hAPP(U_3019,bool,hAPP(U_3019,fun(U_3019,bool),ord_less_eq(U_3019),zero_zero(U_3019)),U_3018))
    | ~ hBOOL(hAPP(U_3019,bool,hAPP(U_3019,fun(U_3019,bool),ord_less(U_3019),hAPP(U_3019,U_3019,hAPP(U_3019,fun(U_3019,U_3019),times_times(U_3019),U_3018),U_3017)),hAPP(U_3019,U_3019,hAPP(U_3019,fun(U_3019,U_3019),times_times(U_3019),U_3018),U_3016)))
    | ~ linord20386208strict(U_3019) ),
    inference(clausify,[status(thm)],[f_780_3]) ).

fof(f_781_1,plain,
    ! [X_a] :
      ( ! [C,A_1,B] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))
          | ~ 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(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B))) )
      | ~ linordered_semiring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_710_mult__left__less__imp__less]) ).

fof(f_781_2,plain,
    ! [U_3023] :
      ( ! [U_3022,U_3021,U_3020] :
          ( hBOOL(hAPP(U_3023,bool,hAPP(U_3023,fun(U_3023,bool),ord_less(U_3023),U_3021),U_3020))
          | ~ hBOOL(hAPP(U_3023,bool,hAPP(U_3023,fun(U_3023,bool),ord_less_eq(U_3023),zero_zero(U_3023)),U_3022))
          | ~ hBOOL(hAPP(U_3023,bool,hAPP(U_3023,fun(U_3023,bool),ord_less(U_3023),hAPP(U_3023,U_3023,hAPP(U_3023,fun(U_3023,U_3023),times_times(U_3023),U_3022),U_3021)),hAPP(U_3023,U_3023,hAPP(U_3023,fun(U_3023,U_3023),times_times(U_3023),U_3022),U_3020))) )
      | ~ linordered_semiring(U_3023) ),
    inference(variable_rename,[status(thm)],[f_781_1]) ).

fof(f_781_3,plain,
    ! [U_3022,U_3021,U_3023,U_3020] :
      ( hBOOL(hAPP(U_3023,bool,hAPP(U_3023,fun(U_3023,bool),ord_less(U_3023),U_3021),U_3020))
      | ~ hBOOL(hAPP(U_3023,bool,hAPP(U_3023,fun(U_3023,bool),ord_less_eq(U_3023),zero_zero(U_3023)),U_3022))
      | ~ hBOOL(hAPP(U_3023,bool,hAPP(U_3023,fun(U_3023,bool),ord_less(U_3023),hAPP(U_3023,U_3023,hAPP(U_3023,fun(U_3023,U_3023),times_times(U_3023),U_3022),U_3021)),hAPP(U_3023,U_3023,hAPP(U_3023,fun(U_3023,U_3023),times_times(U_3023),U_3022),U_3020)))
      | ~ linordered_semiring(U_3023) ),
    inference(definitional_conversion,[status(esa)],[f_781_2]) ).

cnf(f_781_4,plain,
    ( hBOOL(hAPP(U_3023,bool,hAPP(U_3023,fun(U_3023,bool),ord_less(U_3023),U_3021),U_3020))
    | ~ hBOOL(hAPP(U_3023,bool,hAPP(U_3023,fun(U_3023,bool),ord_less_eq(U_3023),zero_zero(U_3023)),U_3022))
    | ~ hBOOL(hAPP(U_3023,bool,hAPP(U_3023,fun(U_3023,bool),ord_less(U_3023),hAPP(U_3023,U_3023,hAPP(U_3023,fun(U_3023,U_3023),times_times(U_3023),U_3022),U_3021)),hAPP(U_3023,U_3023,hAPP(U_3023,fun(U_3023,U_3023),times_times(U_3023),U_3022),U_3020)))
    | ~ linordered_semiring(U_3023) ),
    inference(clausify,[status(thm)],[f_781_3]) ).

fof(f_782_1,plain,
    ! [X_a] :
      ( ! [A_1,C,B] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))
          | ~ 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(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C))) )
      | ~ linord20386208strict(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_711_mult__less__imp__less__right]) ).

fof(f_782_2,plain,
    ! [U_3027] :
      ( ! [U_3026,U_3025,U_3024] :
          ( hBOOL(hAPP(U_3027,bool,hAPP(U_3027,fun(U_3027,bool),ord_less(U_3027),U_3026),U_3024))
          | ~ hBOOL(hAPP(U_3027,bool,hAPP(U_3027,fun(U_3027,bool),ord_less_eq(U_3027),zero_zero(U_3027)),U_3025))
          | ~ hBOOL(hAPP(U_3027,bool,hAPP(U_3027,fun(U_3027,bool),ord_less(U_3027),hAPP(U_3027,U_3027,hAPP(U_3027,fun(U_3027,U_3027),times_times(U_3027),U_3026),U_3025)),hAPP(U_3027,U_3027,hAPP(U_3027,fun(U_3027,U_3027),times_times(U_3027),U_3024),U_3025))) )
      | ~ linord20386208strict(U_3027) ),
    inference(variable_rename,[status(thm)],[f_782_1]) ).

fof(f_782_3,plain,
    ! [U_3025,U_3024,U_3027,U_3026] :
      ( hBOOL(hAPP(U_3027,bool,hAPP(U_3027,fun(U_3027,bool),ord_less(U_3027),U_3026),U_3024))
      | ~ hBOOL(hAPP(U_3027,bool,hAPP(U_3027,fun(U_3027,bool),ord_less_eq(U_3027),zero_zero(U_3027)),U_3025))
      | ~ hBOOL(hAPP(U_3027,bool,hAPP(U_3027,fun(U_3027,bool),ord_less(U_3027),hAPP(U_3027,U_3027,hAPP(U_3027,fun(U_3027,U_3027),times_times(U_3027),U_3026),U_3025)),hAPP(U_3027,U_3027,hAPP(U_3027,fun(U_3027,U_3027),times_times(U_3027),U_3024),U_3025)))
      | ~ linord20386208strict(U_3027) ),
    inference(definitional_conversion,[status(esa)],[f_782_2]) ).

cnf(f_782_4,plain,
    ( hBOOL(hAPP(U_3027,bool,hAPP(U_3027,fun(U_3027,bool),ord_less(U_3027),U_3026),U_3024))
    | ~ hBOOL(hAPP(U_3027,bool,hAPP(U_3027,fun(U_3027,bool),ord_less_eq(U_3027),zero_zero(U_3027)),U_3025))
    | ~ hBOOL(hAPP(U_3027,bool,hAPP(U_3027,fun(U_3027,bool),ord_less(U_3027),hAPP(U_3027,U_3027,hAPP(U_3027,fun(U_3027,U_3027),times_times(U_3027),U_3026),U_3025)),hAPP(U_3027,U_3027,hAPP(U_3027,fun(U_3027,U_3027),times_times(U_3027),U_3024),U_3025)))
    | ~ linord20386208strict(U_3027) ),
    inference(clausify,[status(thm)],[f_782_3]) ).

fof(f_783_1,plain,
    ! [X_a] :
      ( ! [A_1,C,B] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))
          | ~ 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(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C))) )
      | ~ linordered_semiring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_712_mult__right__less__imp__less]) ).

fof(f_783_2,plain,
    ! [U_3031] :
      ( ! [U_3030,U_3029,U_3028] :
          ( hBOOL(hAPP(U_3031,bool,hAPP(U_3031,fun(U_3031,bool),ord_less(U_3031),U_3030),U_3028))
          | ~ hBOOL(hAPP(U_3031,bool,hAPP(U_3031,fun(U_3031,bool),ord_less_eq(U_3031),zero_zero(U_3031)),U_3029))
          | ~ hBOOL(hAPP(U_3031,bool,hAPP(U_3031,fun(U_3031,bool),ord_less(U_3031),hAPP(U_3031,U_3031,hAPP(U_3031,fun(U_3031,U_3031),times_times(U_3031),U_3030),U_3029)),hAPP(U_3031,U_3031,hAPP(U_3031,fun(U_3031,U_3031),times_times(U_3031),U_3028),U_3029))) )
      | ~ linordered_semiring(U_3031) ),
    inference(variable_rename,[status(thm)],[f_783_1]) ).

fof(f_783_3,plain,
    ! [U_3030,U_3029,U_3028,U_3031] :
      ( hBOOL(hAPP(U_3031,bool,hAPP(U_3031,fun(U_3031,bool),ord_less(U_3031),U_3030),U_3028))
      | ~ hBOOL(hAPP(U_3031,bool,hAPP(U_3031,fun(U_3031,bool),ord_less_eq(U_3031),zero_zero(U_3031)),U_3029))
      | ~ hBOOL(hAPP(U_3031,bool,hAPP(U_3031,fun(U_3031,bool),ord_less(U_3031),hAPP(U_3031,U_3031,hAPP(U_3031,fun(U_3031,U_3031),times_times(U_3031),U_3030),U_3029)),hAPP(U_3031,U_3031,hAPP(U_3031,fun(U_3031,U_3031),times_times(U_3031),U_3028),U_3029)))
      | ~ linordered_semiring(U_3031) ),
    inference(definitional_conversion,[status(esa)],[f_783_2]) ).

cnf(f_783_4,plain,
    ( hBOOL(hAPP(U_3031,bool,hAPP(U_3031,fun(U_3031,bool),ord_less(U_3031),U_3030),U_3028))
    | ~ hBOOL(hAPP(U_3031,bool,hAPP(U_3031,fun(U_3031,bool),ord_less_eq(U_3031),zero_zero(U_3031)),U_3029))
    | ~ hBOOL(hAPP(U_3031,bool,hAPP(U_3031,fun(U_3031,bool),ord_less(U_3031),hAPP(U_3031,U_3031,hAPP(U_3031,fun(U_3031,U_3031),times_times(U_3031),U_3030),U_3029)),hAPP(U_3031,U_3031,hAPP(U_3031,fun(U_3031,U_3031),times_times(U_3031),U_3028),U_3029)))
    | ~ linordered_semiring(U_3031) ),
    inference(clausify,[status(thm)],[f_783_3]) ).

fof(f_784_1,plain,
    ! [X_a] :
      ( ! [C,D,A_1,B] :
          ( 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),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D)))
          | ~ 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(X_a),zero_zero(X_a)),A_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_eq(X_a),A_1),B)) )
      | ~ linord20386208strict(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_713_mult__le__less__imp__less]) ).

fof(f_784_2,plain,
    ! [U_3036] :
      ( ! [U_3035,U_3034,U_3033,U_3032] :
          ( hBOOL(hAPP(U_3036,bool,hAPP(U_3036,fun(U_3036,bool),ord_less(U_3036),hAPP(U_3036,U_3036,hAPP(U_3036,fun(U_3036,U_3036),times_times(U_3036),U_3033),U_3035)),hAPP(U_3036,U_3036,hAPP(U_3036,fun(U_3036,U_3036),times_times(U_3036),U_3032),U_3034)))
          | ~ hBOOL(hAPP(U_3036,bool,hAPP(U_3036,fun(U_3036,bool),ord_less_eq(U_3036),zero_zero(U_3036)),U_3035))
          | ~ hBOOL(hAPP(U_3036,bool,hAPP(U_3036,fun(U_3036,bool),ord_less(U_3036),zero_zero(U_3036)),U_3033))
          | ~ hBOOL(hAPP(U_3036,bool,hAPP(U_3036,fun(U_3036,bool),ord_less(U_3036),U_3035),U_3034))
          | ~ hBOOL(hAPP(U_3036,bool,hAPP(U_3036,fun(U_3036,bool),ord_less_eq(U_3036),U_3033),U_3032)) )
      | ~ linord20386208strict(U_3036) ),
    inference(variable_rename,[status(thm)],[f_784_1]) ).

fof(f_784_3,plain,
    ! [U_3034,U_3033,U_3036,U_3032,U_3035] :
      ( hBOOL(hAPP(U_3036,bool,hAPP(U_3036,fun(U_3036,bool),ord_less(U_3036),hAPP(U_3036,U_3036,hAPP(U_3036,fun(U_3036,U_3036),times_times(U_3036),U_3033),U_3035)),hAPP(U_3036,U_3036,hAPP(U_3036,fun(U_3036,U_3036),times_times(U_3036),U_3032),U_3034)))
      | ~ hBOOL(hAPP(U_3036,bool,hAPP(U_3036,fun(U_3036,bool),ord_less_eq(U_3036),zero_zero(U_3036)),U_3035))
      | ~ hBOOL(hAPP(U_3036,bool,hAPP(U_3036,fun(U_3036,bool),ord_less(U_3036),zero_zero(U_3036)),U_3033))
      | ~ hBOOL(hAPP(U_3036,bool,hAPP(U_3036,fun(U_3036,bool),ord_less(U_3036),U_3035),U_3034))
      | ~ hBOOL(hAPP(U_3036,bool,hAPP(U_3036,fun(U_3036,bool),ord_less_eq(U_3036),U_3033),U_3032))
      | ~ linord20386208strict(U_3036) ),
    inference(definitional_conversion,[status(esa)],[f_784_2]) ).

cnf(f_784_4,plain,
    ( hBOOL(hAPP(U_3036,bool,hAPP(U_3036,fun(U_3036,bool),ord_less(U_3036),hAPP(U_3036,U_3036,hAPP(U_3036,fun(U_3036,U_3036),times_times(U_3036),U_3033),U_3035)),hAPP(U_3036,U_3036,hAPP(U_3036,fun(U_3036,U_3036),times_times(U_3036),U_3032),U_3034)))
    | ~ hBOOL(hAPP(U_3036,bool,hAPP(U_3036,fun(U_3036,bool),ord_less_eq(U_3036),zero_zero(U_3036)),U_3035))
    | ~ hBOOL(hAPP(U_3036,bool,hAPP(U_3036,fun(U_3036,bool),ord_less(U_3036),zero_zero(U_3036)),U_3033))
    | ~ hBOOL(hAPP(U_3036,bool,hAPP(U_3036,fun(U_3036,bool),ord_less(U_3036),U_3035),U_3034))
    | ~ hBOOL(hAPP(U_3036,bool,hAPP(U_3036,fun(U_3036,bool),ord_less_eq(U_3036),U_3033),U_3032))
    | ~ linord20386208strict(U_3036) ),
    inference(clausify,[status(thm)],[f_784_3]) ).

fof(f_785_1,plain,
    ! [X_a] :
      ( ! [C,D,A_1,B] :
          ( 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),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C))
          | ~ 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),C),D))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) )
      | ~ linord20386208strict(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_714_mult__less__le__imp__less]) ).

fof(f_785_2,plain,
    ! [U_3041] :
      ( ! [U_3040,U_3039,U_3038,U_3037] :
          ( hBOOL(hAPP(U_3041,bool,hAPP(U_3041,fun(U_3041,bool),ord_less(U_3041),hAPP(U_3041,U_3041,hAPP(U_3041,fun(U_3041,U_3041),times_times(U_3041),U_3038),U_3040)),hAPP(U_3041,U_3041,hAPP(U_3041,fun(U_3041,U_3041),times_times(U_3041),U_3037),U_3039)))
          | ~ hBOOL(hAPP(U_3041,bool,hAPP(U_3041,fun(U_3041,bool),ord_less(U_3041),zero_zero(U_3041)),U_3040))
          | ~ hBOOL(hAPP(U_3041,bool,hAPP(U_3041,fun(U_3041,bool),ord_less_eq(U_3041),zero_zero(U_3041)),U_3038))
          | ~ hBOOL(hAPP(U_3041,bool,hAPP(U_3041,fun(U_3041,bool),ord_less_eq(U_3041),U_3040),U_3039))
          | ~ hBOOL(hAPP(U_3041,bool,hAPP(U_3041,fun(U_3041,bool),ord_less(U_3041),U_3038),U_3037)) )
      | ~ linord20386208strict(U_3041) ),
    inference(variable_rename,[status(thm)],[f_785_1]) ).

fof(f_785_3,plain,
    ! [U_3039,U_3041,U_3040,U_3037,U_3038] :
      ( hBOOL(hAPP(U_3041,bool,hAPP(U_3041,fun(U_3041,bool),ord_less(U_3041),hAPP(U_3041,U_3041,hAPP(U_3041,fun(U_3041,U_3041),times_times(U_3041),U_3038),U_3040)),hAPP(U_3041,U_3041,hAPP(U_3041,fun(U_3041,U_3041),times_times(U_3041),U_3037),U_3039)))
      | ~ hBOOL(hAPP(U_3041,bool,hAPP(U_3041,fun(U_3041,bool),ord_less(U_3041),zero_zero(U_3041)),U_3040))
      | ~ hBOOL(hAPP(U_3041,bool,hAPP(U_3041,fun(U_3041,bool),ord_less_eq(U_3041),zero_zero(U_3041)),U_3038))
      | ~ hBOOL(hAPP(U_3041,bool,hAPP(U_3041,fun(U_3041,bool),ord_less_eq(U_3041),U_3040),U_3039))
      | ~ hBOOL(hAPP(U_3041,bool,hAPP(U_3041,fun(U_3041,bool),ord_less(U_3041),U_3038),U_3037))
      | ~ linord20386208strict(U_3041) ),
    inference(definitional_conversion,[status(esa)],[f_785_2]) ).

cnf(f_785_4,plain,
    ( hBOOL(hAPP(U_3041,bool,hAPP(U_3041,fun(U_3041,bool),ord_less(U_3041),hAPP(U_3041,U_3041,hAPP(U_3041,fun(U_3041,U_3041),times_times(U_3041),U_3038),U_3040)),hAPP(U_3041,U_3041,hAPP(U_3041,fun(U_3041,U_3041),times_times(U_3041),U_3037),U_3039)))
    | ~ hBOOL(hAPP(U_3041,bool,hAPP(U_3041,fun(U_3041,bool),ord_less(U_3041),zero_zero(U_3041)),U_3040))
    | ~ hBOOL(hAPP(U_3041,bool,hAPP(U_3041,fun(U_3041,bool),ord_less_eq(U_3041),zero_zero(U_3041)),U_3038))
    | ~ hBOOL(hAPP(U_3041,bool,hAPP(U_3041,fun(U_3041,bool),ord_less_eq(U_3041),U_3040),U_3039))
    | ~ hBOOL(hAPP(U_3041,bool,hAPP(U_3041,fun(U_3041,bool),ord_less(U_3041),U_3038),U_3037))
    | ~ linord20386208strict(U_3041) ),
    inference(clausify,[status(thm)],[f_785_3]) ).

fof(f_786_1,plain,
    ! [X_a] :
      ( ! [C,D,A_1,B] :
          ( 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),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D)))
          | ~ 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),zero_zero(X_a)),A_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),A_1),B)) )
      | ~ linord20386208strict(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_715_mult__strict__mono_H]) ).

fof(f_786_2,plain,
    ! [U_3046] :
      ( ! [U_3045,U_3044,U_3043,U_3042] :
          ( hBOOL(hAPP(U_3046,bool,hAPP(U_3046,fun(U_3046,bool),ord_less(U_3046),hAPP(U_3046,U_3046,hAPP(U_3046,fun(U_3046,U_3046),times_times(U_3046),U_3043),U_3045)),hAPP(U_3046,U_3046,hAPP(U_3046,fun(U_3046,U_3046),times_times(U_3046),U_3042),U_3044)))
          | ~ hBOOL(hAPP(U_3046,bool,hAPP(U_3046,fun(U_3046,bool),ord_less_eq(U_3046),zero_zero(U_3046)),U_3045))
          | ~ hBOOL(hAPP(U_3046,bool,hAPP(U_3046,fun(U_3046,bool),ord_less_eq(U_3046),zero_zero(U_3046)),U_3043))
          | ~ hBOOL(hAPP(U_3046,bool,hAPP(U_3046,fun(U_3046,bool),ord_less(U_3046),U_3045),U_3044))
          | ~ hBOOL(hAPP(U_3046,bool,hAPP(U_3046,fun(U_3046,bool),ord_less(U_3046),U_3043),U_3042)) )
      | ~ linord20386208strict(U_3046) ),
    inference(variable_rename,[status(thm)],[f_786_1]) ).

fof(f_786_3,plain,
    ! [U_3044,U_3042,U_3045,U_3043,U_3046] :
      ( hBOOL(hAPP(U_3046,bool,hAPP(U_3046,fun(U_3046,bool),ord_less(U_3046),hAPP(U_3046,U_3046,hAPP(U_3046,fun(U_3046,U_3046),times_times(U_3046),U_3043),U_3045)),hAPP(U_3046,U_3046,hAPP(U_3046,fun(U_3046,U_3046),times_times(U_3046),U_3042),U_3044)))
      | ~ hBOOL(hAPP(U_3046,bool,hAPP(U_3046,fun(U_3046,bool),ord_less_eq(U_3046),zero_zero(U_3046)),U_3045))
      | ~ hBOOL(hAPP(U_3046,bool,hAPP(U_3046,fun(U_3046,bool),ord_less_eq(U_3046),zero_zero(U_3046)),U_3043))
      | ~ hBOOL(hAPP(U_3046,bool,hAPP(U_3046,fun(U_3046,bool),ord_less(U_3046),U_3045),U_3044))
      | ~ hBOOL(hAPP(U_3046,bool,hAPP(U_3046,fun(U_3046,bool),ord_less(U_3046),U_3043),U_3042))
      | ~ linord20386208strict(U_3046) ),
    inference(definitional_conversion,[status(esa)],[f_786_2]) ).

cnf(f_786_4,plain,
    ( hBOOL(hAPP(U_3046,bool,hAPP(U_3046,fun(U_3046,bool),ord_less(U_3046),hAPP(U_3046,U_3046,hAPP(U_3046,fun(U_3046,U_3046),times_times(U_3046),U_3043),U_3045)),hAPP(U_3046,U_3046,hAPP(U_3046,fun(U_3046,U_3046),times_times(U_3046),U_3042),U_3044)))
    | ~ hBOOL(hAPP(U_3046,bool,hAPP(U_3046,fun(U_3046,bool),ord_less_eq(U_3046),zero_zero(U_3046)),U_3045))
    | ~ hBOOL(hAPP(U_3046,bool,hAPP(U_3046,fun(U_3046,bool),ord_less_eq(U_3046),zero_zero(U_3046)),U_3043))
    | ~ hBOOL(hAPP(U_3046,bool,hAPP(U_3046,fun(U_3046,bool),ord_less(U_3046),U_3045),U_3044))
    | ~ hBOOL(hAPP(U_3046,bool,hAPP(U_3046,fun(U_3046,bool),ord_less(U_3046),U_3043),U_3042))
    | ~ linord20386208strict(U_3046) ),
    inference(clausify,[status(thm)],[f_786_3]) ).

fof(f_787_1,plain,
    ! [X_a] :
      ( ! [C,D,A_1,B] :
          ( 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),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D)))
          | ~ 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(X_a),zero_zero(X_a)),B))
          | ~ 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)) )
      | ~ linord20386208strict(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_716_mult__strict__mono]) ).

fof(f_787_2,plain,
    ! [U_3051] :
      ( ! [U_3050,U_3049,U_3048,U_3047] :
          ( hBOOL(hAPP(U_3051,bool,hAPP(U_3051,fun(U_3051,bool),ord_less(U_3051),hAPP(U_3051,U_3051,hAPP(U_3051,fun(U_3051,U_3051),times_times(U_3051),U_3048),U_3050)),hAPP(U_3051,U_3051,hAPP(U_3051,fun(U_3051,U_3051),times_times(U_3051),U_3047),U_3049)))
          | ~ hBOOL(hAPP(U_3051,bool,hAPP(U_3051,fun(U_3051,bool),ord_less_eq(U_3051),zero_zero(U_3051)),U_3050))
          | ~ hBOOL(hAPP(U_3051,bool,hAPP(U_3051,fun(U_3051,bool),ord_less(U_3051),zero_zero(U_3051)),U_3047))
          | ~ hBOOL(hAPP(U_3051,bool,hAPP(U_3051,fun(U_3051,bool),ord_less(U_3051),U_3050),U_3049))
          | ~ hBOOL(hAPP(U_3051,bool,hAPP(U_3051,fun(U_3051,bool),ord_less(U_3051),U_3048),U_3047)) )
      | ~ linord20386208strict(U_3051) ),
    inference(variable_rename,[status(thm)],[f_787_1]) ).

fof(f_787_3,plain,
    ! [U_3049,U_3050,U_3048,U_3051,U_3047] :
      ( hBOOL(hAPP(U_3051,bool,hAPP(U_3051,fun(U_3051,bool),ord_less(U_3051),hAPP(U_3051,U_3051,hAPP(U_3051,fun(U_3051,U_3051),times_times(U_3051),U_3048),U_3050)),hAPP(U_3051,U_3051,hAPP(U_3051,fun(U_3051,U_3051),times_times(U_3051),U_3047),U_3049)))
      | ~ hBOOL(hAPP(U_3051,bool,hAPP(U_3051,fun(U_3051,bool),ord_less_eq(U_3051),zero_zero(U_3051)),U_3050))
      | ~ hBOOL(hAPP(U_3051,bool,hAPP(U_3051,fun(U_3051,bool),ord_less(U_3051),zero_zero(U_3051)),U_3047))
      | ~ hBOOL(hAPP(U_3051,bool,hAPP(U_3051,fun(U_3051,bool),ord_less(U_3051),U_3050),U_3049))
      | ~ hBOOL(hAPP(U_3051,bool,hAPP(U_3051,fun(U_3051,bool),ord_less(U_3051),U_3048),U_3047))
      | ~ linord20386208strict(U_3051) ),
    inference(definitional_conversion,[status(esa)],[f_787_2]) ).

cnf(f_787_4,plain,
    ( hBOOL(hAPP(U_3051,bool,hAPP(U_3051,fun(U_3051,bool),ord_less(U_3051),hAPP(U_3051,U_3051,hAPP(U_3051,fun(U_3051,U_3051),times_times(U_3051),U_3048),U_3050)),hAPP(U_3051,U_3051,hAPP(U_3051,fun(U_3051,U_3051),times_times(U_3051),U_3047),U_3049)))
    | ~ hBOOL(hAPP(U_3051,bool,hAPP(U_3051,fun(U_3051,bool),ord_less_eq(U_3051),zero_zero(U_3051)),U_3050))
    | ~ hBOOL(hAPP(U_3051,bool,hAPP(U_3051,fun(U_3051,bool),ord_less(U_3051),zero_zero(U_3051)),U_3047))
    | ~ hBOOL(hAPP(U_3051,bool,hAPP(U_3051,fun(U_3051,bool),ord_less(U_3051),U_3050),U_3049))
    | ~ hBOOL(hAPP(U_3051,bool,hAPP(U_3051,fun(U_3051,bool),ord_less(U_3051),U_3048),U_3047))
    | ~ linord20386208strict(U_3051) ),
    inference(clausify,[status(thm)],[f_787_3]) ).

fof(f_788_1,plain,
    ! [X_b] :
      ( ! [A_2,B_3,C_1] :
          ( ( ( 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),times_times(X_b),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),B_3)))
              | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),B_3),A_2)) )
            & ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),B_3),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),times_times(X_b),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),B_3))) ) )
          | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),zero_zero(X_b))) )
      | ~ linord581940658strict(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_717_mult__le__cancel__left__neg]) ).

fof(f_788_2,plain,
    ! [U_3055] :
      ( ! [U_3054,U_3053,U_3052] :
          ( ( ( hBOOL(hAPP(U_3055,bool,hAPP(U_3055,fun(U_3055,bool),ord_less_eq(U_3055),hAPP(U_3055,U_3055,hAPP(U_3055,fun(U_3055,U_3055),times_times(U_3055),U_3052),U_3054)),hAPP(U_3055,U_3055,hAPP(U_3055,fun(U_3055,U_3055),times_times(U_3055),U_3052),U_3053)))
              | ~ hBOOL(hAPP(U_3055,bool,hAPP(U_3055,fun(U_3055,bool),ord_less_eq(U_3055),U_3053),U_3054)) )
            & ( hBOOL(hAPP(U_3055,bool,hAPP(U_3055,fun(U_3055,bool),ord_less_eq(U_3055),U_3053),U_3054))
              | ~ hBOOL(hAPP(U_3055,bool,hAPP(U_3055,fun(U_3055,bool),ord_less_eq(U_3055),hAPP(U_3055,U_3055,hAPP(U_3055,fun(U_3055,U_3055),times_times(U_3055),U_3052),U_3054)),hAPP(U_3055,U_3055,hAPP(U_3055,fun(U_3055,U_3055),times_times(U_3055),U_3052),U_3053))) ) )
          | ~ hBOOL(hAPP(U_3055,bool,hAPP(U_3055,fun(U_3055,bool),ord_less(U_3055),U_3052),zero_zero(U_3055))) )
      | ~ linord581940658strict(U_3055) ),
    inference(variable_rename,[status(thm)],[f_788_1]) ).

fof(f_788_3,plain,
    ( ! [U_3053,U_3054,U_3052,U_3055] :
        ( hBOOL(hAPP(U_3055,bool,hAPP(U_3055,fun(U_3055,bool),ord_less_eq(U_3055),hAPP(U_3055,U_3055,hAPP(U_3055,fun(U_3055,U_3055),times_times(U_3055),U_3052),U_3054)),hAPP(U_3055,U_3055,hAPP(U_3055,fun(U_3055,U_3055),times_times(U_3055),U_3052),U_3053)))
        | ~ hBOOL(hAPP(U_3055,bool,hAPP(U_3055,fun(U_3055,bool),ord_less_eq(U_3055),U_3053),U_3054))
        | ~ sP215(U_3053,U_3054,U_3052,U_3055) )
    & ! [U_3053,U_3054,U_3052,U_3055] :
        ( hBOOL(hAPP(U_3055,bool,hAPP(U_3055,fun(U_3055,bool),ord_less_eq(U_3055),U_3053),U_3054))
        | ~ hBOOL(hAPP(U_3055,bool,hAPP(U_3055,fun(U_3055,bool),ord_less_eq(U_3055),hAPP(U_3055,U_3055,hAPP(U_3055,fun(U_3055,U_3055),times_times(U_3055),U_3052),U_3054)),hAPP(U_3055,U_3055,hAPP(U_3055,fun(U_3055,U_3055),times_times(U_3055),U_3052),U_3053)))
        | ~ sP215(U_3053,U_3054,U_3052,U_3055) )
    & ! [U_3053,U_3054,U_3052,U_3055] :
        ( sP215(U_3053,U_3054,U_3052,U_3055)
        | ~ hBOOL(hAPP(U_3055,bool,hAPP(U_3055,fun(U_3055,bool),ord_less(U_3055),U_3052),zero_zero(U_3055)))
        | ~ linord581940658strict(U_3055) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP215])],[f_788_2]) ).

cnf(f_788_4,plain,
    ( sP215(U_3053,U_3054,U_3052,U_3055)
    | ~ hBOOL(hAPP(U_3055,bool,hAPP(U_3055,fun(U_3055,bool),ord_less(U_3055),U_3052),zero_zero(U_3055)))
    | ~ linord581940658strict(U_3055) ),
    inference(clausify,[status(thm)],[f_788_3]) ).

cnf(f_788_5,plain,
    ( hBOOL(hAPP(U_3055,bool,hAPP(U_3055,fun(U_3055,bool),ord_less_eq(U_3055),U_3053),U_3054))
    | ~ hBOOL(hAPP(U_3055,bool,hAPP(U_3055,fun(U_3055,bool),ord_less_eq(U_3055),hAPP(U_3055,U_3055,hAPP(U_3055,fun(U_3055,U_3055),times_times(U_3055),U_3052),U_3054)),hAPP(U_3055,U_3055,hAPP(U_3055,fun(U_3055,U_3055),times_times(U_3055),U_3052),U_3053)))
    | ~ sP215(U_3053,U_3054,U_3052,U_3055) ),
    inference(clausify,[status(thm)],[f_788_3]) ).

cnf(f_788_6,plain,
    ( hBOOL(hAPP(U_3055,bool,hAPP(U_3055,fun(U_3055,bool),ord_less_eq(U_3055),hAPP(U_3055,U_3055,hAPP(U_3055,fun(U_3055,U_3055),times_times(U_3055),U_3052),U_3054)),hAPP(U_3055,U_3055,hAPP(U_3055,fun(U_3055,U_3055),times_times(U_3055),U_3052),U_3053)))
    | ~ hBOOL(hAPP(U_3055,bool,hAPP(U_3055,fun(U_3055,bool),ord_less_eq(U_3055),U_3053),U_3054))
    | ~ sP215(U_3053,U_3054,U_3052,U_3055) ),
    inference(clausify,[status(thm)],[f_788_3]) ).

fof(f_789_1,plain,
    ! [X_b] :
      ( ! [A_2,B_3,C_1] :
          ( ( ( 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),times_times(X_b),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),B_3)))
              | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),B_3)) )
            & ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),B_3))
              | ~ 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),times_times(X_b),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),B_3))) ) )
          | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),C_1)) )
      | ~ linord581940658strict(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_718_mult__le__cancel__left__pos]) ).

fof(f_789_2,plain,
    ! [U_3059] :
      ( ! [U_3058,U_3057,U_3056] :
          ( ( ( hBOOL(hAPP(U_3059,bool,hAPP(U_3059,fun(U_3059,bool),ord_less_eq(U_3059),hAPP(U_3059,U_3059,hAPP(U_3059,fun(U_3059,U_3059),times_times(U_3059),U_3056),U_3058)),hAPP(U_3059,U_3059,hAPP(U_3059,fun(U_3059,U_3059),times_times(U_3059),U_3056),U_3057)))
              | ~ hBOOL(hAPP(U_3059,bool,hAPP(U_3059,fun(U_3059,bool),ord_less_eq(U_3059),U_3058),U_3057)) )
            & ( hBOOL(hAPP(U_3059,bool,hAPP(U_3059,fun(U_3059,bool),ord_less_eq(U_3059),U_3058),U_3057))
              | ~ hBOOL(hAPP(U_3059,bool,hAPP(U_3059,fun(U_3059,bool),ord_less_eq(U_3059),hAPP(U_3059,U_3059,hAPP(U_3059,fun(U_3059,U_3059),times_times(U_3059),U_3056),U_3058)),hAPP(U_3059,U_3059,hAPP(U_3059,fun(U_3059,U_3059),times_times(U_3059),U_3056),U_3057))) ) )
          | ~ hBOOL(hAPP(U_3059,bool,hAPP(U_3059,fun(U_3059,bool),ord_less(U_3059),zero_zero(U_3059)),U_3056)) )
      | ~ linord581940658strict(U_3059) ),
    inference(variable_rename,[status(thm)],[f_789_1]) ).

fof(f_789_3,plain,
    ( ! [U_3059,U_3056,U_3057,U_3058] :
        ( hBOOL(hAPP(U_3059,bool,hAPP(U_3059,fun(U_3059,bool),ord_less_eq(U_3059),hAPP(U_3059,U_3059,hAPP(U_3059,fun(U_3059,U_3059),times_times(U_3059),U_3056),U_3058)),hAPP(U_3059,U_3059,hAPP(U_3059,fun(U_3059,U_3059),times_times(U_3059),U_3056),U_3057)))
        | ~ hBOOL(hAPP(U_3059,bool,hAPP(U_3059,fun(U_3059,bool),ord_less_eq(U_3059),U_3058),U_3057))
        | ~ sP216(U_3059,U_3056,U_3057,U_3058) )
    & ! [U_3059,U_3056,U_3057,U_3058] :
        ( hBOOL(hAPP(U_3059,bool,hAPP(U_3059,fun(U_3059,bool),ord_less_eq(U_3059),U_3058),U_3057))
        | ~ hBOOL(hAPP(U_3059,bool,hAPP(U_3059,fun(U_3059,bool),ord_less_eq(U_3059),hAPP(U_3059,U_3059,hAPP(U_3059,fun(U_3059,U_3059),times_times(U_3059),U_3056),U_3058)),hAPP(U_3059,U_3059,hAPP(U_3059,fun(U_3059,U_3059),times_times(U_3059),U_3056),U_3057)))
        | ~ sP216(U_3059,U_3056,U_3057,U_3058) )
    & ! [U_3059,U_3056,U_3057,U_3058] :
        ( sP216(U_3059,U_3056,U_3057,U_3058)
        | ~ hBOOL(hAPP(U_3059,bool,hAPP(U_3059,fun(U_3059,bool),ord_less(U_3059),zero_zero(U_3059)),U_3056))
        | ~ linord581940658strict(U_3059) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP216])],[f_789_2]) ).

cnf(f_789_4,plain,
    ( sP216(U_3059,U_3056,U_3057,U_3058)
    | ~ hBOOL(hAPP(U_3059,bool,hAPP(U_3059,fun(U_3059,bool),ord_less(U_3059),zero_zero(U_3059)),U_3056))
    | ~ linord581940658strict(U_3059) ),
    inference(clausify,[status(thm)],[f_789_3]) ).

cnf(f_789_5,plain,
    ( hBOOL(hAPP(U_3059,bool,hAPP(U_3059,fun(U_3059,bool),ord_less_eq(U_3059),U_3058),U_3057))
    | ~ hBOOL(hAPP(U_3059,bool,hAPP(U_3059,fun(U_3059,bool),ord_less_eq(U_3059),hAPP(U_3059,U_3059,hAPP(U_3059,fun(U_3059,U_3059),times_times(U_3059),U_3056),U_3058)),hAPP(U_3059,U_3059,hAPP(U_3059,fun(U_3059,U_3059),times_times(U_3059),U_3056),U_3057)))
    | ~ sP216(U_3059,U_3056,U_3057,U_3058) ),
    inference(clausify,[status(thm)],[f_789_3]) ).

cnf(f_789_6,plain,
    ( hBOOL(hAPP(U_3059,bool,hAPP(U_3059,fun(U_3059,bool),ord_less_eq(U_3059),hAPP(U_3059,U_3059,hAPP(U_3059,fun(U_3059,U_3059),times_times(U_3059),U_3056),U_3058)),hAPP(U_3059,U_3059,hAPP(U_3059,fun(U_3059,U_3059),times_times(U_3059),U_3056),U_3057)))
    | ~ hBOOL(hAPP(U_3059,bool,hAPP(U_3059,fun(U_3059,bool),ord_less_eq(U_3059),U_3058),U_3057))
    | ~ sP216(U_3059,U_3056,U_3057,U_3058) ),
    inference(clausify,[status(thm)],[f_789_3]) ).

fof(f_790_1,plain,
    ! [X_b] :
      ( ! [X_1,Y_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),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),X_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Y_2),Y_2))),zero_zero(X_b)))
            | ti(X_b,Y_2) != zero_zero(X_b)
            | ti(X_b,X_1) != zero_zero(X_b) )
          & ( ( ti(X_b,Y_2) = zero_zero(X_b)
              & ti(X_b,X_1) = 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),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),X_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Y_2),Y_2))),zero_zero(X_b))) ) )
      | ~ linord581940658strict(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_719_sum__squares__le__zero__iff]) ).

fof(f_790_2,plain,
    ! [U_3062] :
      ( ! [U_3061,U_3060] :
          ( ( hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),ord_less_eq(U_3062),hAPP(U_3062,U_3062,hAPP(U_3062,fun(U_3062,U_3062),plus_plus(U_3062),hAPP(U_3062,U_3062,hAPP(U_3062,fun(U_3062,U_3062),times_times(U_3062),U_3061),U_3061)),hAPP(U_3062,U_3062,hAPP(U_3062,fun(U_3062,U_3062),times_times(U_3062),U_3060),U_3060))),zero_zero(U_3062)))
            | ti(U_3062,U_3060) != zero_zero(U_3062)
            | ti(U_3062,U_3061) != zero_zero(U_3062) )
          & ( ( ti(U_3062,U_3060) = zero_zero(U_3062)
              & ti(U_3062,U_3061) = zero_zero(U_3062) )
            | ~ hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),ord_less_eq(U_3062),hAPP(U_3062,U_3062,hAPP(U_3062,fun(U_3062,U_3062),plus_plus(U_3062),hAPP(U_3062,U_3062,hAPP(U_3062,fun(U_3062,U_3062),times_times(U_3062),U_3061),U_3061)),hAPP(U_3062,U_3062,hAPP(U_3062,fun(U_3062,U_3062),times_times(U_3062),U_3060),U_3060))),zero_zero(U_3062))) ) )
      | ~ linord581940658strict(U_3062) ),
    inference(variable_rename,[status(thm)],[f_790_1]) ).

fof(f_790_3,plain,
    ! [U_3062] :
      ( ( ! [U_3066,U_3064] :
            ( hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),ord_less_eq(U_3062),hAPP(U_3062,U_3062,hAPP(U_3062,fun(U_3062,U_3062),plus_plus(U_3062),hAPP(U_3062,U_3062,hAPP(U_3062,fun(U_3062,U_3062),times_times(U_3062),U_3066),U_3066)),hAPP(U_3062,U_3062,hAPP(U_3062,fun(U_3062,U_3062),times_times(U_3062),U_3064),U_3064))),zero_zero(U_3062)))
            | ti(U_3062,U_3064) != zero_zero(U_3062)
            | ti(U_3062,U_3066) != zero_zero(U_3062) )
        & ! [U_3065,U_3063] :
            ( ( ti(U_3062,U_3063) = zero_zero(U_3062)
              & ti(U_3062,U_3065) = zero_zero(U_3062) )
            | ~ hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),ord_less_eq(U_3062),hAPP(U_3062,U_3062,hAPP(U_3062,fun(U_3062,U_3062),plus_plus(U_3062),hAPP(U_3062,U_3062,hAPP(U_3062,fun(U_3062,U_3062),times_times(U_3062),U_3065),U_3065)),hAPP(U_3062,U_3062,hAPP(U_3062,fun(U_3062,U_3062),times_times(U_3062),U_3063),U_3063))),zero_zero(U_3062))) ) )
      | ~ linord581940658strict(U_3062) ),
    inference(miniscope,[status(thm)],[f_790_2]) ).

fof(f_790_4,plain,
    ( ! [U_3062,U_3065,U_3063] :
        ( ti(U_3062,U_3063) = zero_zero(U_3062)
        | ~ sP217(U_3062,U_3065,U_3063) )
    & ! [U_3062,U_3065,U_3063] :
        ( ti(U_3062,U_3065) = zero_zero(U_3062)
        | ~ sP217(U_3062,U_3065,U_3063) )
    & ! [U_3062,U_3065,U_3064,U_3063,U_3066] :
        ( hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),ord_less_eq(U_3062),hAPP(U_3062,U_3062,hAPP(U_3062,fun(U_3062,U_3062),plus_plus(U_3062),hAPP(U_3062,U_3062,hAPP(U_3062,fun(U_3062,U_3062),times_times(U_3062),U_3066),U_3066)),hAPP(U_3062,U_3062,hAPP(U_3062,fun(U_3062,U_3062),times_times(U_3062),U_3064),U_3064))),zero_zero(U_3062)))
        | ti(U_3062,U_3064) != zero_zero(U_3062)
        | ti(U_3062,U_3066) != zero_zero(U_3062)
        | ~ sP218(U_3062,U_3065,U_3064,U_3063,U_3066) )
    & ! [U_3062,U_3065,U_3064,U_3063,U_3066] :
        ( sP217(U_3062,U_3065,U_3063)
        | ~ hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),ord_less_eq(U_3062),hAPP(U_3062,U_3062,hAPP(U_3062,fun(U_3062,U_3062),plus_plus(U_3062),hAPP(U_3062,U_3062,hAPP(U_3062,fun(U_3062,U_3062),times_times(U_3062),U_3065),U_3065)),hAPP(U_3062,U_3062,hAPP(U_3062,fun(U_3062,U_3062),times_times(U_3062),U_3063),U_3063))),zero_zero(U_3062)))
        | ~ sP218(U_3062,U_3065,U_3064,U_3063,U_3066) )
    & ! [U_3062,U_3065,U_3064,U_3063,U_3066] :
        ( sP218(U_3062,U_3065,U_3064,U_3063,U_3066)
        | ~ linord581940658strict(U_3062) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP217,sP218])],[f_790_3]) ).

cnf(f_790_5,plain,
    ( sP218(U_3062,U_3065,U_3064,U_3063,U_3066)
    | ~ linord581940658strict(U_3062) ),
    inference(clausify,[status(thm)],[f_790_4]) ).

cnf(f_790_6,plain,
    ( sP217(U_3062,U_3065,U_3063)
    | ~ hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),ord_less_eq(U_3062),hAPP(U_3062,U_3062,hAPP(U_3062,fun(U_3062,U_3062),plus_plus(U_3062),hAPP(U_3062,U_3062,hAPP(U_3062,fun(U_3062,U_3062),times_times(U_3062),U_3065),U_3065)),hAPP(U_3062,U_3062,hAPP(U_3062,fun(U_3062,U_3062),times_times(U_3062),U_3063),U_3063))),zero_zero(U_3062)))
    | ~ sP218(U_3062,U_3065,U_3064,U_3063,U_3066) ),
    inference(clausify,[status(thm)],[f_790_4]) ).

cnf(f_790_7,plain,
    ( hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),ord_less_eq(U_3062),hAPP(U_3062,U_3062,hAPP(U_3062,fun(U_3062,U_3062),plus_plus(U_3062),hAPP(U_3062,U_3062,hAPP(U_3062,fun(U_3062,U_3062),times_times(U_3062),U_3066),U_3066)),hAPP(U_3062,U_3062,hAPP(U_3062,fun(U_3062,U_3062),times_times(U_3062),U_3064),U_3064))),zero_zero(U_3062)))
    | ti(U_3062,U_3064) != zero_zero(U_3062)
    | ti(U_3062,U_3066) != zero_zero(U_3062)
    | ~ sP218(U_3062,U_3065,U_3064,U_3063,U_3066) ),
    inference(clausify,[status(thm)],[f_790_4]) ).

cnf(f_790_8,plain,
    ( ti(U_3062,U_3065) = zero_zero(U_3062)
    | ~ sP217(U_3062,U_3065,U_3063) ),
    inference(clausify,[status(thm)],[f_790_4]) ).

cnf(f_790_9,plain,
    ( ti(U_3062,U_3063) = zero_zero(U_3062)
    | ~ sP217(U_3062,U_3065,U_3063) ),
    inference(clausify,[status(thm)],[f_790_4]) ).

fof(f_791_1,plain,
    ! [X_a] :
      ( ! [X,Y] : 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),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),Y))))
      | ~ linordered_ring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_720_sum__squares__ge__zero]) ).

fof(f_791_2,plain,
    ! [U_3069] :
      ( ! [U_3068,U_3067] : hBOOL(hAPP(U_3069,bool,hAPP(U_3069,fun(U_3069,bool),ord_less_eq(U_3069),zero_zero(U_3069)),hAPP(U_3069,U_3069,hAPP(U_3069,fun(U_3069,U_3069),plus_plus(U_3069),hAPP(U_3069,U_3069,hAPP(U_3069,fun(U_3069,U_3069),times_times(U_3069),U_3068),U_3068)),hAPP(U_3069,U_3069,hAPP(U_3069,fun(U_3069,U_3069),times_times(U_3069),U_3067),U_3067))))
      | ~ linordered_ring(U_3069) ),
    inference(variable_rename,[status(thm)],[f_791_1]) ).

fof(f_791_3,plain,
    ! [U_3069,U_3067,U_3068] :
      ( hBOOL(hAPP(U_3069,bool,hAPP(U_3069,fun(U_3069,bool),ord_less_eq(U_3069),zero_zero(U_3069)),hAPP(U_3069,U_3069,hAPP(U_3069,fun(U_3069,U_3069),plus_plus(U_3069),hAPP(U_3069,U_3069,hAPP(U_3069,fun(U_3069,U_3069),times_times(U_3069),U_3068),U_3068)),hAPP(U_3069,U_3069,hAPP(U_3069,fun(U_3069,U_3069),times_times(U_3069),U_3067),U_3067))))
      | ~ linordered_ring(U_3069) ),
    inference(definitional_conversion,[status(esa)],[f_791_2]) ).

cnf(f_791_4,plain,
    ( hBOOL(hAPP(U_3069,bool,hAPP(U_3069,fun(U_3069,bool),ord_less_eq(U_3069),zero_zero(U_3069)),hAPP(U_3069,U_3069,hAPP(U_3069,fun(U_3069,U_3069),plus_plus(U_3069),hAPP(U_3069,U_3069,hAPP(U_3069,fun(U_3069,U_3069),times_times(U_3069),U_3068),U_3068)),hAPP(U_3069,U_3069,hAPP(U_3069,fun(U_3069,U_3069),times_times(U_3069),U_3067),U_3067))))
    | ~ linordered_ring(U_3069) ),
    inference(clausify,[status(thm)],[f_791_3]) ).

fof(f_792_1,plain,
    ! [X_a] :
      ( ! [X,Y] : ~ 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),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),Y))),zero_zero(X_a)))
      | ~ linordered_ring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_721_not__sum__squares__lt__zero]) ).

fof(f_792_2,plain,
    ! [U_3072] :
      ( ! [U_3071,U_3070] : ~ hBOOL(hAPP(U_3072,bool,hAPP(U_3072,fun(U_3072,bool),ord_less(U_3072),hAPP(U_3072,U_3072,hAPP(U_3072,fun(U_3072,U_3072),plus_plus(U_3072),hAPP(U_3072,U_3072,hAPP(U_3072,fun(U_3072,U_3072),times_times(U_3072),U_3071),U_3071)),hAPP(U_3072,U_3072,hAPP(U_3072,fun(U_3072,U_3072),times_times(U_3072),U_3070),U_3070))),zero_zero(U_3072)))
      | ~ linordered_ring(U_3072) ),
    inference(variable_rename,[status(thm)],[f_792_1]) ).

fof(f_792_3,plain,
    ! [U_3072,U_3070,U_3071] :
      ( ~ hBOOL(hAPP(U_3072,bool,hAPP(U_3072,fun(U_3072,bool),ord_less(U_3072),hAPP(U_3072,U_3072,hAPP(U_3072,fun(U_3072,U_3072),plus_plus(U_3072),hAPP(U_3072,U_3072,hAPP(U_3072,fun(U_3072,U_3072),times_times(U_3072),U_3071),U_3071)),hAPP(U_3072,U_3072,hAPP(U_3072,fun(U_3072,U_3072),times_times(U_3072),U_3070),U_3070))),zero_zero(U_3072)))
      | ~ linordered_ring(U_3072) ),
    inference(definitional_conversion,[status(esa)],[f_792_2]) ).

cnf(f_792_4,plain,
    ( ~ hBOOL(hAPP(U_3072,bool,hAPP(U_3072,fun(U_3072,bool),ord_less(U_3072),hAPP(U_3072,U_3072,hAPP(U_3072,fun(U_3072,U_3072),plus_plus(U_3072),hAPP(U_3072,U_3072,hAPP(U_3072,fun(U_3072,U_3072),times_times(U_3072),U_3071),U_3071)),hAPP(U_3072,U_3072,hAPP(U_3072,fun(U_3072,U_3072),times_times(U_3072),U_3070),U_3070))),zero_zero(U_3072)))
    | ~ linordered_ring(U_3072) ),
    inference(clausify,[status(thm)],[f_792_3]) ).

fof(f_793_1,plain,
    ! [X_b] :
      ( ! [X_1,Y_2] :
          ( ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),X_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Y_2),Y_2))))
            | ( ti(X_b,Y_2) = zero_zero(X_b)
              & ti(X_b,X_1) = zero_zero(X_b) ) )
          & ( ti(X_b,Y_2) != zero_zero(X_b)
            | ti(X_b,X_1) != zero_zero(X_b)
            | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),X_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Y_2),Y_2)))) ) )
      | ~ linord581940658strict(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_722_sum__squares__gt__zero__iff]) ).

fof(f_793_2,plain,
    ! [U_3075] :
      ( ! [U_3074,U_3073] :
          ( ( hBOOL(hAPP(U_3075,bool,hAPP(U_3075,fun(U_3075,bool),ord_less(U_3075),zero_zero(U_3075)),hAPP(U_3075,U_3075,hAPP(U_3075,fun(U_3075,U_3075),plus_plus(U_3075),hAPP(U_3075,U_3075,hAPP(U_3075,fun(U_3075,U_3075),times_times(U_3075),U_3074),U_3074)),hAPP(U_3075,U_3075,hAPP(U_3075,fun(U_3075,U_3075),times_times(U_3075),U_3073),U_3073))))
            | ( ti(U_3075,U_3073) = zero_zero(U_3075)
              & ti(U_3075,U_3074) = zero_zero(U_3075) ) )
          & ( ti(U_3075,U_3073) != zero_zero(U_3075)
            | ti(U_3075,U_3074) != zero_zero(U_3075)
            | ~ hBOOL(hAPP(U_3075,bool,hAPP(U_3075,fun(U_3075,bool),ord_less(U_3075),zero_zero(U_3075)),hAPP(U_3075,U_3075,hAPP(U_3075,fun(U_3075,U_3075),plus_plus(U_3075),hAPP(U_3075,U_3075,hAPP(U_3075,fun(U_3075,U_3075),times_times(U_3075),U_3074),U_3074)),hAPP(U_3075,U_3075,hAPP(U_3075,fun(U_3075,U_3075),times_times(U_3075),U_3073),U_3073)))) ) )
      | ~ linord581940658strict(U_3075) ),
    inference(variable_rename,[status(thm)],[f_793_1]) ).

fof(f_793_3,plain,
    ! [U_3075] :
      ( ( ! [U_3079,U_3077] :
            ( hBOOL(hAPP(U_3075,bool,hAPP(U_3075,fun(U_3075,bool),ord_less(U_3075),zero_zero(U_3075)),hAPP(U_3075,U_3075,hAPP(U_3075,fun(U_3075,U_3075),plus_plus(U_3075),hAPP(U_3075,U_3075,hAPP(U_3075,fun(U_3075,U_3075),times_times(U_3075),U_3079),U_3079)),hAPP(U_3075,U_3075,hAPP(U_3075,fun(U_3075,U_3075),times_times(U_3075),U_3077),U_3077))))
            | ( ti(U_3075,U_3077) = zero_zero(U_3075)
              & ti(U_3075,U_3079) = zero_zero(U_3075) ) )
        & ! [U_3078,U_3076] :
            ( ti(U_3075,U_3076) != zero_zero(U_3075)
            | ti(U_3075,U_3078) != zero_zero(U_3075)
            | ~ hBOOL(hAPP(U_3075,bool,hAPP(U_3075,fun(U_3075,bool),ord_less(U_3075),zero_zero(U_3075)),hAPP(U_3075,U_3075,hAPP(U_3075,fun(U_3075,U_3075),plus_plus(U_3075),hAPP(U_3075,U_3075,hAPP(U_3075,fun(U_3075,U_3075),times_times(U_3075),U_3078),U_3078)),hAPP(U_3075,U_3075,hAPP(U_3075,fun(U_3075,U_3075),times_times(U_3075),U_3076),U_3076)))) ) )
      | ~ linord581940658strict(U_3075) ),
    inference(miniscope,[status(thm)],[f_793_2]) ).

fof(f_793_4,plain,
    ( ! [U_3075,U_3077,U_3079] :
        ( ti(U_3075,U_3077) = zero_zero(U_3075)
        | ~ sP219(U_3075,U_3077,U_3079) )
    & ! [U_3075,U_3077,U_3079] :
        ( ti(U_3075,U_3079) = zero_zero(U_3075)
        | ~ sP219(U_3075,U_3077,U_3079) )
    & ! [U_3075,U_3077,U_3076,U_3078,U_3079] :
        ( hBOOL(hAPP(U_3075,bool,hAPP(U_3075,fun(U_3075,bool),ord_less(U_3075),zero_zero(U_3075)),hAPP(U_3075,U_3075,hAPP(U_3075,fun(U_3075,U_3075),plus_plus(U_3075),hAPP(U_3075,U_3075,hAPP(U_3075,fun(U_3075,U_3075),times_times(U_3075),U_3079),U_3079)),hAPP(U_3075,U_3075,hAPP(U_3075,fun(U_3075,U_3075),times_times(U_3075),U_3077),U_3077))))
        | sP219(U_3075,U_3077,U_3079)
        | ~ sP220(U_3075,U_3077,U_3076,U_3078,U_3079) )
    & ! [U_3075,U_3077,U_3076,U_3078,U_3079] :
        ( ti(U_3075,U_3076) != zero_zero(U_3075)
        | ti(U_3075,U_3078) != zero_zero(U_3075)
        | ~ hBOOL(hAPP(U_3075,bool,hAPP(U_3075,fun(U_3075,bool),ord_less(U_3075),zero_zero(U_3075)),hAPP(U_3075,U_3075,hAPP(U_3075,fun(U_3075,U_3075),plus_plus(U_3075),hAPP(U_3075,U_3075,hAPP(U_3075,fun(U_3075,U_3075),times_times(U_3075),U_3078),U_3078)),hAPP(U_3075,U_3075,hAPP(U_3075,fun(U_3075,U_3075),times_times(U_3075),U_3076),U_3076))))
        | ~ sP220(U_3075,U_3077,U_3076,U_3078,U_3079) )
    & ! [U_3075,U_3077,U_3076,U_3078,U_3079] :
        ( sP220(U_3075,U_3077,U_3076,U_3078,U_3079)
        | ~ linord581940658strict(U_3075) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP219,sP220])],[f_793_3]) ).

cnf(f_793_5,plain,
    ( sP220(U_3075,U_3077,U_3076,U_3078,U_3079)
    | ~ linord581940658strict(U_3075) ),
    inference(clausify,[status(thm)],[f_793_4]) ).

cnf(f_793_6,plain,
    ( ti(U_3075,U_3076) != zero_zero(U_3075)
    | ti(U_3075,U_3078) != zero_zero(U_3075)
    | ~ hBOOL(hAPP(U_3075,bool,hAPP(U_3075,fun(U_3075,bool),ord_less(U_3075),zero_zero(U_3075)),hAPP(U_3075,U_3075,hAPP(U_3075,fun(U_3075,U_3075),plus_plus(U_3075),hAPP(U_3075,U_3075,hAPP(U_3075,fun(U_3075,U_3075),times_times(U_3075),U_3078),U_3078)),hAPP(U_3075,U_3075,hAPP(U_3075,fun(U_3075,U_3075),times_times(U_3075),U_3076),U_3076))))
    | ~ sP220(U_3075,U_3077,U_3076,U_3078,U_3079) ),
    inference(clausify,[status(thm)],[f_793_4]) ).

cnf(f_793_7,plain,
    ( hBOOL(hAPP(U_3075,bool,hAPP(U_3075,fun(U_3075,bool),ord_less(U_3075),zero_zero(U_3075)),hAPP(U_3075,U_3075,hAPP(U_3075,fun(U_3075,U_3075),plus_plus(U_3075),hAPP(U_3075,U_3075,hAPP(U_3075,fun(U_3075,U_3075),times_times(U_3075),U_3079),U_3079)),hAPP(U_3075,U_3075,hAPP(U_3075,fun(U_3075,U_3075),times_times(U_3075),U_3077),U_3077))))
    | sP219(U_3075,U_3077,U_3079)
    | ~ sP220(U_3075,U_3077,U_3076,U_3078,U_3079) ),
    inference(clausify,[status(thm)],[f_793_4]) ).

cnf(f_793_8,plain,
    ( ti(U_3075,U_3079) = zero_zero(U_3075)
    | ~ sP219(U_3075,U_3077,U_3079) ),
    inference(clausify,[status(thm)],[f_793_4]) ).

cnf(f_793_9,plain,
    ( ti(U_3075,U_3077) = zero_zero(U_3075)
    | ~ sP219(U_3075,U_3077,U_3079) ),
    inference(clausify,[status(thm)],[f_793_4]) ).

fof(f_794_1,plain,
    ! [X_a] :
      ( ! [Y,X] :
          ( 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),times_times(X_a),Y),X)),X))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),one_one(X_a)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Y))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X)) )
      | ~ linordered_idom(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_723_mult__left__le__one__le]) ).

fof(f_794_2,plain,
    ! [U_3082] :
      ( ! [U_3081,U_3080] :
          ( hBOOL(hAPP(U_3082,bool,hAPP(U_3082,fun(U_3082,bool),ord_less_eq(U_3082),hAPP(U_3082,U_3082,hAPP(U_3082,fun(U_3082,U_3082),times_times(U_3082),U_3081),U_3080)),U_3080))
          | ~ hBOOL(hAPP(U_3082,bool,hAPP(U_3082,fun(U_3082,bool),ord_less_eq(U_3082),U_3081),one_one(U_3082)))
          | ~ hBOOL(hAPP(U_3082,bool,hAPP(U_3082,fun(U_3082,bool),ord_less_eq(U_3082),zero_zero(U_3082)),U_3081))
          | ~ hBOOL(hAPP(U_3082,bool,hAPP(U_3082,fun(U_3082,bool),ord_less_eq(U_3082),zero_zero(U_3082)),U_3080)) )
      | ~ linordered_idom(U_3082) ),
    inference(variable_rename,[status(thm)],[f_794_1]) ).

fof(f_794_3,plain,
    ! [U_3080,U_3082,U_3081] :
      ( hBOOL(hAPP(U_3082,bool,hAPP(U_3082,fun(U_3082,bool),ord_less_eq(U_3082),hAPP(U_3082,U_3082,hAPP(U_3082,fun(U_3082,U_3082),times_times(U_3082),U_3081),U_3080)),U_3080))
      | ~ hBOOL(hAPP(U_3082,bool,hAPP(U_3082,fun(U_3082,bool),ord_less_eq(U_3082),U_3081),one_one(U_3082)))
      | ~ hBOOL(hAPP(U_3082,bool,hAPP(U_3082,fun(U_3082,bool),ord_less_eq(U_3082),zero_zero(U_3082)),U_3081))
      | ~ hBOOL(hAPP(U_3082,bool,hAPP(U_3082,fun(U_3082,bool),ord_less_eq(U_3082),zero_zero(U_3082)),U_3080))
      | ~ linordered_idom(U_3082) ),
    inference(definitional_conversion,[status(esa)],[f_794_2]) ).

cnf(f_794_4,plain,
    ( hBOOL(hAPP(U_3082,bool,hAPP(U_3082,fun(U_3082,bool),ord_less_eq(U_3082),hAPP(U_3082,U_3082,hAPP(U_3082,fun(U_3082,U_3082),times_times(U_3082),U_3081),U_3080)),U_3080))
    | ~ hBOOL(hAPP(U_3082,bool,hAPP(U_3082,fun(U_3082,bool),ord_less_eq(U_3082),U_3081),one_one(U_3082)))
    | ~ hBOOL(hAPP(U_3082,bool,hAPP(U_3082,fun(U_3082,bool),ord_less_eq(U_3082),zero_zero(U_3082)),U_3081))
    | ~ hBOOL(hAPP(U_3082,bool,hAPP(U_3082,fun(U_3082,bool),ord_less_eq(U_3082),zero_zero(U_3082)),U_3080))
    | ~ linordered_idom(U_3082) ),
    inference(clausify,[status(thm)],[f_794_3]) ).

fof(f_795_1,plain,
    ! [X_a] :
      ( ! [Y,X] :
          ( 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),times_times(X_a),X),Y)),X))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),one_one(X_a)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Y))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X)) )
      | ~ linordered_idom(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_724_mult__right__le__one__le]) ).

fof(f_795_2,plain,
    ! [U_3085] :
      ( ! [U_3084,U_3083] :
          ( hBOOL(hAPP(U_3085,bool,hAPP(U_3085,fun(U_3085,bool),ord_less_eq(U_3085),hAPP(U_3085,U_3085,hAPP(U_3085,fun(U_3085,U_3085),times_times(U_3085),U_3083),U_3084)),U_3083))
          | ~ hBOOL(hAPP(U_3085,bool,hAPP(U_3085,fun(U_3085,bool),ord_less_eq(U_3085),U_3084),one_one(U_3085)))
          | ~ hBOOL(hAPP(U_3085,bool,hAPP(U_3085,fun(U_3085,bool),ord_less_eq(U_3085),zero_zero(U_3085)),U_3084))
          | ~ hBOOL(hAPP(U_3085,bool,hAPP(U_3085,fun(U_3085,bool),ord_less_eq(U_3085),zero_zero(U_3085)),U_3083)) )
      | ~ linordered_idom(U_3085) ),
    inference(variable_rename,[status(thm)],[f_795_1]) ).

fof(f_795_3,plain,
    ! [U_3083,U_3085,U_3084] :
      ( hBOOL(hAPP(U_3085,bool,hAPP(U_3085,fun(U_3085,bool),ord_less_eq(U_3085),hAPP(U_3085,U_3085,hAPP(U_3085,fun(U_3085,U_3085),times_times(U_3085),U_3083),U_3084)),U_3083))
      | ~ hBOOL(hAPP(U_3085,bool,hAPP(U_3085,fun(U_3085,bool),ord_less_eq(U_3085),U_3084),one_one(U_3085)))
      | ~ hBOOL(hAPP(U_3085,bool,hAPP(U_3085,fun(U_3085,bool),ord_less_eq(U_3085),zero_zero(U_3085)),U_3084))
      | ~ hBOOL(hAPP(U_3085,bool,hAPP(U_3085,fun(U_3085,bool),ord_less_eq(U_3085),zero_zero(U_3085)),U_3083))
      | ~ linordered_idom(U_3085) ),
    inference(definitional_conversion,[status(esa)],[f_795_2]) ).

cnf(f_795_4,plain,
    ( hBOOL(hAPP(U_3085,bool,hAPP(U_3085,fun(U_3085,bool),ord_less_eq(U_3085),hAPP(U_3085,U_3085,hAPP(U_3085,fun(U_3085,U_3085),times_times(U_3085),U_3083),U_3084)),U_3083))
    | ~ hBOOL(hAPP(U_3085,bool,hAPP(U_3085,fun(U_3085,bool),ord_less_eq(U_3085),U_3084),one_one(U_3085)))
    | ~ hBOOL(hAPP(U_3085,bool,hAPP(U_3085,fun(U_3085,bool),ord_less_eq(U_3085),zero_zero(U_3085)),U_3084))
    | ~ hBOOL(hAPP(U_3085,bool,hAPP(U_3085,fun(U_3085,bool),ord_less_eq(U_3085),zero_zero(U_3085)),U_3083))
    | ~ linordered_idom(U_3085) ),
    inference(clausify,[status(thm)],[f_795_3]) ).

fof(f_796_1,plain,
    ! [X_b] :
      ( ! [A_2,E,C_1,B_3,D_1] :
          ( ( 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),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),E)),D_1)))
            | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),C_1),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),B_3),A_2)),E)),D_1))) )
          & ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),C_1),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),B_3),A_2)),E)),D_1)))
            | ~ 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),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),E)),D_1))) ) )
      | ~ ordered_ring(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_725_le__add__iff2]) ).

fof(f_796_2,plain,
    ! [U_3091] :
      ( ! [U_3090,U_3089,U_3088,U_3087,U_3086] :
          ( ( hBOOL(hAPP(U_3091,bool,hAPP(U_3091,fun(U_3091,bool),ord_less_eq(U_3091),hAPP(U_3091,U_3091,hAPP(U_3091,fun(U_3091,U_3091),plus_plus(U_3091),hAPP(U_3091,U_3091,hAPP(U_3091,fun(U_3091,U_3091),times_times(U_3091),U_3090),U_3089)),U_3088)),hAPP(U_3091,U_3091,hAPP(U_3091,fun(U_3091,U_3091),plus_plus(U_3091),hAPP(U_3091,U_3091,hAPP(U_3091,fun(U_3091,U_3091),times_times(U_3091),U_3087),U_3089)),U_3086)))
            | ~ hBOOL(hAPP(U_3091,bool,hAPP(U_3091,fun(U_3091,bool),ord_less_eq(U_3091),U_3088),hAPP(U_3091,U_3091,hAPP(U_3091,fun(U_3091,U_3091),plus_plus(U_3091),hAPP(U_3091,U_3091,hAPP(U_3091,fun(U_3091,U_3091),times_times(U_3091),hAPP(U_3091,U_3091,hAPP(U_3091,fun(U_3091,U_3091),minus_minus(U_3091),U_3087),U_3090)),U_3089)),U_3086))) )
          & ( hBOOL(hAPP(U_3091,bool,hAPP(U_3091,fun(U_3091,bool),ord_less_eq(U_3091),U_3088),hAPP(U_3091,U_3091,hAPP(U_3091,fun(U_3091,U_3091),plus_plus(U_3091),hAPP(U_3091,U_3091,hAPP(U_3091,fun(U_3091,U_3091),times_times(U_3091),hAPP(U_3091,U_3091,hAPP(U_3091,fun(U_3091,U_3091),minus_minus(U_3091),U_3087),U_3090)),U_3089)),U_3086)))
            | ~ hBOOL(hAPP(U_3091,bool,hAPP(U_3091,fun(U_3091,bool),ord_less_eq(U_3091),hAPP(U_3091,U_3091,hAPP(U_3091,fun(U_3091,U_3091),plus_plus(U_3091),hAPP(U_3091,U_3091,hAPP(U_3091,fun(U_3091,U_3091),times_times(U_3091),U_3090),U_3089)),U_3088)),hAPP(U_3091,U_3091,hAPP(U_3091,fun(U_3091,U_3091),plus_plus(U_3091),hAPP(U_3091,U_3091,hAPP(U_3091,fun(U_3091,U_3091),times_times(U_3091),U_3087),U_3089)),U_3086))) ) )
      | ~ ordered_ring(U_3091) ),
    inference(variable_rename,[status(thm)],[f_796_1]) ).

fof(f_796_3,plain,
    ! [U_3091] :
      ( ( ! [U_3101,U_3099,U_3097,U_3095,U_3093] :
            ( hBOOL(hAPP(U_3091,bool,hAPP(U_3091,fun(U_3091,bool),ord_less_eq(U_3091),hAPP(U_3091,U_3091,hAPP(U_3091,fun(U_3091,U_3091),plus_plus(U_3091),hAPP(U_3091,U_3091,hAPP(U_3091,fun(U_3091,U_3091),times_times(U_3091),U_3101),U_3099)),U_3097)),hAPP(U_3091,U_3091,hAPP(U_3091,fun(U_3091,U_3091),plus_plus(U_3091),hAPP(U_3091,U_3091,hAPP(U_3091,fun(U_3091,U_3091),times_times(U_3091),U_3095),U_3099)),U_3093)))
            | ~ hBOOL(hAPP(U_3091,bool,hAPP(U_3091,fun(U_3091,bool),ord_less_eq(U_3091),U_3097),hAPP(U_3091,U_3091,hAPP(U_3091,fun(U_3091,U_3091),plus_plus(U_3091),hAPP(U_3091,U_3091,hAPP(U_3091,fun(U_3091,U_3091),times_times(U_3091),hAPP(U_3091,U_3091,hAPP(U_3091,fun(U_3091,U_3091),minus_minus(U_3091),U_3095),U_3101)),U_3099)),U_3093))) )
        & ! [U_3100,U_3098,U_3096,U_3094,U_3092] :
            ( hBOOL(hAPP(U_3091,bool,hAPP(U_3091,fun(U_3091,bool),ord_less_eq(U_3091),U_3096),hAPP(U_3091,U_3091,hAPP(U_3091,fun(U_3091,U_3091),plus_plus(U_3091),hAPP(U_3091,U_3091,hAPP(U_3091,fun(U_3091,U_3091),times_times(U_3091),hAPP(U_3091,U_3091,hAPP(U_3091,fun(U_3091,U_3091),minus_minus(U_3091),U_3094),U_3100)),U_3098)),U_3092)))
            | ~ hBOOL(hAPP(U_3091,bool,hAPP(U_3091,fun(U_3091,bool),ord_less_eq(U_3091),hAPP(U_3091,U_3091,hAPP(U_3091,fun(U_3091,U_3091),plus_plus(U_3091),hAPP(U_3091,U_3091,hAPP(U_3091,fun(U_3091,U_3091),times_times(U_3091),U_3100),U_3098)),U_3096)),hAPP(U_3091,U_3091,hAPP(U_3091,fun(U_3091,U_3091),plus_plus(U_3091),hAPP(U_3091,U_3091,hAPP(U_3091,fun(U_3091,U_3091),times_times(U_3091),U_3094),U_3098)),U_3092))) ) )
      | ~ ordered_ring(U_3091) ),
    inference(miniscope,[status(thm)],[f_796_2]) ).

fof(f_796_4,plain,
    ( ! [U_3091,U_3096,U_3100,U_3092,U_3097,U_3094,U_3093,U_3098,U_3095,U_3099,U_3101] :
        ( hBOOL(hAPP(U_3091,bool,hAPP(U_3091,fun(U_3091,bool),ord_less_eq(U_3091),hAPP(U_3091,U_3091,hAPP(U_3091,fun(U_3091,U_3091),plus_plus(U_3091),hAPP(U_3091,U_3091,hAPP(U_3091,fun(U_3091,U_3091),times_times(U_3091),U_3101),U_3099)),U_3097)),hAPP(U_3091,U_3091,hAPP(U_3091,fun(U_3091,U_3091),plus_plus(U_3091),hAPP(U_3091,U_3091,hAPP(U_3091,fun(U_3091,U_3091),times_times(U_3091),U_3095),U_3099)),U_3093)))
        | ~ hBOOL(hAPP(U_3091,bool,hAPP(U_3091,fun(U_3091,bool),ord_less_eq(U_3091),U_3097),hAPP(U_3091,U_3091,hAPP(U_3091,fun(U_3091,U_3091),plus_plus(U_3091),hAPP(U_3091,U_3091,hAPP(U_3091,fun(U_3091,U_3091),times_times(U_3091),hAPP(U_3091,U_3091,hAPP(U_3091,fun(U_3091,U_3091),minus_minus(U_3091),U_3095),U_3101)),U_3099)),U_3093)))
        | ~ sP221(U_3091,U_3096,U_3100,U_3092,U_3097,U_3094,U_3093,U_3098,U_3095,U_3099,U_3101) )
    & ! [U_3091,U_3096,U_3100,U_3092,U_3097,U_3094,U_3093,U_3098,U_3095,U_3099,U_3101] :
        ( hBOOL(hAPP(U_3091,bool,hAPP(U_3091,fun(U_3091,bool),ord_less_eq(U_3091),U_3096),hAPP(U_3091,U_3091,hAPP(U_3091,fun(U_3091,U_3091),plus_plus(U_3091),hAPP(U_3091,U_3091,hAPP(U_3091,fun(U_3091,U_3091),times_times(U_3091),hAPP(U_3091,U_3091,hAPP(U_3091,fun(U_3091,U_3091),minus_minus(U_3091),U_3094),U_3100)),U_3098)),U_3092)))
        | ~ hBOOL(hAPP(U_3091,bool,hAPP(U_3091,fun(U_3091,bool),ord_less_eq(U_3091),hAPP(U_3091,U_3091,hAPP(U_3091,fun(U_3091,U_3091),plus_plus(U_3091),hAPP(U_3091,U_3091,hAPP(U_3091,fun(U_3091,U_3091),times_times(U_3091),U_3100),U_3098)),U_3096)),hAPP(U_3091,U_3091,hAPP(U_3091,fun(U_3091,U_3091),plus_plus(U_3091),hAPP(U_3091,U_3091,hAPP(U_3091,fun(U_3091,U_3091),times_times(U_3091),U_3094),U_3098)),U_3092)))
        | ~ sP221(U_3091,U_3096,U_3100,U_3092,U_3097,U_3094,U_3093,U_3098,U_3095,U_3099,U_3101) )
    & ! [U_3091,U_3096,U_3100,U_3092,U_3097,U_3094,U_3093,U_3098,U_3095,U_3099,U_3101] :
        ( sP221(U_3091,U_3096,U_3100,U_3092,U_3097,U_3094,U_3093,U_3098,U_3095,U_3099,U_3101)
        | ~ ordered_ring(U_3091) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP221])],[f_796_3]) ).

cnf(f_796_5,plain,
    ( sP221(U_3091,U_3096,U_3100,U_3092,U_3097,U_3094,U_3093,U_3098,U_3095,U_3099,U_3101)
    | ~ ordered_ring(U_3091) ),
    inference(clausify,[status(thm)],[f_796_4]) ).

cnf(f_796_6,plain,
    ( hBOOL(hAPP(U_3091,bool,hAPP(U_3091,fun(U_3091,bool),ord_less_eq(U_3091),U_3096),hAPP(U_3091,U_3091,hAPP(U_3091,fun(U_3091,U_3091),plus_plus(U_3091),hAPP(U_3091,U_3091,hAPP(U_3091,fun(U_3091,U_3091),times_times(U_3091),hAPP(U_3091,U_3091,hAPP(U_3091,fun(U_3091,U_3091),minus_minus(U_3091),U_3094),U_3100)),U_3098)),U_3092)))
    | ~ hBOOL(hAPP(U_3091,bool,hAPP(U_3091,fun(U_3091,bool),ord_less_eq(U_3091),hAPP(U_3091,U_3091,hAPP(U_3091,fun(U_3091,U_3091),plus_plus(U_3091),hAPP(U_3091,U_3091,hAPP(U_3091,fun(U_3091,U_3091),times_times(U_3091),U_3100),U_3098)),U_3096)),hAPP(U_3091,U_3091,hAPP(U_3091,fun(U_3091,U_3091),plus_plus(U_3091),hAPP(U_3091,U_3091,hAPP(U_3091,fun(U_3091,U_3091),times_times(U_3091),U_3094),U_3098)),U_3092)))
    | ~ sP221(U_3091,U_3096,U_3100,U_3092,U_3097,U_3094,U_3093,U_3098,U_3095,U_3099,U_3101) ),
    inference(clausify,[status(thm)],[f_796_4]) ).

cnf(f_796_7,plain,
    ( hBOOL(hAPP(U_3091,bool,hAPP(U_3091,fun(U_3091,bool),ord_less_eq(U_3091),hAPP(U_3091,U_3091,hAPP(U_3091,fun(U_3091,U_3091),plus_plus(U_3091),hAPP(U_3091,U_3091,hAPP(U_3091,fun(U_3091,U_3091),times_times(U_3091),U_3101),U_3099)),U_3097)),hAPP(U_3091,U_3091,hAPP(U_3091,fun(U_3091,U_3091),plus_plus(U_3091),hAPP(U_3091,U_3091,hAPP(U_3091,fun(U_3091,U_3091),times_times(U_3091),U_3095),U_3099)),U_3093)))
    | ~ hBOOL(hAPP(U_3091,bool,hAPP(U_3091,fun(U_3091,bool),ord_less_eq(U_3091),U_3097),hAPP(U_3091,U_3091,hAPP(U_3091,fun(U_3091,U_3091),plus_plus(U_3091),hAPP(U_3091,U_3091,hAPP(U_3091,fun(U_3091,U_3091),times_times(U_3091),hAPP(U_3091,U_3091,hAPP(U_3091,fun(U_3091,U_3091),minus_minus(U_3091),U_3095),U_3101)),U_3099)),U_3093)))
    | ~ sP221(U_3091,U_3096,U_3100,U_3092,U_3097,U_3094,U_3093,U_3098,U_3095,U_3099,U_3101) ),
    inference(clausify,[status(thm)],[f_796_4]) ).

fof(f_797_1,plain,
    ! [X_b] :
      ( ! [A_2,E,C_1,B_3,D_1] :
          ( ( 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),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),E)),D_1)))
            | ~ 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),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3)),E)),C_1)),D_1)) )
          & ( 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),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3)),E)),C_1)),D_1))
            | ~ 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),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),E)),D_1))) ) )
      | ~ ordered_ring(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_726_le__add__iff1]) ).

fof(f_797_2,plain,
    ! [U_3107] :
      ( ! [U_3106,U_3105,U_3104,U_3103,U_3102] :
          ( ( hBOOL(hAPP(U_3107,bool,hAPP(U_3107,fun(U_3107,bool),ord_less_eq(U_3107),hAPP(U_3107,U_3107,hAPP(U_3107,fun(U_3107,U_3107),plus_plus(U_3107),hAPP(U_3107,U_3107,hAPP(U_3107,fun(U_3107,U_3107),times_times(U_3107),U_3106),U_3105)),U_3104)),hAPP(U_3107,U_3107,hAPP(U_3107,fun(U_3107,U_3107),plus_plus(U_3107),hAPP(U_3107,U_3107,hAPP(U_3107,fun(U_3107,U_3107),times_times(U_3107),U_3103),U_3105)),U_3102)))
            | ~ hBOOL(hAPP(U_3107,bool,hAPP(U_3107,fun(U_3107,bool),ord_less_eq(U_3107),hAPP(U_3107,U_3107,hAPP(U_3107,fun(U_3107,U_3107),plus_plus(U_3107),hAPP(U_3107,U_3107,hAPP(U_3107,fun(U_3107,U_3107),times_times(U_3107),hAPP(U_3107,U_3107,hAPP(U_3107,fun(U_3107,U_3107),minus_minus(U_3107),U_3106),U_3103)),U_3105)),U_3104)),U_3102)) )
          & ( hBOOL(hAPP(U_3107,bool,hAPP(U_3107,fun(U_3107,bool),ord_less_eq(U_3107),hAPP(U_3107,U_3107,hAPP(U_3107,fun(U_3107,U_3107),plus_plus(U_3107),hAPP(U_3107,U_3107,hAPP(U_3107,fun(U_3107,U_3107),times_times(U_3107),hAPP(U_3107,U_3107,hAPP(U_3107,fun(U_3107,U_3107),minus_minus(U_3107),U_3106),U_3103)),U_3105)),U_3104)),U_3102))
            | ~ hBOOL(hAPP(U_3107,bool,hAPP(U_3107,fun(U_3107,bool),ord_less_eq(U_3107),hAPP(U_3107,U_3107,hAPP(U_3107,fun(U_3107,U_3107),plus_plus(U_3107),hAPP(U_3107,U_3107,hAPP(U_3107,fun(U_3107,U_3107),times_times(U_3107),U_3106),U_3105)),U_3104)),hAPP(U_3107,U_3107,hAPP(U_3107,fun(U_3107,U_3107),plus_plus(U_3107),hAPP(U_3107,U_3107,hAPP(U_3107,fun(U_3107,U_3107),times_times(U_3107),U_3103),U_3105)),U_3102))) ) )
      | ~ ordered_ring(U_3107) ),
    inference(variable_rename,[status(thm)],[f_797_1]) ).

fof(f_797_3,plain,
    ! [U_3107] :
      ( ( ! [U_3117,U_3115,U_3113,U_3111,U_3109] :
            ( hBOOL(hAPP(U_3107,bool,hAPP(U_3107,fun(U_3107,bool),ord_less_eq(U_3107),hAPP(U_3107,U_3107,hAPP(U_3107,fun(U_3107,U_3107),plus_plus(U_3107),hAPP(U_3107,U_3107,hAPP(U_3107,fun(U_3107,U_3107),times_times(U_3107),U_3117),U_3115)),U_3113)),hAPP(U_3107,U_3107,hAPP(U_3107,fun(U_3107,U_3107),plus_plus(U_3107),hAPP(U_3107,U_3107,hAPP(U_3107,fun(U_3107,U_3107),times_times(U_3107),U_3111),U_3115)),U_3109)))
            | ~ hBOOL(hAPP(U_3107,bool,hAPP(U_3107,fun(U_3107,bool),ord_less_eq(U_3107),hAPP(U_3107,U_3107,hAPP(U_3107,fun(U_3107,U_3107),plus_plus(U_3107),hAPP(U_3107,U_3107,hAPP(U_3107,fun(U_3107,U_3107),times_times(U_3107),hAPP(U_3107,U_3107,hAPP(U_3107,fun(U_3107,U_3107),minus_minus(U_3107),U_3117),U_3111)),U_3115)),U_3113)),U_3109)) )
        & ! [U_3116,U_3114,U_3112,U_3110,U_3108] :
            ( hBOOL(hAPP(U_3107,bool,hAPP(U_3107,fun(U_3107,bool),ord_less_eq(U_3107),hAPP(U_3107,U_3107,hAPP(U_3107,fun(U_3107,U_3107),plus_plus(U_3107),hAPP(U_3107,U_3107,hAPP(U_3107,fun(U_3107,U_3107),times_times(U_3107),hAPP(U_3107,U_3107,hAPP(U_3107,fun(U_3107,U_3107),minus_minus(U_3107),U_3116),U_3110)),U_3114)),U_3112)),U_3108))
            | ~ hBOOL(hAPP(U_3107,bool,hAPP(U_3107,fun(U_3107,bool),ord_less_eq(U_3107),hAPP(U_3107,U_3107,hAPP(U_3107,fun(U_3107,U_3107),plus_plus(U_3107),hAPP(U_3107,U_3107,hAPP(U_3107,fun(U_3107,U_3107),times_times(U_3107),U_3116),U_3114)),U_3112)),hAPP(U_3107,U_3107,hAPP(U_3107,fun(U_3107,U_3107),plus_plus(U_3107),hAPP(U_3107,U_3107,hAPP(U_3107,fun(U_3107,U_3107),times_times(U_3107),U_3110),U_3114)),U_3108))) ) )
      | ~ ordered_ring(U_3107) ),
    inference(miniscope,[status(thm)],[f_797_2]) ).

fof(f_797_4,plain,
    ( ! [U_3116,U_3112,U_3107,U_3108,U_3109,U_3110,U_3114,U_3111,U_3113,U_3115,U_3117] :
        ( hBOOL(hAPP(U_3107,bool,hAPP(U_3107,fun(U_3107,bool),ord_less_eq(U_3107),hAPP(U_3107,U_3107,hAPP(U_3107,fun(U_3107,U_3107),plus_plus(U_3107),hAPP(U_3107,U_3107,hAPP(U_3107,fun(U_3107,U_3107),times_times(U_3107),U_3117),U_3115)),U_3113)),hAPP(U_3107,U_3107,hAPP(U_3107,fun(U_3107,U_3107),plus_plus(U_3107),hAPP(U_3107,U_3107,hAPP(U_3107,fun(U_3107,U_3107),times_times(U_3107),U_3111),U_3115)),U_3109)))
        | ~ hBOOL(hAPP(U_3107,bool,hAPP(U_3107,fun(U_3107,bool),ord_less_eq(U_3107),hAPP(U_3107,U_3107,hAPP(U_3107,fun(U_3107,U_3107),plus_plus(U_3107),hAPP(U_3107,U_3107,hAPP(U_3107,fun(U_3107,U_3107),times_times(U_3107),hAPP(U_3107,U_3107,hAPP(U_3107,fun(U_3107,U_3107),minus_minus(U_3107),U_3117),U_3111)),U_3115)),U_3113)),U_3109))
        | ~ sP222(U_3116,U_3112,U_3107,U_3108,U_3109,U_3110,U_3114,U_3111,U_3113,U_3115,U_3117) )
    & ! [U_3116,U_3112,U_3107,U_3108,U_3109,U_3110,U_3114,U_3111,U_3113,U_3115,U_3117] :
        ( hBOOL(hAPP(U_3107,bool,hAPP(U_3107,fun(U_3107,bool),ord_less_eq(U_3107),hAPP(U_3107,U_3107,hAPP(U_3107,fun(U_3107,U_3107),plus_plus(U_3107),hAPP(U_3107,U_3107,hAPP(U_3107,fun(U_3107,U_3107),times_times(U_3107),hAPP(U_3107,U_3107,hAPP(U_3107,fun(U_3107,U_3107),minus_minus(U_3107),U_3116),U_3110)),U_3114)),U_3112)),U_3108))
        | ~ hBOOL(hAPP(U_3107,bool,hAPP(U_3107,fun(U_3107,bool),ord_less_eq(U_3107),hAPP(U_3107,U_3107,hAPP(U_3107,fun(U_3107,U_3107),plus_plus(U_3107),hAPP(U_3107,U_3107,hAPP(U_3107,fun(U_3107,U_3107),times_times(U_3107),U_3116),U_3114)),U_3112)),hAPP(U_3107,U_3107,hAPP(U_3107,fun(U_3107,U_3107),plus_plus(U_3107),hAPP(U_3107,U_3107,hAPP(U_3107,fun(U_3107,U_3107),times_times(U_3107),U_3110),U_3114)),U_3108)))
        | ~ sP222(U_3116,U_3112,U_3107,U_3108,U_3109,U_3110,U_3114,U_3111,U_3113,U_3115,U_3117) )
    & ! [U_3116,U_3112,U_3107,U_3108,U_3109,U_3110,U_3114,U_3111,U_3113,U_3115,U_3117] :
        ( sP222(U_3116,U_3112,U_3107,U_3108,U_3109,U_3110,U_3114,U_3111,U_3113,U_3115,U_3117)
        | ~ ordered_ring(U_3107) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP222])],[f_797_3]) ).

cnf(f_797_5,plain,
    ( sP222(U_3116,U_3112,U_3107,U_3108,U_3109,U_3110,U_3114,U_3111,U_3113,U_3115,U_3117)
    | ~ ordered_ring(U_3107) ),
    inference(clausify,[status(thm)],[f_797_4]) ).

cnf(f_797_6,plain,
    ( hBOOL(hAPP(U_3107,bool,hAPP(U_3107,fun(U_3107,bool),ord_less_eq(U_3107),hAPP(U_3107,U_3107,hAPP(U_3107,fun(U_3107,U_3107),plus_plus(U_3107),hAPP(U_3107,U_3107,hAPP(U_3107,fun(U_3107,U_3107),times_times(U_3107),hAPP(U_3107,U_3107,hAPP(U_3107,fun(U_3107,U_3107),minus_minus(U_3107),U_3116),U_3110)),U_3114)),U_3112)),U_3108))
    | ~ hBOOL(hAPP(U_3107,bool,hAPP(U_3107,fun(U_3107,bool),ord_less_eq(U_3107),hAPP(U_3107,U_3107,hAPP(U_3107,fun(U_3107,U_3107),plus_plus(U_3107),hAPP(U_3107,U_3107,hAPP(U_3107,fun(U_3107,U_3107),times_times(U_3107),U_3116),U_3114)),U_3112)),hAPP(U_3107,U_3107,hAPP(U_3107,fun(U_3107,U_3107),plus_plus(U_3107),hAPP(U_3107,U_3107,hAPP(U_3107,fun(U_3107,U_3107),times_times(U_3107),U_3110),U_3114)),U_3108)))
    | ~ sP222(U_3116,U_3112,U_3107,U_3108,U_3109,U_3110,U_3114,U_3111,U_3113,U_3115,U_3117) ),
    inference(clausify,[status(thm)],[f_797_4]) ).

cnf(f_797_7,plain,
    ( hBOOL(hAPP(U_3107,bool,hAPP(U_3107,fun(U_3107,bool),ord_less_eq(U_3107),hAPP(U_3107,U_3107,hAPP(U_3107,fun(U_3107,U_3107),plus_plus(U_3107),hAPP(U_3107,U_3107,hAPP(U_3107,fun(U_3107,U_3107),times_times(U_3107),U_3117),U_3115)),U_3113)),hAPP(U_3107,U_3107,hAPP(U_3107,fun(U_3107,U_3107),plus_plus(U_3107),hAPP(U_3107,U_3107,hAPP(U_3107,fun(U_3107,U_3107),times_times(U_3107),U_3111),U_3115)),U_3109)))
    | ~ hBOOL(hAPP(U_3107,bool,hAPP(U_3107,fun(U_3107,bool),ord_less_eq(U_3107),hAPP(U_3107,U_3107,hAPP(U_3107,fun(U_3107,U_3107),plus_plus(U_3107),hAPP(U_3107,U_3107,hAPP(U_3107,fun(U_3107,U_3107),times_times(U_3107),hAPP(U_3107,U_3107,hAPP(U_3107,fun(U_3107,U_3107),minus_minus(U_3107),U_3117),U_3111)),U_3115)),U_3113)),U_3109))
    | ~ sP222(U_3116,U_3112,U_3107,U_3108,U_3109,U_3110,U_3114,U_3111,U_3113,U_3115,U_3117) ),
    inference(clausify,[status(thm)],[f_797_4]) ).

fof(f_798_1,plain,
    ! [X_b] :
      ( ! [A_2,E,C_1,B_3,D_1] :
          ( ( 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),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),E)),D_1)))
            | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),B_3),A_2)),E)),D_1))) )
          & ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),B_3),A_2)),E)),D_1)))
            | ~ 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),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),E)),D_1))) ) )
      | ~ ordered_ring(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_727_less__add__iff2]) ).

fof(f_798_2,plain,
    ! [U_3123] :
      ( ! [U_3122,U_3121,U_3120,U_3119,U_3118] :
          ( ( hBOOL(hAPP(U_3123,bool,hAPP(U_3123,fun(U_3123,bool),ord_less(U_3123),hAPP(U_3123,U_3123,hAPP(U_3123,fun(U_3123,U_3123),plus_plus(U_3123),hAPP(U_3123,U_3123,hAPP(U_3123,fun(U_3123,U_3123),times_times(U_3123),U_3122),U_3121)),U_3120)),hAPP(U_3123,U_3123,hAPP(U_3123,fun(U_3123,U_3123),plus_plus(U_3123),hAPP(U_3123,U_3123,hAPP(U_3123,fun(U_3123,U_3123),times_times(U_3123),U_3119),U_3121)),U_3118)))
            | ~ hBOOL(hAPP(U_3123,bool,hAPP(U_3123,fun(U_3123,bool),ord_less(U_3123),U_3120),hAPP(U_3123,U_3123,hAPP(U_3123,fun(U_3123,U_3123),plus_plus(U_3123),hAPP(U_3123,U_3123,hAPP(U_3123,fun(U_3123,U_3123),times_times(U_3123),hAPP(U_3123,U_3123,hAPP(U_3123,fun(U_3123,U_3123),minus_minus(U_3123),U_3119),U_3122)),U_3121)),U_3118))) )
          & ( hBOOL(hAPP(U_3123,bool,hAPP(U_3123,fun(U_3123,bool),ord_less(U_3123),U_3120),hAPP(U_3123,U_3123,hAPP(U_3123,fun(U_3123,U_3123),plus_plus(U_3123),hAPP(U_3123,U_3123,hAPP(U_3123,fun(U_3123,U_3123),times_times(U_3123),hAPP(U_3123,U_3123,hAPP(U_3123,fun(U_3123,U_3123),minus_minus(U_3123),U_3119),U_3122)),U_3121)),U_3118)))
            | ~ hBOOL(hAPP(U_3123,bool,hAPP(U_3123,fun(U_3123,bool),ord_less(U_3123),hAPP(U_3123,U_3123,hAPP(U_3123,fun(U_3123,U_3123),plus_plus(U_3123),hAPP(U_3123,U_3123,hAPP(U_3123,fun(U_3123,U_3123),times_times(U_3123),U_3122),U_3121)),U_3120)),hAPP(U_3123,U_3123,hAPP(U_3123,fun(U_3123,U_3123),plus_plus(U_3123),hAPP(U_3123,U_3123,hAPP(U_3123,fun(U_3123,U_3123),times_times(U_3123),U_3119),U_3121)),U_3118))) ) )
      | ~ ordered_ring(U_3123) ),
    inference(variable_rename,[status(thm)],[f_798_1]) ).

fof(f_798_3,plain,
    ! [U_3123] :
      ( ( ! [U_3133,U_3131,U_3129,U_3127,U_3125] :
            ( hBOOL(hAPP(U_3123,bool,hAPP(U_3123,fun(U_3123,bool),ord_less(U_3123),hAPP(U_3123,U_3123,hAPP(U_3123,fun(U_3123,U_3123),plus_plus(U_3123),hAPP(U_3123,U_3123,hAPP(U_3123,fun(U_3123,U_3123),times_times(U_3123),U_3133),U_3131)),U_3129)),hAPP(U_3123,U_3123,hAPP(U_3123,fun(U_3123,U_3123),plus_plus(U_3123),hAPP(U_3123,U_3123,hAPP(U_3123,fun(U_3123,U_3123),times_times(U_3123),U_3127),U_3131)),U_3125)))
            | ~ hBOOL(hAPP(U_3123,bool,hAPP(U_3123,fun(U_3123,bool),ord_less(U_3123),U_3129),hAPP(U_3123,U_3123,hAPP(U_3123,fun(U_3123,U_3123),plus_plus(U_3123),hAPP(U_3123,U_3123,hAPP(U_3123,fun(U_3123,U_3123),times_times(U_3123),hAPP(U_3123,U_3123,hAPP(U_3123,fun(U_3123,U_3123),minus_minus(U_3123),U_3127),U_3133)),U_3131)),U_3125))) )
        & ! [U_3132,U_3130,U_3128,U_3126,U_3124] :
            ( hBOOL(hAPP(U_3123,bool,hAPP(U_3123,fun(U_3123,bool),ord_less(U_3123),U_3128),hAPP(U_3123,U_3123,hAPP(U_3123,fun(U_3123,U_3123),plus_plus(U_3123),hAPP(U_3123,U_3123,hAPP(U_3123,fun(U_3123,U_3123),times_times(U_3123),hAPP(U_3123,U_3123,hAPP(U_3123,fun(U_3123,U_3123),minus_minus(U_3123),U_3126),U_3132)),U_3130)),U_3124)))
            | ~ hBOOL(hAPP(U_3123,bool,hAPP(U_3123,fun(U_3123,bool),ord_less(U_3123),hAPP(U_3123,U_3123,hAPP(U_3123,fun(U_3123,U_3123),plus_plus(U_3123),hAPP(U_3123,U_3123,hAPP(U_3123,fun(U_3123,U_3123),times_times(U_3123),U_3132),U_3130)),U_3128)),hAPP(U_3123,U_3123,hAPP(U_3123,fun(U_3123,U_3123),plus_plus(U_3123),hAPP(U_3123,U_3123,hAPP(U_3123,fun(U_3123,U_3123),times_times(U_3123),U_3126),U_3130)),U_3124))) ) )
      | ~ ordered_ring(U_3123) ),
    inference(miniscope,[status(thm)],[f_798_2]) ).

fof(f_798_4,plain,
    ( ! [U_3123,U_3132,U_3128,U_3124,U_3129,U_3126,U_3125,U_3130,U_3127,U_3131,U_3133] :
        ( hBOOL(hAPP(U_3123,bool,hAPP(U_3123,fun(U_3123,bool),ord_less(U_3123),hAPP(U_3123,U_3123,hAPP(U_3123,fun(U_3123,U_3123),plus_plus(U_3123),hAPP(U_3123,U_3123,hAPP(U_3123,fun(U_3123,U_3123),times_times(U_3123),U_3133),U_3131)),U_3129)),hAPP(U_3123,U_3123,hAPP(U_3123,fun(U_3123,U_3123),plus_plus(U_3123),hAPP(U_3123,U_3123,hAPP(U_3123,fun(U_3123,U_3123),times_times(U_3123),U_3127),U_3131)),U_3125)))
        | ~ hBOOL(hAPP(U_3123,bool,hAPP(U_3123,fun(U_3123,bool),ord_less(U_3123),U_3129),hAPP(U_3123,U_3123,hAPP(U_3123,fun(U_3123,U_3123),plus_plus(U_3123),hAPP(U_3123,U_3123,hAPP(U_3123,fun(U_3123,U_3123),times_times(U_3123),hAPP(U_3123,U_3123,hAPP(U_3123,fun(U_3123,U_3123),minus_minus(U_3123),U_3127),U_3133)),U_3131)),U_3125)))
        | ~ sP223(U_3123,U_3132,U_3128,U_3124,U_3129,U_3126,U_3125,U_3130,U_3127,U_3131,U_3133) )
    & ! [U_3123,U_3132,U_3128,U_3124,U_3129,U_3126,U_3125,U_3130,U_3127,U_3131,U_3133] :
        ( hBOOL(hAPP(U_3123,bool,hAPP(U_3123,fun(U_3123,bool),ord_less(U_3123),U_3128),hAPP(U_3123,U_3123,hAPP(U_3123,fun(U_3123,U_3123),plus_plus(U_3123),hAPP(U_3123,U_3123,hAPP(U_3123,fun(U_3123,U_3123),times_times(U_3123),hAPP(U_3123,U_3123,hAPP(U_3123,fun(U_3123,U_3123),minus_minus(U_3123),U_3126),U_3132)),U_3130)),U_3124)))
        | ~ hBOOL(hAPP(U_3123,bool,hAPP(U_3123,fun(U_3123,bool),ord_less(U_3123),hAPP(U_3123,U_3123,hAPP(U_3123,fun(U_3123,U_3123),plus_plus(U_3123),hAPP(U_3123,U_3123,hAPP(U_3123,fun(U_3123,U_3123),times_times(U_3123),U_3132),U_3130)),U_3128)),hAPP(U_3123,U_3123,hAPP(U_3123,fun(U_3123,U_3123),plus_plus(U_3123),hAPP(U_3123,U_3123,hAPP(U_3123,fun(U_3123,U_3123),times_times(U_3123),U_3126),U_3130)),U_3124)))
        | ~ sP223(U_3123,U_3132,U_3128,U_3124,U_3129,U_3126,U_3125,U_3130,U_3127,U_3131,U_3133) )
    & ! [U_3123,U_3132,U_3128,U_3124,U_3129,U_3126,U_3125,U_3130,U_3127,U_3131,U_3133] :
        ( sP223(U_3123,U_3132,U_3128,U_3124,U_3129,U_3126,U_3125,U_3130,U_3127,U_3131,U_3133)
        | ~ ordered_ring(U_3123) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP223])],[f_798_3]) ).

cnf(f_798_5,plain,
    ( sP223(U_3123,U_3132,U_3128,U_3124,U_3129,U_3126,U_3125,U_3130,U_3127,U_3131,U_3133)
    | ~ ordered_ring(U_3123) ),
    inference(clausify,[status(thm)],[f_798_4]) ).

cnf(f_798_6,plain,
    ( hBOOL(hAPP(U_3123,bool,hAPP(U_3123,fun(U_3123,bool),ord_less(U_3123),U_3128),hAPP(U_3123,U_3123,hAPP(U_3123,fun(U_3123,U_3123),plus_plus(U_3123),hAPP(U_3123,U_3123,hAPP(U_3123,fun(U_3123,U_3123),times_times(U_3123),hAPP(U_3123,U_3123,hAPP(U_3123,fun(U_3123,U_3123),minus_minus(U_3123),U_3126),U_3132)),U_3130)),U_3124)))
    | ~ hBOOL(hAPP(U_3123,bool,hAPP(U_3123,fun(U_3123,bool),ord_less(U_3123),hAPP(U_3123,U_3123,hAPP(U_3123,fun(U_3123,U_3123),plus_plus(U_3123),hAPP(U_3123,U_3123,hAPP(U_3123,fun(U_3123,U_3123),times_times(U_3123),U_3132),U_3130)),U_3128)),hAPP(U_3123,U_3123,hAPP(U_3123,fun(U_3123,U_3123),plus_plus(U_3123),hAPP(U_3123,U_3123,hAPP(U_3123,fun(U_3123,U_3123),times_times(U_3123),U_3126),U_3130)),U_3124)))
    | ~ sP223(U_3123,U_3132,U_3128,U_3124,U_3129,U_3126,U_3125,U_3130,U_3127,U_3131,U_3133) ),
    inference(clausify,[status(thm)],[f_798_4]) ).

cnf(f_798_7,plain,
    ( hBOOL(hAPP(U_3123,bool,hAPP(U_3123,fun(U_3123,bool),ord_less(U_3123),hAPP(U_3123,U_3123,hAPP(U_3123,fun(U_3123,U_3123),plus_plus(U_3123),hAPP(U_3123,U_3123,hAPP(U_3123,fun(U_3123,U_3123),times_times(U_3123),U_3133),U_3131)),U_3129)),hAPP(U_3123,U_3123,hAPP(U_3123,fun(U_3123,U_3123),plus_plus(U_3123),hAPP(U_3123,U_3123,hAPP(U_3123,fun(U_3123,U_3123),times_times(U_3123),U_3127),U_3131)),U_3125)))
    | ~ hBOOL(hAPP(U_3123,bool,hAPP(U_3123,fun(U_3123,bool),ord_less(U_3123),U_3129),hAPP(U_3123,U_3123,hAPP(U_3123,fun(U_3123,U_3123),plus_plus(U_3123),hAPP(U_3123,U_3123,hAPP(U_3123,fun(U_3123,U_3123),times_times(U_3123),hAPP(U_3123,U_3123,hAPP(U_3123,fun(U_3123,U_3123),minus_minus(U_3123),U_3127),U_3133)),U_3131)),U_3125)))
    | ~ sP223(U_3123,U_3132,U_3128,U_3124,U_3129,U_3126,U_3125,U_3130,U_3127,U_3131,U_3133) ),
    inference(clausify,[status(thm)],[f_798_4]) ).

fof(f_799_1,plain,
    ! [X_b] :
      ( ! [A_2,E,C_1,B_3,D_1] :
          ( ( 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),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),E)),D_1)))
            | ~ 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),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3)),E)),C_1)),D_1)) )
          & ( 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),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3)),E)),C_1)),D_1))
            | ~ 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),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),E)),D_1))) ) )
      | ~ ordered_ring(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_728_less__add__iff1]) ).

fof(f_799_2,plain,
    ! [U_3139] :
      ( ! [U_3138,U_3137,U_3136,U_3135,U_3134] :
          ( ( hBOOL(hAPP(U_3139,bool,hAPP(U_3139,fun(U_3139,bool),ord_less(U_3139),hAPP(U_3139,U_3139,hAPP(U_3139,fun(U_3139,U_3139),plus_plus(U_3139),hAPP(U_3139,U_3139,hAPP(U_3139,fun(U_3139,U_3139),times_times(U_3139),U_3138),U_3137)),U_3136)),hAPP(U_3139,U_3139,hAPP(U_3139,fun(U_3139,U_3139),plus_plus(U_3139),hAPP(U_3139,U_3139,hAPP(U_3139,fun(U_3139,U_3139),times_times(U_3139),U_3135),U_3137)),U_3134)))
            | ~ hBOOL(hAPP(U_3139,bool,hAPP(U_3139,fun(U_3139,bool),ord_less(U_3139),hAPP(U_3139,U_3139,hAPP(U_3139,fun(U_3139,U_3139),plus_plus(U_3139),hAPP(U_3139,U_3139,hAPP(U_3139,fun(U_3139,U_3139),times_times(U_3139),hAPP(U_3139,U_3139,hAPP(U_3139,fun(U_3139,U_3139),minus_minus(U_3139),U_3138),U_3135)),U_3137)),U_3136)),U_3134)) )
          & ( hBOOL(hAPP(U_3139,bool,hAPP(U_3139,fun(U_3139,bool),ord_less(U_3139),hAPP(U_3139,U_3139,hAPP(U_3139,fun(U_3139,U_3139),plus_plus(U_3139),hAPP(U_3139,U_3139,hAPP(U_3139,fun(U_3139,U_3139),times_times(U_3139),hAPP(U_3139,U_3139,hAPP(U_3139,fun(U_3139,U_3139),minus_minus(U_3139),U_3138),U_3135)),U_3137)),U_3136)),U_3134))
            | ~ hBOOL(hAPP(U_3139,bool,hAPP(U_3139,fun(U_3139,bool),ord_less(U_3139),hAPP(U_3139,U_3139,hAPP(U_3139,fun(U_3139,U_3139),plus_plus(U_3139),hAPP(U_3139,U_3139,hAPP(U_3139,fun(U_3139,U_3139),times_times(U_3139),U_3138),U_3137)),U_3136)),hAPP(U_3139,U_3139,hAPP(U_3139,fun(U_3139,U_3139),plus_plus(U_3139),hAPP(U_3139,U_3139,hAPP(U_3139,fun(U_3139,U_3139),times_times(U_3139),U_3135),U_3137)),U_3134))) ) )
      | ~ ordered_ring(U_3139) ),
    inference(variable_rename,[status(thm)],[f_799_1]) ).

fof(f_799_3,plain,
    ! [U_3139] :
      ( ( ! [U_3149,U_3147,U_3145,U_3143,U_3141] :
            ( hBOOL(hAPP(U_3139,bool,hAPP(U_3139,fun(U_3139,bool),ord_less(U_3139),hAPP(U_3139,U_3139,hAPP(U_3139,fun(U_3139,U_3139),plus_plus(U_3139),hAPP(U_3139,U_3139,hAPP(U_3139,fun(U_3139,U_3139),times_times(U_3139),U_3149),U_3147)),U_3145)),hAPP(U_3139,U_3139,hAPP(U_3139,fun(U_3139,U_3139),plus_plus(U_3139),hAPP(U_3139,U_3139,hAPP(U_3139,fun(U_3139,U_3139),times_times(U_3139),U_3143),U_3147)),U_3141)))
            | ~ hBOOL(hAPP(U_3139,bool,hAPP(U_3139,fun(U_3139,bool),ord_less(U_3139),hAPP(U_3139,U_3139,hAPP(U_3139,fun(U_3139,U_3139),plus_plus(U_3139),hAPP(U_3139,U_3139,hAPP(U_3139,fun(U_3139,U_3139),times_times(U_3139),hAPP(U_3139,U_3139,hAPP(U_3139,fun(U_3139,U_3139),minus_minus(U_3139),U_3149),U_3143)),U_3147)),U_3145)),U_3141)) )
        & ! [U_3148,U_3146,U_3144,U_3142,U_3140] :
            ( hBOOL(hAPP(U_3139,bool,hAPP(U_3139,fun(U_3139,bool),ord_less(U_3139),hAPP(U_3139,U_3139,hAPP(U_3139,fun(U_3139,U_3139),plus_plus(U_3139),hAPP(U_3139,U_3139,hAPP(U_3139,fun(U_3139,U_3139),times_times(U_3139),hAPP(U_3139,U_3139,hAPP(U_3139,fun(U_3139,U_3139),minus_minus(U_3139),U_3148),U_3142)),U_3146)),U_3144)),U_3140))
            | ~ hBOOL(hAPP(U_3139,bool,hAPP(U_3139,fun(U_3139,bool),ord_less(U_3139),hAPP(U_3139,U_3139,hAPP(U_3139,fun(U_3139,U_3139),plus_plus(U_3139),hAPP(U_3139,U_3139,hAPP(U_3139,fun(U_3139,U_3139),times_times(U_3139),U_3148),U_3146)),U_3144)),hAPP(U_3139,U_3139,hAPP(U_3139,fun(U_3139,U_3139),plus_plus(U_3139),hAPP(U_3139,U_3139,hAPP(U_3139,fun(U_3139,U_3139),times_times(U_3139),U_3142),U_3146)),U_3140))) ) )
      | ~ ordered_ring(U_3139) ),
    inference(miniscope,[status(thm)],[f_799_2]) ).

fof(f_799_4,plain,
    ( ! [U_3139,U_3148,U_3144,U_3140,U_3141,U_3142,U_3146,U_3143,U_3145,U_3147,U_3149] :
        ( hBOOL(hAPP(U_3139,bool,hAPP(U_3139,fun(U_3139,bool),ord_less(U_3139),hAPP(U_3139,U_3139,hAPP(U_3139,fun(U_3139,U_3139),plus_plus(U_3139),hAPP(U_3139,U_3139,hAPP(U_3139,fun(U_3139,U_3139),times_times(U_3139),U_3149),U_3147)),U_3145)),hAPP(U_3139,U_3139,hAPP(U_3139,fun(U_3139,U_3139),plus_plus(U_3139),hAPP(U_3139,U_3139,hAPP(U_3139,fun(U_3139,U_3139),times_times(U_3139),U_3143),U_3147)),U_3141)))
        | ~ hBOOL(hAPP(U_3139,bool,hAPP(U_3139,fun(U_3139,bool),ord_less(U_3139),hAPP(U_3139,U_3139,hAPP(U_3139,fun(U_3139,U_3139),plus_plus(U_3139),hAPP(U_3139,U_3139,hAPP(U_3139,fun(U_3139,U_3139),times_times(U_3139),hAPP(U_3139,U_3139,hAPP(U_3139,fun(U_3139,U_3139),minus_minus(U_3139),U_3149),U_3143)),U_3147)),U_3145)),U_3141))
        | ~ sP224(U_3139,U_3148,U_3144,U_3140,U_3141,U_3142,U_3146,U_3143,U_3145,U_3147,U_3149) )
    & ! [U_3139,U_3148,U_3144,U_3140,U_3141,U_3142,U_3146,U_3143,U_3145,U_3147,U_3149] :
        ( hBOOL(hAPP(U_3139,bool,hAPP(U_3139,fun(U_3139,bool),ord_less(U_3139),hAPP(U_3139,U_3139,hAPP(U_3139,fun(U_3139,U_3139),plus_plus(U_3139),hAPP(U_3139,U_3139,hAPP(U_3139,fun(U_3139,U_3139),times_times(U_3139),hAPP(U_3139,U_3139,hAPP(U_3139,fun(U_3139,U_3139),minus_minus(U_3139),U_3148),U_3142)),U_3146)),U_3144)),U_3140))
        | ~ hBOOL(hAPP(U_3139,bool,hAPP(U_3139,fun(U_3139,bool),ord_less(U_3139),hAPP(U_3139,U_3139,hAPP(U_3139,fun(U_3139,U_3139),plus_plus(U_3139),hAPP(U_3139,U_3139,hAPP(U_3139,fun(U_3139,U_3139),times_times(U_3139),U_3148),U_3146)),U_3144)),hAPP(U_3139,U_3139,hAPP(U_3139,fun(U_3139,U_3139),plus_plus(U_3139),hAPP(U_3139,U_3139,hAPP(U_3139,fun(U_3139,U_3139),times_times(U_3139),U_3142),U_3146)),U_3140)))
        | ~ sP224(U_3139,U_3148,U_3144,U_3140,U_3141,U_3142,U_3146,U_3143,U_3145,U_3147,U_3149) )
    & ! [U_3139,U_3148,U_3144,U_3140,U_3141,U_3142,U_3146,U_3143,U_3145,U_3147,U_3149] :
        ( sP224(U_3139,U_3148,U_3144,U_3140,U_3141,U_3142,U_3146,U_3143,U_3145,U_3147,U_3149)
        | ~ ordered_ring(U_3139) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP224])],[f_799_3]) ).

cnf(f_799_5,plain,
    ( sP224(U_3139,U_3148,U_3144,U_3140,U_3141,U_3142,U_3146,U_3143,U_3145,U_3147,U_3149)
    | ~ ordered_ring(U_3139) ),
    inference(clausify,[status(thm)],[f_799_4]) ).

cnf(f_799_6,plain,
    ( hBOOL(hAPP(U_3139,bool,hAPP(U_3139,fun(U_3139,bool),ord_less(U_3139),hAPP(U_3139,U_3139,hAPP(U_3139,fun(U_3139,U_3139),plus_plus(U_3139),hAPP(U_3139,U_3139,hAPP(U_3139,fun(U_3139,U_3139),times_times(U_3139),hAPP(U_3139,U_3139,hAPP(U_3139,fun(U_3139,U_3139),minus_minus(U_3139),U_3148),U_3142)),U_3146)),U_3144)),U_3140))
    | ~ hBOOL(hAPP(U_3139,bool,hAPP(U_3139,fun(U_3139,bool),ord_less(U_3139),hAPP(U_3139,U_3139,hAPP(U_3139,fun(U_3139,U_3139),plus_plus(U_3139),hAPP(U_3139,U_3139,hAPP(U_3139,fun(U_3139,U_3139),times_times(U_3139),U_3148),U_3146)),U_3144)),hAPP(U_3139,U_3139,hAPP(U_3139,fun(U_3139,U_3139),plus_plus(U_3139),hAPP(U_3139,U_3139,hAPP(U_3139,fun(U_3139,U_3139),times_times(U_3139),U_3142),U_3146)),U_3140)))
    | ~ sP224(U_3139,U_3148,U_3144,U_3140,U_3141,U_3142,U_3146,U_3143,U_3145,U_3147,U_3149) ),
    inference(clausify,[status(thm)],[f_799_4]) ).

cnf(f_799_7,plain,
    ( hBOOL(hAPP(U_3139,bool,hAPP(U_3139,fun(U_3139,bool),ord_less(U_3139),hAPP(U_3139,U_3139,hAPP(U_3139,fun(U_3139,U_3139),plus_plus(U_3139),hAPP(U_3139,U_3139,hAPP(U_3139,fun(U_3139,U_3139),times_times(U_3139),U_3149),U_3147)),U_3145)),hAPP(U_3139,U_3139,hAPP(U_3139,fun(U_3139,U_3139),plus_plus(U_3139),hAPP(U_3139,U_3139,hAPP(U_3139,fun(U_3139,U_3139),times_times(U_3139),U_3143),U_3147)),U_3141)))
    | ~ hBOOL(hAPP(U_3139,bool,hAPP(U_3139,fun(U_3139,bool),ord_less(U_3139),hAPP(U_3139,U_3139,hAPP(U_3139,fun(U_3139,U_3139),plus_plus(U_3139),hAPP(U_3139,U_3139,hAPP(U_3139,fun(U_3139,U_3139),times_times(U_3139),hAPP(U_3139,U_3139,hAPP(U_3139,fun(U_3139,U_3139),minus_minus(U_3139),U_3149),U_3143)),U_3147)),U_3145)),U_3141))
    | ~ sP224(U_3139,U_3148,U_3144,U_3140,U_3141,U_3142,U_3146,U_3143,U_3145,U_3147,U_3149) ),
    inference(clausify,[status(thm)],[f_799_4]) ).

fof(f_800_1,plain,
    ! [M_1,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),M_1))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),N)) ),
    inference(fof_nnf,[status(thm)],[fact_729_n__less__m__mult__n]) ).

fof(f_800_2,plain,
    ! [U_3151,U_3150] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3150),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3151),U_3150)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_3151))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_3150)) ),
    inference(variable_rename,[status(thm)],[f_800_1]) ).

fof(f_800_3,plain,
    ! [U_3150,U_3151] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3150),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3151),U_3150)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_3151))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_3150)) ),
    inference(definitional_conversion,[status(esa)],[f_800_2]) ).

cnf(f_800_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3150),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3151),U_3150)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_3151))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_3150)) ),
    inference(clausify,[status(thm)],[f_800_3]) ).

fof(f_801_1,plain,
    ! [M_1,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),M_1)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),M_1))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),N)) ),
    inference(fof_nnf,[status(thm)],[fact_730_n__less__n__mult__m]) ).

fof(f_801_2,plain,
    ! [U_3153,U_3152] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3152),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3152),U_3153)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_3153))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_3152)) ),
    inference(variable_rename,[status(thm)],[f_801_1]) ).

fof(f_801_3,plain,
    ! [U_3153,U_3152] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3152),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3152),U_3153)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_3153))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_3152)) ),
    inference(definitional_conversion,[status(esa)],[f_801_2]) ).

cnf(f_801_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3152),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3152),U_3153)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_3153))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_3152)) ),
    inference(clausify,[status(thm)],[f_801_3]) ).

fof(f_802_1,plain,
    ! [M_1,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),M_1))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),N)) ),
    inference(fof_nnf,[status(thm)],[fact_731_one__less__mult]) ).

fof(f_802_2,plain,
    ! [U_3155,U_3154] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3155),U_3154)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_3155))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_3154)) ),
    inference(variable_rename,[status(thm)],[f_802_1]) ).

fof(f_802_3,plain,
    ! [U_3155,U_3154] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3155),U_3154)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_3155))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_3154)) ),
    inference(definitional_conversion,[status(esa)],[f_802_2]) ).

cnf(f_802_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3155),U_3154)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_3155))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_3154)) ),
    inference(clausify,[status(thm)],[f_802_3]) ).

fof(f_803_1,plain,
    ! [M,Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),Na))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),M)) )
      & ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),Na))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),M)) )
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_732_one__le__mult__iff]) ).

fof(f_803_2,plain,
    ! [U_3157,U_3156] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3157),U_3156)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_3156))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_3157)) )
      & ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_3156))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_3157)) )
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3157),U_3156))) ) ),
    inference(variable_rename,[status(thm)],[f_803_1]) ).

fof(f_803_3,plain,
    ( ! [U_3161,U_3159] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3161),U_3159)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_3159))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_3161)) )
    & ! [U_3160,U_3158] :
        ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_3158))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_3160)) )
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3160),U_3158))) ) ),
    inference(miniscope,[status(thm)],[f_803_2]) ).

fof(f_803_4,plain,
    ( ! [U_3160,U_3158] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_3158))
        | ~ sP225(U_3160,U_3158) )
    & ! [U_3160,U_3158] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_3160))
        | ~ sP225(U_3160,U_3158) )
    & ! [U_3159,U_3161] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3161),U_3159)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_3159))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_3161)) )
    & ! [U_3160,U_3158] :
        ( sP225(U_3160,U_3158)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3160),U_3158))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP225])],[f_803_3]) ).

cnf(f_803_5,plain,
    ( sP225(U_3160,U_3158)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3160),U_3158))) ),
    inference(clausify,[status(thm)],[f_803_4]) ).

cnf(f_803_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3161),U_3159)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_3159))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_3161)) ),
    inference(clausify,[status(thm)],[f_803_4]) ).

cnf(f_803_7,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_3160))
    | ~ sP225(U_3160,U_3158) ),
    inference(clausify,[status(thm)],[f_803_4]) ).

cnf(f_803_8,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_3158))
    | ~ sP225(U_3160,U_3158) ),
    inference(clausify,[status(thm)],[f_803_4]) ).

fof(f_804_1,plain,
    ! [K,M,Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na)))
        | ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) ) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_733_mult__le__cancel1]) ).

fof(f_804_2,plain,
    ! [U_3164,U_3163,U_3162] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3164),U_3163)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3164),U_3162)))
        | ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3163),U_3162))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_3164)) ) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3163),U_3162))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_3164))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3164),U_3163)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3164),U_3162))) ) ),
    inference(variable_rename,[status(thm)],[f_804_1]) ).

fof(f_804_3,plain,
    ( ! [U_3170,U_3168,U_3166] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3170),U_3168)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3170),U_3166)))
        | ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3168),U_3166))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_3170)) ) )
    & ! [U_3169,U_3167,U_3165] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3167),U_3165))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_3169))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3169),U_3167)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3169),U_3165))) ) ),
    inference(miniscope,[status(thm)],[f_804_2]) ).

fof(f_804_4,plain,
    ( ! [U_3166,U_3168,U_3170] :
        ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3168),U_3166))
        | ~ sP226(U_3166,U_3168,U_3170) )
    & ! [U_3166,U_3168,U_3170] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_3170))
        | ~ sP226(U_3166,U_3168,U_3170) )
    & ! [U_3166,U_3168,U_3170] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3170),U_3168)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3170),U_3166)))
        | sP226(U_3166,U_3168,U_3170) )
    & ! [U_3165,U_3167,U_3169] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3167),U_3165))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_3169))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3169),U_3167)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3169),U_3165))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP226])],[f_804_3]) ).

cnf(f_804_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3167),U_3165))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_3169))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3169),U_3167)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3169),U_3165))) ),
    inference(clausify,[status(thm)],[f_804_4]) ).

cnf(f_804_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3170),U_3168)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3170),U_3166)))
    | sP226(U_3166,U_3168,U_3170) ),
    inference(clausify,[status(thm)],[f_804_4]) ).

cnf(f_804_7,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_3170))
    | ~ sP226(U_3166,U_3168,U_3170) ),
    inference(clausify,[status(thm)],[f_804_4]) ).

cnf(f_804_8,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3168),U_3166))
    | ~ sP226(U_3166,U_3168,U_3170) ),
    inference(clausify,[status(thm)],[f_804_4]) ).

fof(f_805_1,plain,
    ! [M,K,Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Na),K)))
        | ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) ) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Na),K))) ) ),
    inference(fof_nnf,[status(thm)],[fact_734_mult__le__cancel2]) ).

fof(f_805_2,plain,
    ! [U_3173,U_3172,U_3171] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3173),U_3172)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3171),U_3172)))
        | ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3173),U_3171))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_3172)) ) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3173),U_3171))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_3172))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3173),U_3172)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3171),U_3172))) ) ),
    inference(variable_rename,[status(thm)],[f_805_1]) ).

fof(f_805_3,plain,
    ( ! [U_3179,U_3177,U_3175] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3179),U_3177)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3175),U_3177)))
        | ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3179),U_3175))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_3177)) ) )
    & ! [U_3178,U_3176,U_3174] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3178),U_3174))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_3176))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3178),U_3176)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3174),U_3176))) ) ),
    inference(miniscope,[status(thm)],[f_805_2]) ).

fof(f_805_4,plain,
    ( ! [U_3175,U_3177,U_3179] :
        ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3179),U_3175))
        | ~ sP227(U_3175,U_3177,U_3179) )
    & ! [U_3175,U_3177,U_3179] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_3177))
        | ~ sP227(U_3175,U_3177,U_3179) )
    & ! [U_3175,U_3177,U_3179] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3179),U_3177)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3175),U_3177)))
        | sP227(U_3175,U_3177,U_3179) )
    & ! [U_3174,U_3176,U_3178] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3178),U_3174))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_3176))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3178),U_3176)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3174),U_3176))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP227])],[f_805_3]) ).

cnf(f_805_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3178),U_3174))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_3176))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3178),U_3176)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3174),U_3176))) ),
    inference(clausify,[status(thm)],[f_805_4]) ).

cnf(f_805_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3179),U_3177)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3175),U_3177)))
    | sP227(U_3175,U_3177,U_3179) ),
    inference(clausify,[status(thm)],[f_805_4]) ).

cnf(f_805_7,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_3177))
    | ~ sP227(U_3175,U_3177,U_3179) ),
    inference(clausify,[status(thm)],[f_805_4]) ).

cnf(f_805_8,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3179),U_3175))
    | ~ sP227(U_3175,U_3177,U_3179) ),
    inference(clausify,[status(thm)],[f_805_4]) ).

fof(f_806_1,plain,
    ! [X_b,X_c] :
      ( ! [G,Z_2,A_2,A_3] :
          ( hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),G),Z_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),A_3)) = hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),times_times(X_c),hAPP(X_b,X_c,G,A_2)),hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),G),Z_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))
          | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) )
      | ~ ab_semigroup_mult(X_c) ),
    inference(fof_nnf,[status(thm)],[fact_735_fold__image__insert]) ).

fof(f_806_2,plain,
    ! [U_3185,U_3184] :
      ( ! [U_3183,U_3182,U_3181,U_3180] :
          ( hAPP(fun(U_3185,bool),U_3184,hAPP(U_3184,fun(fun(U_3185,bool),U_3184),hAPP(fun(U_3185,U_3184),fun(U_3184,fun(fun(U_3185,bool),U_3184)),hAPP(fun(U_3184,fun(U_3184,U_3184)),fun(fun(U_3185,U_3184),fun(U_3184,fun(fun(U_3185,bool),U_3184))),finite_fold_image(U_3184,U_3185),times_times(U_3184)),U_3183),U_3182),hAPP(fun(U_3185,bool),fun(U_3185,bool),hAPP(U_3185,fun(fun(U_3185,bool),fun(U_3185,bool)),insert(U_3185),U_3181),U_3180)) = hAPP(U_3184,U_3184,hAPP(U_3184,fun(U_3184,U_3184),times_times(U_3184),hAPP(U_3185,U_3184,U_3183,U_3181)),hAPP(fun(U_3185,bool),U_3184,hAPP(U_3184,fun(fun(U_3185,bool),U_3184),hAPP(fun(U_3185,U_3184),fun(U_3184,fun(fun(U_3185,bool),U_3184)),hAPP(fun(U_3184,fun(U_3184,U_3184)),fun(fun(U_3185,U_3184),fun(U_3184,fun(fun(U_3185,bool),U_3184))),finite_fold_image(U_3184,U_3185),times_times(U_3184)),U_3183),U_3182),U_3180))
          | hBOOL(hAPP(fun(U_3185,bool),bool,hAPP(U_3185,fun(fun(U_3185,bool),bool),member(U_3185),U_3181),U_3180))
          | ~ hBOOL(hAPP(fun(U_3185,bool),bool,finite_finite(U_3185),U_3180)) )
      | ~ ab_semigroup_mult(U_3184) ),
    inference(variable_rename,[status(thm)],[f_806_1]) ).

fof(f_806_3,plain,
    ! [U_3181,U_3184,U_3180,U_3183,U_3182,U_3185] :
      ( hAPP(fun(U_3185,bool),U_3184,hAPP(U_3184,fun(fun(U_3185,bool),U_3184),hAPP(fun(U_3185,U_3184),fun(U_3184,fun(fun(U_3185,bool),U_3184)),hAPP(fun(U_3184,fun(U_3184,U_3184)),fun(fun(U_3185,U_3184),fun(U_3184,fun(fun(U_3185,bool),U_3184))),finite_fold_image(U_3184,U_3185),times_times(U_3184)),U_3183),U_3182),hAPP(fun(U_3185,bool),fun(U_3185,bool),hAPP(U_3185,fun(fun(U_3185,bool),fun(U_3185,bool)),insert(U_3185),U_3181),U_3180)) = hAPP(U_3184,U_3184,hAPP(U_3184,fun(U_3184,U_3184),times_times(U_3184),hAPP(U_3185,U_3184,U_3183,U_3181)),hAPP(fun(U_3185,bool),U_3184,hAPP(U_3184,fun(fun(U_3185,bool),U_3184),hAPP(fun(U_3185,U_3184),fun(U_3184,fun(fun(U_3185,bool),U_3184)),hAPP(fun(U_3184,fun(U_3184,U_3184)),fun(fun(U_3185,U_3184),fun(U_3184,fun(fun(U_3185,bool),U_3184))),finite_fold_image(U_3184,U_3185),times_times(U_3184)),U_3183),U_3182),U_3180))
      | hBOOL(hAPP(fun(U_3185,bool),bool,hAPP(U_3185,fun(fun(U_3185,bool),bool),member(U_3185),U_3181),U_3180))
      | ~ hBOOL(hAPP(fun(U_3185,bool),bool,finite_finite(U_3185),U_3180))
      | ~ ab_semigroup_mult(U_3184) ),
    inference(definitional_conversion,[status(esa)],[f_806_2]) ).

cnf(f_806_4,plain,
    ( hAPP(fun(U_3185,bool),U_3184,hAPP(U_3184,fun(fun(U_3185,bool),U_3184),hAPP(fun(U_3185,U_3184),fun(U_3184,fun(fun(U_3185,bool),U_3184)),hAPP(fun(U_3184,fun(U_3184,U_3184)),fun(fun(U_3185,U_3184),fun(U_3184,fun(fun(U_3185,bool),U_3184))),finite_fold_image(U_3184,U_3185),times_times(U_3184)),U_3183),U_3182),hAPP(fun(U_3185,bool),fun(U_3185,bool),hAPP(U_3185,fun(fun(U_3185,bool),fun(U_3185,bool)),insert(U_3185),U_3181),U_3180)) = hAPP(U_3184,U_3184,hAPP(U_3184,fun(U_3184,U_3184),times_times(U_3184),hAPP(U_3185,U_3184,U_3183,U_3181)),hAPP(fun(U_3185,bool),U_3184,hAPP(U_3184,fun(fun(U_3185,bool),U_3184),hAPP(fun(U_3185,U_3184),fun(U_3184,fun(fun(U_3185,bool),U_3184)),hAPP(fun(U_3184,fun(U_3184,U_3184)),fun(fun(U_3185,U_3184),fun(U_3184,fun(fun(U_3185,bool),U_3184))),finite_fold_image(U_3184,U_3185),times_times(U_3184)),U_3183),U_3182),U_3180))
    | hBOOL(hAPP(fun(U_3185,bool),bool,hAPP(U_3185,fun(fun(U_3185,bool),bool),member(U_3185),U_3181),U_3180))
    | ~ hBOOL(hAPP(fun(U_3185,bool),bool,finite_finite(U_3185),U_3180))
    | ~ ab_semigroup_mult(U_3184) ),
    inference(clausify,[status(thm)],[f_806_3]) ).

fof(f_807_1,plain,
    ! [X_b,X_c] :
      ( ! [G,H,A_3] :
          ( hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),hAPP(fun(X_b,X_c),fun(X_b,X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_b,X_c)),combs(X_b,X_c,X_c),hAPP(fun(X_b,X_c),fun(X_b,fun(X_c,X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_b,fun(X_c,X_c))),combb(X_c,fun(X_c,X_c),X_b),times_times(X_c)),G)),H)),one_one(X_c)),A_3) = hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),times_times(X_c),hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),G),one_one(X_c)),A_3)),hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),H),one_one(X_c)),A_3))
          | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) )
      | ~ comm_monoid_mult(X_c) ),
    inference(fof_nnf,[status(thm)],[fact_736_fold__image__distrib]) ).

fof(f_807_2,plain,
    ! [U_3190,U_3189] :
      ( ! [U_3188,U_3187,U_3186] :
          ( hAPP(fun(U_3190,bool),U_3189,hAPP(U_3189,fun(fun(U_3190,bool),U_3189),hAPP(fun(U_3190,U_3189),fun(U_3189,fun(fun(U_3190,bool),U_3189)),hAPP(fun(U_3189,fun(U_3189,U_3189)),fun(fun(U_3190,U_3189),fun(U_3189,fun(fun(U_3190,bool),U_3189))),finite_fold_image(U_3189,U_3190),times_times(U_3189)),hAPP(fun(U_3190,U_3189),fun(U_3190,U_3189),hAPP(fun(U_3190,fun(U_3189,U_3189)),fun(fun(U_3190,U_3189),fun(U_3190,U_3189)),combs(U_3190,U_3189,U_3189),hAPP(fun(U_3190,U_3189),fun(U_3190,fun(U_3189,U_3189)),hAPP(fun(U_3189,fun(U_3189,U_3189)),fun(fun(U_3190,U_3189),fun(U_3190,fun(U_3189,U_3189))),combb(U_3189,fun(U_3189,U_3189),U_3190),times_times(U_3189)),U_3188)),U_3187)),one_one(U_3189)),U_3186) = hAPP(U_3189,U_3189,hAPP(U_3189,fun(U_3189,U_3189),times_times(U_3189),hAPP(fun(U_3190,bool),U_3189,hAPP(U_3189,fun(fun(U_3190,bool),U_3189),hAPP(fun(U_3190,U_3189),fun(U_3189,fun(fun(U_3190,bool),U_3189)),hAPP(fun(U_3189,fun(U_3189,U_3189)),fun(fun(U_3190,U_3189),fun(U_3189,fun(fun(U_3190,bool),U_3189))),finite_fold_image(U_3189,U_3190),times_times(U_3189)),U_3188),one_one(U_3189)),U_3186)),hAPP(fun(U_3190,bool),U_3189,hAPP(U_3189,fun(fun(U_3190,bool),U_3189),hAPP(fun(U_3190,U_3189),fun(U_3189,fun(fun(U_3190,bool),U_3189)),hAPP(fun(U_3189,fun(U_3189,U_3189)),fun(fun(U_3190,U_3189),fun(U_3189,fun(fun(U_3190,bool),U_3189))),finite_fold_image(U_3189,U_3190),times_times(U_3189)),U_3187),one_one(U_3189)),U_3186))
          | ~ hBOOL(hAPP(fun(U_3190,bool),bool,finite_finite(U_3190),U_3186)) )
      | ~ comm_monoid_mult(U_3189) ),
    inference(variable_rename,[status(thm)],[f_807_1]) ).

fof(f_807_3,plain,
    ! [U_3186,U_3187,U_3189,U_3188,U_3190] :
      ( hAPP(fun(U_3190,bool),U_3189,hAPP(U_3189,fun(fun(U_3190,bool),U_3189),hAPP(fun(U_3190,U_3189),fun(U_3189,fun(fun(U_3190,bool),U_3189)),hAPP(fun(U_3189,fun(U_3189,U_3189)),fun(fun(U_3190,U_3189),fun(U_3189,fun(fun(U_3190,bool),U_3189))),finite_fold_image(U_3189,U_3190),times_times(U_3189)),hAPP(fun(U_3190,U_3189),fun(U_3190,U_3189),hAPP(fun(U_3190,fun(U_3189,U_3189)),fun(fun(U_3190,U_3189),fun(U_3190,U_3189)),combs(U_3190,U_3189,U_3189),hAPP(fun(U_3190,U_3189),fun(U_3190,fun(U_3189,U_3189)),hAPP(fun(U_3189,fun(U_3189,U_3189)),fun(fun(U_3190,U_3189),fun(U_3190,fun(U_3189,U_3189))),combb(U_3189,fun(U_3189,U_3189),U_3190),times_times(U_3189)),U_3188)),U_3187)),one_one(U_3189)),U_3186) = hAPP(U_3189,U_3189,hAPP(U_3189,fun(U_3189,U_3189),times_times(U_3189),hAPP(fun(U_3190,bool),U_3189,hAPP(U_3189,fun(fun(U_3190,bool),U_3189),hAPP(fun(U_3190,U_3189),fun(U_3189,fun(fun(U_3190,bool),U_3189)),hAPP(fun(U_3189,fun(U_3189,U_3189)),fun(fun(U_3190,U_3189),fun(U_3189,fun(fun(U_3190,bool),U_3189))),finite_fold_image(U_3189,U_3190),times_times(U_3189)),U_3188),one_one(U_3189)),U_3186)),hAPP(fun(U_3190,bool),U_3189,hAPP(U_3189,fun(fun(U_3190,bool),U_3189),hAPP(fun(U_3190,U_3189),fun(U_3189,fun(fun(U_3190,bool),U_3189)),hAPP(fun(U_3189,fun(U_3189,U_3189)),fun(fun(U_3190,U_3189),fun(U_3189,fun(fun(U_3190,bool),U_3189))),finite_fold_image(U_3189,U_3190),times_times(U_3189)),U_3187),one_one(U_3189)),U_3186))
      | ~ hBOOL(hAPP(fun(U_3190,bool),bool,finite_finite(U_3190),U_3186))
      | ~ comm_monoid_mult(U_3189) ),
    inference(definitional_conversion,[status(esa)],[f_807_2]) ).

cnf(f_807_4,plain,
    ( hAPP(fun(U_3190,bool),U_3189,hAPP(U_3189,fun(fun(U_3190,bool),U_3189),hAPP(fun(U_3190,U_3189),fun(U_3189,fun(fun(U_3190,bool),U_3189)),hAPP(fun(U_3189,fun(U_3189,U_3189)),fun(fun(U_3190,U_3189),fun(U_3189,fun(fun(U_3190,bool),U_3189))),finite_fold_image(U_3189,U_3190),times_times(U_3189)),hAPP(fun(U_3190,U_3189),fun(U_3190,U_3189),hAPP(fun(U_3190,fun(U_3189,U_3189)),fun(fun(U_3190,U_3189),fun(U_3190,U_3189)),combs(U_3190,U_3189,U_3189),hAPP(fun(U_3190,U_3189),fun(U_3190,fun(U_3189,U_3189)),hAPP(fun(U_3189,fun(U_3189,U_3189)),fun(fun(U_3190,U_3189),fun(U_3190,fun(U_3189,U_3189))),combb(U_3189,fun(U_3189,U_3189),U_3190),times_times(U_3189)),U_3188)),U_3187)),one_one(U_3189)),U_3186) = hAPP(U_3189,U_3189,hAPP(U_3189,fun(U_3189,U_3189),times_times(U_3189),hAPP(fun(U_3190,bool),U_3189,hAPP(U_3189,fun(fun(U_3190,bool),U_3189),hAPP(fun(U_3190,U_3189),fun(U_3189,fun(fun(U_3190,bool),U_3189)),hAPP(fun(U_3189,fun(U_3189,U_3189)),fun(fun(U_3190,U_3189),fun(U_3189,fun(fun(U_3190,bool),U_3189))),finite_fold_image(U_3189,U_3190),times_times(U_3189)),U_3188),one_one(U_3189)),U_3186)),hAPP(fun(U_3190,bool),U_3189,hAPP(U_3189,fun(fun(U_3190,bool),U_3189),hAPP(fun(U_3190,U_3189),fun(U_3189,fun(fun(U_3190,bool),U_3189)),hAPP(fun(U_3189,fun(U_3189,U_3189)),fun(fun(U_3190,U_3189),fun(U_3189,fun(fun(U_3190,bool),U_3189))),finite_fold_image(U_3189,U_3190),times_times(U_3189)),U_3187),one_one(U_3189)),U_3186))
    | ~ hBOOL(hAPP(fun(U_3190,bool),bool,finite_finite(U_3190),U_3186))
    | ~ comm_monoid_mult(U_3189) ),
    inference(clausify,[status(thm)],[f_807_3]) ).

fof(f_808_1,plain,
    ! [X_a] :
      ( ! [V,U_1,Y,X,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),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),U_1),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),V),Y))),A_1))
          | hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),U_1),V) != one_one(X_a)
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),V))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),U_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),A_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),A_1)) )
      | ~ linord1278240602ring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_737_convex__bound__le]) ).

fof(f_808_2,plain,
    ! [U_3196] :
      ( ! [U_3195,U_3194,U_3193,U_3192,U_3191] :
          ( hBOOL(hAPP(U_3196,bool,hAPP(U_3196,fun(U_3196,bool),ord_less_eq(U_3196),hAPP(U_3196,U_3196,hAPP(U_3196,fun(U_3196,U_3196),plus_plus(U_3196),hAPP(U_3196,U_3196,hAPP(U_3196,fun(U_3196,U_3196),times_times(U_3196),U_3194),U_3192)),hAPP(U_3196,U_3196,hAPP(U_3196,fun(U_3196,U_3196),times_times(U_3196),U_3195),U_3193))),U_3191))
          | hAPP(U_3196,U_3196,hAPP(U_3196,fun(U_3196,U_3196),plus_plus(U_3196),U_3194),U_3195) != one_one(U_3196)
          | ~ hBOOL(hAPP(U_3196,bool,hAPP(U_3196,fun(U_3196,bool),ord_less_eq(U_3196),zero_zero(U_3196)),U_3195))
          | ~ hBOOL(hAPP(U_3196,bool,hAPP(U_3196,fun(U_3196,bool),ord_less_eq(U_3196),zero_zero(U_3196)),U_3194))
          | ~ hBOOL(hAPP(U_3196,bool,hAPP(U_3196,fun(U_3196,bool),ord_less_eq(U_3196),U_3193),U_3191))
          | ~ hBOOL(hAPP(U_3196,bool,hAPP(U_3196,fun(U_3196,bool),ord_less_eq(U_3196),U_3192),U_3191)) )
      | ~ linord1278240602ring_1(U_3196) ),
    inference(variable_rename,[status(thm)],[f_808_1]) ).

fof(f_808_3,plain,
    ! [U_3191,U_3196,U_3192,U_3193,U_3194,U_3195] :
      ( hBOOL(hAPP(U_3196,bool,hAPP(U_3196,fun(U_3196,bool),ord_less_eq(U_3196),hAPP(U_3196,U_3196,hAPP(U_3196,fun(U_3196,U_3196),plus_plus(U_3196),hAPP(U_3196,U_3196,hAPP(U_3196,fun(U_3196,U_3196),times_times(U_3196),U_3194),U_3192)),hAPP(U_3196,U_3196,hAPP(U_3196,fun(U_3196,U_3196),times_times(U_3196),U_3195),U_3193))),U_3191))
      | hAPP(U_3196,U_3196,hAPP(U_3196,fun(U_3196,U_3196),plus_plus(U_3196),U_3194),U_3195) != one_one(U_3196)
      | ~ hBOOL(hAPP(U_3196,bool,hAPP(U_3196,fun(U_3196,bool),ord_less_eq(U_3196),zero_zero(U_3196)),U_3195))
      | ~ hBOOL(hAPP(U_3196,bool,hAPP(U_3196,fun(U_3196,bool),ord_less_eq(U_3196),zero_zero(U_3196)),U_3194))
      | ~ hBOOL(hAPP(U_3196,bool,hAPP(U_3196,fun(U_3196,bool),ord_less_eq(U_3196),U_3193),U_3191))
      | ~ hBOOL(hAPP(U_3196,bool,hAPP(U_3196,fun(U_3196,bool),ord_less_eq(U_3196),U_3192),U_3191))
      | ~ linord1278240602ring_1(U_3196) ),
    inference(definitional_conversion,[status(esa)],[f_808_2]) ).

cnf(f_808_4,plain,
    ( hBOOL(hAPP(U_3196,bool,hAPP(U_3196,fun(U_3196,bool),ord_less_eq(U_3196),hAPP(U_3196,U_3196,hAPP(U_3196,fun(U_3196,U_3196),plus_plus(U_3196),hAPP(U_3196,U_3196,hAPP(U_3196,fun(U_3196,U_3196),times_times(U_3196),U_3194),U_3192)),hAPP(U_3196,U_3196,hAPP(U_3196,fun(U_3196,U_3196),times_times(U_3196),U_3195),U_3193))),U_3191))
    | hAPP(U_3196,U_3196,hAPP(U_3196,fun(U_3196,U_3196),plus_plus(U_3196),U_3194),U_3195) != one_one(U_3196)
    | ~ hBOOL(hAPP(U_3196,bool,hAPP(U_3196,fun(U_3196,bool),ord_less_eq(U_3196),zero_zero(U_3196)),U_3195))
    | ~ hBOOL(hAPP(U_3196,bool,hAPP(U_3196,fun(U_3196,bool),ord_less_eq(U_3196),zero_zero(U_3196)),U_3194))
    | ~ hBOOL(hAPP(U_3196,bool,hAPP(U_3196,fun(U_3196,bool),ord_less_eq(U_3196),U_3193),U_3191))
    | ~ hBOOL(hAPP(U_3196,bool,hAPP(U_3196,fun(U_3196,bool),ord_less_eq(U_3196),U_3192),U_3191))
    | ~ linord1278240602ring_1(U_3196) ),
    inference(clausify,[status(thm)],[f_808_3]) ).

fof(f_809_1,plain,
    ! [N,M_1] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),one_one(nat))),N))
        | M_1 = zero_zero(nat) )
      & ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N) = zero_zero(nat)
        | M_1 != zero_zero(nat) ) ),
    inference(fof_nnf,[status(thm)],[fact_738_mult__eq__if]) ).

fof(f_809_2,plain,
    ! [U_3198,U_3197] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3197),U_3198) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_3198),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3197),one_one(nat))),U_3198))
        | U_3197 = zero_zero(nat) )
      & ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3197),U_3198) = zero_zero(nat)
        | U_3197 != zero_zero(nat) ) ),
    inference(variable_rename,[status(thm)],[f_809_1]) ).

fof(f_809_3,plain,
    ( ! [U_3202,U_3200] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3200),U_3202) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_3202),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3200),one_one(nat))),U_3202))
        | U_3200 = zero_zero(nat) )
    & ! [U_3201,U_3199] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3199),U_3201) = zero_zero(nat)
        | U_3199 != zero_zero(nat) ) ),
    inference(miniscope,[status(thm)],[f_809_2]) ).

fof(f_809_4,plain,
    ( ! [U_3200,U_3202] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3200),U_3202) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_3202),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3200),one_one(nat))),U_3202))
        | U_3200 = zero_zero(nat) )
    & ! [U_3199,U_3201] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3199),U_3201) = zero_zero(nat)
        | U_3199 != zero_zero(nat) ) ),
    inference(definitional_conversion,[status(esa)],[f_809_3]) ).

cnf(f_809_5,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3199),U_3201) = zero_zero(nat)
    | U_3199 != zero_zero(nat) ),
    inference(clausify,[status(thm)],[f_809_4]) ).

cnf(f_809_6,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3200),U_3202) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_3202),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3200),one_one(nat))),U_3202))
    | U_3200 = zero_zero(nat) ),
    inference(clausify,[status(thm)],[f_809_4]) ).

fof(f_810_1,plain,
    ! [X_b] :
      ( ! [A_2] :
          ( hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),one_one(X_b)),A_2)),A_2) != zero_zero(X_b)
          | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),ring_1_Ints(X_b))) )
      | ~ ring_char_0(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_739_Ints__odd__nonzero]) ).

fof(f_810_2,plain,
    ! [U_3204] :
      ( ! [U_3203] :
          ( hAPP(U_3204,U_3204,hAPP(U_3204,fun(U_3204,U_3204),plus_plus(U_3204),hAPP(U_3204,U_3204,hAPP(U_3204,fun(U_3204,U_3204),plus_plus(U_3204),one_one(U_3204)),U_3203)),U_3203) != zero_zero(U_3204)
          | ~ hBOOL(hAPP(fun(U_3204,bool),bool,hAPP(U_3204,fun(fun(U_3204,bool),bool),member(U_3204),U_3203),ring_1_Ints(U_3204))) )
      | ~ ring_char_0(U_3204) ),
    inference(variable_rename,[status(thm)],[f_810_1]) ).

fof(f_810_3,plain,
    ! [U_3203,U_3204] :
      ( hAPP(U_3204,U_3204,hAPP(U_3204,fun(U_3204,U_3204),plus_plus(U_3204),hAPP(U_3204,U_3204,hAPP(U_3204,fun(U_3204,U_3204),plus_plus(U_3204),one_one(U_3204)),U_3203)),U_3203) != zero_zero(U_3204)
      | ~ hBOOL(hAPP(fun(U_3204,bool),bool,hAPP(U_3204,fun(fun(U_3204,bool),bool),member(U_3204),U_3203),ring_1_Ints(U_3204)))
      | ~ ring_char_0(U_3204) ),
    inference(definitional_conversion,[status(esa)],[f_810_2]) ).

cnf(f_810_4,plain,
    ( hAPP(U_3204,U_3204,hAPP(U_3204,fun(U_3204,U_3204),plus_plus(U_3204),hAPP(U_3204,U_3204,hAPP(U_3204,fun(U_3204,U_3204),plus_plus(U_3204),one_one(U_3204)),U_3203)),U_3203) != zero_zero(U_3204)
    | ~ hBOOL(hAPP(fun(U_3204,bool),bool,hAPP(U_3204,fun(fun(U_3204,bool),bool),member(U_3204),U_3203),ring_1_Ints(U_3204)))
    | ~ ring_char_0(U_3204) ),
    inference(clausify,[status(thm)],[f_810_3]) ).

fof(f_811_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))
          | ? [Z_3] :
              ( ~ 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),times_times(X_a),Z_3),X)),Y))
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_3),one_one(X_a)))
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Z_3)) ) )
      | ~ linord1117847801e_zero(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_740_field__le__mult__one__interval]) ).

fof(f_811_2,plain,
    ! [U_3208] :
      ( ! [U_3207,U_3206] :
          ( hBOOL(hAPP(U_3208,bool,hAPP(U_3208,fun(U_3208,bool),ord_less_eq(U_3208),U_3207),U_3206))
          | ? [U_3205] :
              ( ~ hBOOL(hAPP(U_3208,bool,hAPP(U_3208,fun(U_3208,bool),ord_less_eq(U_3208),hAPP(U_3208,U_3208,hAPP(U_3208,fun(U_3208,U_3208),times_times(U_3208),U_3205),U_3207)),U_3206))
              & hBOOL(hAPP(U_3208,bool,hAPP(U_3208,fun(U_3208,bool),ord_less(U_3208),U_3205),one_one(U_3208)))
              & hBOOL(hAPP(U_3208,bool,hAPP(U_3208,fun(U_3208,bool),ord_less(U_3208),zero_zero(U_3208)),U_3205)) ) )
      | ~ linord1117847801e_zero(U_3208) ),
    inference(variable_rename,[status(thm)],[f_811_1]) ).

fof(f_811_3,plain,
    ! [U_3208] :
      ( ! [U_3207,U_3206] :
          ( hBOOL(hAPP(U_3208,bool,hAPP(U_3208,fun(U_3208,bool),ord_less_eq(U_3208),U_3207),U_3206))
          | ( ~ hBOOL(hAPP(U_3208,bool,hAPP(U_3208,fun(U_3208,bool),ord_less_eq(U_3208),hAPP(U_3208,U_3208,hAPP(U_3208,fun(U_3208,U_3208),times_times(U_3208),sK100(U_3208,U_3207,U_3206)),U_3207)),U_3206))
            & hBOOL(hAPP(U_3208,bool,hAPP(U_3208,fun(U_3208,bool),ord_less(U_3208),sK100(U_3208,U_3207,U_3206)),one_one(U_3208)))
            & hBOOL(hAPP(U_3208,bool,hAPP(U_3208,fun(U_3208,bool),ord_less(U_3208),zero_zero(U_3208)),sK100(U_3208,U_3207,U_3206))) ) )
      | ~ linord1117847801e_zero(U_3208) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK100]),skolemize(U_3205,sK100(U_3208,U_3207,U_3206))],[f_811_2]) ).

fof(f_811_4,plain,
    ( ! [U_3206,U_3208,U_3207] :
        ( ~ hBOOL(hAPP(U_3208,bool,hAPP(U_3208,fun(U_3208,bool),ord_less_eq(U_3208),hAPP(U_3208,U_3208,hAPP(U_3208,fun(U_3208,U_3208),times_times(U_3208),sK100(U_3208,U_3207,U_3206)),U_3207)),U_3206))
        | ~ sP228(U_3206,U_3208,U_3207) )
    & ! [U_3206,U_3208,U_3207] :
        ( hBOOL(hAPP(U_3208,bool,hAPP(U_3208,fun(U_3208,bool),ord_less(U_3208),sK100(U_3208,U_3207,U_3206)),one_one(U_3208)))
        | ~ sP228(U_3206,U_3208,U_3207) )
    & ! [U_3206,U_3208,U_3207] :
        ( hBOOL(hAPP(U_3208,bool,hAPP(U_3208,fun(U_3208,bool),ord_less(U_3208),zero_zero(U_3208)),sK100(U_3208,U_3207,U_3206)))
        | ~ sP228(U_3206,U_3208,U_3207) )
    & ! [U_3206,U_3208,U_3207] :
        ( hBOOL(hAPP(U_3208,bool,hAPP(U_3208,fun(U_3208,bool),ord_less_eq(U_3208),U_3207),U_3206))
        | sP228(U_3206,U_3208,U_3207)
        | ~ linord1117847801e_zero(U_3208) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP228])],[f_811_3]) ).

cnf(f_811_5,plain,
    ( hBOOL(hAPP(U_3208,bool,hAPP(U_3208,fun(U_3208,bool),ord_less_eq(U_3208),U_3207),U_3206))
    | sP228(U_3206,U_3208,U_3207)
    | ~ linord1117847801e_zero(U_3208) ),
    inference(clausify,[status(thm)],[f_811_4]) ).

cnf(f_811_6,plain,
    ( hBOOL(hAPP(U_3208,bool,hAPP(U_3208,fun(U_3208,bool),ord_less(U_3208),zero_zero(U_3208)),sK100(U_3208,U_3207,U_3206)))
    | ~ sP228(U_3206,U_3208,U_3207) ),
    inference(clausify,[status(thm)],[f_811_4]) ).

cnf(f_811_7,plain,
    ( hBOOL(hAPP(U_3208,bool,hAPP(U_3208,fun(U_3208,bool),ord_less(U_3208),sK100(U_3208,U_3207,U_3206)),one_one(U_3208)))
    | ~ sP228(U_3206,U_3208,U_3207) ),
    inference(clausify,[status(thm)],[f_811_4]) ).

cnf(f_811_8,plain,
    ( ~ hBOOL(hAPP(U_3208,bool,hAPP(U_3208,fun(U_3208,bool),ord_less_eq(U_3208),hAPP(U_3208,U_3208,hAPP(U_3208,fun(U_3208,U_3208),times_times(U_3208),sK100(U_3208,U_3207,U_3206)),U_3207)),U_3206))
    | ~ sP228(U_3206,U_3208,U_3207) ),
    inference(clausify,[status(thm)],[f_811_4]) ).

fof(f_812_1,plain,
    ! [X_b,X_c] :
      ( ! [F,S] :
          ( hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),F),one_one(X_c)),S) = one_one(X_c)
          | ? [X_2] :
              ( hAPP(X_b,X_c,F,X_2) != one_one(X_c)
              & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),S)) )
          | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),S)) )
      | ~ comm_monoid_mult(X_c) ),
    inference(fof_nnf,[status(thm)],[fact_741_fold__image__1]) ).

fof(f_812_2,plain,
    ! [U_3213,U_3212] :
      ( ! [U_3211,U_3210] :
          ( hAPP(fun(U_3213,bool),U_3212,hAPP(U_3212,fun(fun(U_3213,bool),U_3212),hAPP(fun(U_3213,U_3212),fun(U_3212,fun(fun(U_3213,bool),U_3212)),hAPP(fun(U_3212,fun(U_3212,U_3212)),fun(fun(U_3213,U_3212),fun(U_3212,fun(fun(U_3213,bool),U_3212))),finite_fold_image(U_3212,U_3213),times_times(U_3212)),U_3211),one_one(U_3212)),U_3210) = one_one(U_3212)
          | ? [U_3209] :
              ( hAPP(U_3213,U_3212,U_3211,U_3209) != one_one(U_3212)
              & hBOOL(hAPP(fun(U_3213,bool),bool,hAPP(U_3213,fun(fun(U_3213,bool),bool),member(U_3213),U_3209),U_3210)) )
          | ~ hBOOL(hAPP(fun(U_3213,bool),bool,finite_finite(U_3213),U_3210)) )
      | ~ comm_monoid_mult(U_3212) ),
    inference(variable_rename,[status(thm)],[f_812_1]) ).

fof(f_812_3,plain,
    ! [U_3213,U_3212] :
      ( ! [U_3211,U_3210] :
          ( hAPP(fun(U_3213,bool),U_3212,hAPP(U_3212,fun(fun(U_3213,bool),U_3212),hAPP(fun(U_3213,U_3212),fun(U_3212,fun(fun(U_3213,bool),U_3212)),hAPP(fun(U_3212,fun(U_3212,U_3212)),fun(fun(U_3213,U_3212),fun(U_3212,fun(fun(U_3213,bool),U_3212))),finite_fold_image(U_3212,U_3213),times_times(U_3212)),U_3211),one_one(U_3212)),U_3210) = one_one(U_3212)
          | ( hAPP(U_3213,U_3212,U_3211,sK101(U_3213,U_3212,U_3211,U_3210)) != one_one(U_3212)
            & hBOOL(hAPP(fun(U_3213,bool),bool,hAPP(U_3213,fun(fun(U_3213,bool),bool),member(U_3213),sK101(U_3213,U_3212,U_3211,U_3210)),U_3210)) )
          | ~ hBOOL(hAPP(fun(U_3213,bool),bool,finite_finite(U_3213),U_3210)) )
      | ~ comm_monoid_mult(U_3212) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK101]),skolemize(U_3209,sK101(U_3213,U_3212,U_3211,U_3210))],[f_812_2]) ).

fof(f_812_4,plain,
    ( ! [U_3212,U_3210,U_3211,U_3213] :
        ( hAPP(U_3213,U_3212,U_3211,sK101(U_3213,U_3212,U_3211,U_3210)) != one_one(U_3212)
        | ~ sP229(U_3212,U_3210,U_3211,U_3213) )
    & ! [U_3212,U_3210,U_3211,U_3213] :
        ( hBOOL(hAPP(fun(U_3213,bool),bool,hAPP(U_3213,fun(fun(U_3213,bool),bool),member(U_3213),sK101(U_3213,U_3212,U_3211,U_3210)),U_3210))
        | ~ sP229(U_3212,U_3210,U_3211,U_3213) )
    & ! [U_3212,U_3210,U_3211,U_3213] :
        ( hAPP(fun(U_3213,bool),U_3212,hAPP(U_3212,fun(fun(U_3213,bool),U_3212),hAPP(fun(U_3213,U_3212),fun(U_3212,fun(fun(U_3213,bool),U_3212)),hAPP(fun(U_3212,fun(U_3212,U_3212)),fun(fun(U_3213,U_3212),fun(U_3212,fun(fun(U_3213,bool),U_3212))),finite_fold_image(U_3212,U_3213),times_times(U_3212)),U_3211),one_one(U_3212)),U_3210) = one_one(U_3212)
        | sP229(U_3212,U_3210,U_3211,U_3213)
        | ~ hBOOL(hAPP(fun(U_3213,bool),bool,finite_finite(U_3213),U_3210))
        | ~ comm_monoid_mult(U_3212) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP229])],[f_812_3]) ).

cnf(f_812_5,plain,
    ( hAPP(fun(U_3213,bool),U_3212,hAPP(U_3212,fun(fun(U_3213,bool),U_3212),hAPP(fun(U_3213,U_3212),fun(U_3212,fun(fun(U_3213,bool),U_3212)),hAPP(fun(U_3212,fun(U_3212,U_3212)),fun(fun(U_3213,U_3212),fun(U_3212,fun(fun(U_3213,bool),U_3212))),finite_fold_image(U_3212,U_3213),times_times(U_3212)),U_3211),one_one(U_3212)),U_3210) = one_one(U_3212)
    | sP229(U_3212,U_3210,U_3211,U_3213)
    | ~ hBOOL(hAPP(fun(U_3213,bool),bool,finite_finite(U_3213),U_3210))
    | ~ comm_monoid_mult(U_3212) ),
    inference(clausify,[status(thm)],[f_812_4]) ).

cnf(f_812_6,plain,
    ( hBOOL(hAPP(fun(U_3213,bool),bool,hAPP(U_3213,fun(fun(U_3213,bool),bool),member(U_3213),sK101(U_3213,U_3212,U_3211,U_3210)),U_3210))
    | ~ sP229(U_3212,U_3210,U_3211,U_3213) ),
    inference(clausify,[status(thm)],[f_812_4]) ).

cnf(f_812_7,plain,
    ( hAPP(U_3213,U_3212,U_3211,sK101(U_3213,U_3212,U_3211,U_3210)) != one_one(U_3212)
    | ~ sP229(U_3212,U_3210,U_3211,U_3213) ),
    inference(clausify,[status(thm)],[f_812_4]) ).

fof(f_813_1,plain,
    ! [U,M,Na,I_1,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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),Na)))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),I_1)),U)),Na))) )
        & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),I_1)),U)),Na)))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),Na))) ) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_1)) ),
    inference(fof_nnf,[status(thm)],[fact_742_nat__less__add__iff2]) ).

fof(f_813_2,plain,
    ! [U_3218,U_3217,U_3216,U_3215,U_3214] :
      ( ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3215),U_3218)),U_3217)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3214),U_3218)),U_3216)))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3217),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3214),U_3215)),U_3218)),U_3216))) )
        & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3217),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3214),U_3215)),U_3218)),U_3216)))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3215),U_3218)),U_3217)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3214),U_3218)),U_3216))) ) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3215),U_3214)) ),
    inference(variable_rename,[status(thm)],[f_813_1]) ).

fof(f_813_3,plain,
    ( ! [U_3214,U_3215,U_3216,U_3217,U_3218] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3215),U_3218)),U_3217)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3214),U_3218)),U_3216)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3217),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3214),U_3215)),U_3218)),U_3216)))
        | ~ sP230(U_3214,U_3215,U_3216,U_3217,U_3218) )
    & ! [U_3214,U_3215,U_3216,U_3217,U_3218] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3217),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3214),U_3215)),U_3218)),U_3216)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3215),U_3218)),U_3217)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3214),U_3218)),U_3216)))
        | ~ sP230(U_3214,U_3215,U_3216,U_3217,U_3218) )
    & ! [U_3214,U_3215,U_3216,U_3217,U_3218] :
        ( sP230(U_3214,U_3215,U_3216,U_3217,U_3218)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3215),U_3214)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP230])],[f_813_2]) ).

cnf(f_813_4,plain,
    ( sP230(U_3214,U_3215,U_3216,U_3217,U_3218)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3215),U_3214)) ),
    inference(clausify,[status(thm)],[f_813_3]) ).

cnf(f_813_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3217),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3214),U_3215)),U_3218)),U_3216)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3215),U_3218)),U_3217)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3214),U_3218)),U_3216)))
    | ~ sP230(U_3214,U_3215,U_3216,U_3217,U_3218) ),
    inference(clausify,[status(thm)],[f_813_3]) ).

cnf(f_813_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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3215),U_3218)),U_3217)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3214),U_3218)),U_3216)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3217),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3214),U_3215)),U_3218)),U_3216)))
    | ~ sP230(U_3214,U_3215,U_3216,U_3217,U_3218) ),
    inference(clausify,[status(thm)],[f_813_3]) ).

fof(f_814_1,plain,
    ! [M_1,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),M_1),
    inference(fof_nnf,[status(thm)],[fact_743_nat__mult__commute]) ).

fof(f_814_2,plain,
    ! [U_3220,U_3219] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3220),U_3219) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3219),U_3220),
    inference(variable_rename,[status(thm)],[f_814_1]) ).

fof(f_814_3,plain,
    ! [U_3219,U_3220] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3220),U_3219) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3219),U_3220),
    inference(definitional_conversion,[status(esa)],[f_814_2]) ).

cnf(f_814_4,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3220),U_3219) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3219),U_3220),
    inference(clausify,[status(thm)],[f_814_3]) ).

fof(f_815_1,plain,
    ! [M_1,N,K_1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N)),K_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),K_1)),
    inference(fof_nnf,[status(thm)],[fact_744_nat__mult__assoc]) ).

fof(f_815_2,plain,
    ! [U_3223,U_3222,U_3221] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3223),U_3222)),U_3221) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3223),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3222),U_3221)),
    inference(variable_rename,[status(thm)],[f_815_1]) ).

fof(f_815_3,plain,
    ! [U_3222,U_3221,U_3223] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3223),U_3222)),U_3221) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3223),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3222),U_3221)),
    inference(definitional_conversion,[status(esa)],[f_815_2]) ).

cnf(f_815_4,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3223),U_3222)),U_3221) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3223),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3222),U_3221)),
    inference(clausify,[status(thm)],[f_815_3]) ).

fof(f_816_1,plain,
    ! [K,L] :
      ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),K)),hAPP(int,int,number_number_of(int),L)))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L)) )
      & ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),K)),hAPP(int,int,number_number_of(int),L))) ) ),
    inference(fof_nnf,[status(thm)],[fact_745_less__number__of__int__code]) ).

fof(f_816_2,plain,
    ! [U_3225,U_3224] :
      ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),U_3225)),hAPP(int,int,number_number_of(int),U_3224)))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3225),U_3224)) )
      & ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3225),U_3224))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),U_3225)),hAPP(int,int,number_number_of(int),U_3224))) ) ),
    inference(variable_rename,[status(thm)],[f_816_1]) ).

fof(f_816_3,plain,
    ( ! [U_3229,U_3227] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),U_3229)),hAPP(int,int,number_number_of(int),U_3227)))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3229),U_3227)) )
    & ! [U_3228,U_3226] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3228),U_3226))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),U_3228)),hAPP(int,int,number_number_of(int),U_3226))) ) ),
    inference(miniscope,[status(thm)],[f_816_2]) ).

fof(f_816_4,plain,
    ( ! [U_3227,U_3229] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),U_3229)),hAPP(int,int,number_number_of(int),U_3227)))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3229),U_3227)) )
    & ! [U_3228,U_3226] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3228),U_3226))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),U_3228)),hAPP(int,int,number_number_of(int),U_3226))) ) ),
    inference(definitional_conversion,[status(esa)],[f_816_3]) ).

cnf(f_816_5,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3228),U_3226))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),U_3228)),hAPP(int,int,number_number_of(int),U_3226))) ),
    inference(clausify,[status(thm)],[f_816_4]) ).

cnf(f_816_6,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),U_3229)),hAPP(int,int,number_number_of(int),U_3227)))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3229),U_3227)) ),
    inference(clausify,[status(thm)],[f_816_4]) ).

fof(f_817_1,plain,
    ! [Z] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),one_one(int)),Z) = Z,
    inference(fof_nnf,[status(thm)],[fact_746_zmult__1]) ).

fof(f_817_2,plain,
    ! [U_3230] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),one_one(int)),U_3230) = U_3230,
    inference(variable_rename,[status(thm)],[f_817_1]) ).

fof(f_817_3,plain,
    ! [U_3230] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),one_one(int)),U_3230) = U_3230,
    inference(definitional_conversion,[status(esa)],[f_817_2]) ).

cnf(f_817_4,plain,
    hAPP(int,int,hAPP(int,fun(int,int),times_times(int),one_one(int)),U_3230) = U_3230,
    inference(clausify,[status(thm)],[f_817_3]) ).

fof(f_818_1,plain,
    ! [Z] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z),one_one(int)) = Z,
    inference(fof_nnf,[status(thm)],[fact_747_zmult__1__right]) ).

fof(f_818_2,plain,
    ! [U_3231] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3231),one_one(int)) = U_3231,
    inference(variable_rename,[status(thm)],[f_818_1]) ).

fof(f_818_3,plain,
    ! [U_3231] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3231),one_one(int)) = U_3231,
    inference(definitional_conversion,[status(esa)],[f_818_2]) ).

cnf(f_818_4,plain,
    hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3231),one_one(int)) = U_3231,
    inference(clausify,[status(thm)],[f_818_3]) ).

fof(f_819_1,plain,
    ! [Z,W] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z),W) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),Z),
    inference(fof_nnf,[status(thm)],[fact_748_zmult__commute]) ).

fof(f_819_2,plain,
    ! [U_3233,U_3232] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3233),U_3232) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3232),U_3233),
    inference(variable_rename,[status(thm)],[f_819_1]) ).

fof(f_819_3,plain,
    ! [U_3232,U_3233] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3233),U_3232) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3232),U_3233),
    inference(definitional_conversion,[status(esa)],[f_819_2]) ).

cnf(f_819_4,plain,
    hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3233),U_3232) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3232),U_3233),
    inference(clausify,[status(thm)],[f_819_3]) ).

fof(f_820_1,plain,
    ! [V,W] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),V)),hAPP(int,int,number_number_of(int),W)) = hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),W)),
    inference(fof_nnf,[status(thm)],[fact_749_times__numeral__code_I5_J]) ).

fof(f_820_2,plain,
    ! [U_3235,U_3234] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),U_3235)),hAPP(int,int,number_number_of(int),U_3234)) = hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3235),U_3234)),
    inference(variable_rename,[status(thm)],[f_820_1]) ).

fof(f_820_3,plain,
    ! [U_3234,U_3235] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),U_3235)),hAPP(int,int,number_number_of(int),U_3234)) = hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3235),U_3234)),
    inference(definitional_conversion,[status(esa)],[f_820_2]) ).

cnf(f_820_4,plain,
    hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),U_3235)),hAPP(int,int,number_number_of(int),U_3234)) = hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3235),U_3234)),
    inference(clausify,[status(thm)],[f_820_3]) ).

fof(f_821_1,plain,
    ! [Z1,Z2,Z3] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z1),Z2)),Z3) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z2),Z3)),
    inference(fof_nnf,[status(thm)],[fact_750_zmult__assoc]) ).

fof(f_821_2,plain,
    ! [U_3238,U_3237,U_3236] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3238),U_3237)),U_3236) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3238),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3237),U_3236)),
    inference(variable_rename,[status(thm)],[f_821_1]) ).

fof(f_821_3,plain,
    ! [U_3236,U_3237,U_3238] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3238),U_3237)),U_3236) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3238),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3237),U_3236)),
    inference(definitional_conversion,[status(esa)],[f_821_2]) ).

cnf(f_821_4,plain,
    hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3238),U_3237)),U_3236) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3238),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3237),U_3236)),
    inference(clausify,[status(thm)],[f_821_3]) ).

fof(f_822_1,plain,
    ! [K,L] :
      ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),K)),hAPP(int,int,number_number_of(int),L)))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),L)) )
      & ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),L))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),K)),hAPP(int,int,number_number_of(int),L))) ) ),
    inference(fof_nnf,[status(thm)],[fact_751_less__eq__number__of__int__code]) ).

fof(f_822_2,plain,
    ! [U_3240,U_3239] :
      ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),U_3240)),hAPP(int,int,number_number_of(int),U_3239)))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3240),U_3239)) )
      & ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3240),U_3239))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),U_3240)),hAPP(int,int,number_number_of(int),U_3239))) ) ),
    inference(variable_rename,[status(thm)],[f_822_1]) ).

fof(f_822_3,plain,
    ( ! [U_3244,U_3242] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),U_3244)),hAPP(int,int,number_number_of(int),U_3242)))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3244),U_3242)) )
    & ! [U_3243,U_3241] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3243),U_3241))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),U_3243)),hAPP(int,int,number_number_of(int),U_3241))) ) ),
    inference(miniscope,[status(thm)],[f_822_2]) ).

fof(f_822_4,plain,
    ( ! [U_3242,U_3244] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),U_3244)),hAPP(int,int,number_number_of(int),U_3242)))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3244),U_3242)) )
    & ! [U_3243,U_3241] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3243),U_3241))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),U_3243)),hAPP(int,int,number_number_of(int),U_3241))) ) ),
    inference(definitional_conversion,[status(esa)],[f_822_3]) ).

cnf(f_822_5,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3243),U_3241))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),U_3243)),hAPP(int,int,number_number_of(int),U_3241))) ),
    inference(clausify,[status(thm)],[f_822_4]) ).

cnf(f_822_6,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),U_3244)),hAPP(int,int,number_number_of(int),U_3242)))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3244),U_3242)) ),
    inference(clausify,[status(thm)],[f_822_4]) ).

fof(f_823_1,plain,
    ! [Z1,Z2,W] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z1),Z2)),W) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z1),W)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z2),W)),
    inference(fof_nnf,[status(thm)],[fact_752_zdiff__zmult__distrib]) ).

fof(f_823_2,plain,
    ! [U_3247,U_3246,U_3245] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3247),U_3246)),U_3245) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3247),U_3245)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3246),U_3245)),
    inference(variable_rename,[status(thm)],[f_823_1]) ).

fof(f_823_3,plain,
    ! [U_3246,U_3245,U_3247] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3247),U_3246)),U_3245) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3247),U_3245)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3246),U_3245)),
    inference(definitional_conversion,[status(esa)],[f_823_2]) ).

cnf(f_823_4,plain,
    hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3247),U_3246)),U_3245) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3247),U_3245)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3246),U_3245)),
    inference(clausify,[status(thm)],[f_823_3]) ).

fof(f_824_1,plain,
    ! [W,Z1,Z2] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z1),Z2)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),Z1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),Z2)),
    inference(fof_nnf,[status(thm)],[fact_753_zdiff__zmult__distrib2]) ).

fof(f_824_2,plain,
    ! [U_3250,U_3249,U_3248] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3250),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3249),U_3248)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3250),U_3249)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3250),U_3248)),
    inference(variable_rename,[status(thm)],[f_824_1]) ).

fof(f_824_3,plain,
    ! [U_3248,U_3250,U_3249] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3250),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3249),U_3248)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3250),U_3249)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3250),U_3248)),
    inference(definitional_conversion,[status(esa)],[f_824_2]) ).

cnf(f_824_4,plain,
    hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3250),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3249),U_3248)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3250),U_3249)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3250),U_3248)),
    inference(clausify,[status(thm)],[f_824_3]) ).

fof(f_825_1,plain,
    ! [W,Z1,Z2] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z1),Z2)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),Z1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),Z2)),
    inference(fof_nnf,[status(thm)],[fact_754_zadd__zmult__distrib2]) ).

fof(f_825_2,plain,
    ! [U_3253,U_3252,U_3251] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3253),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3252),U_3251)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3253),U_3252)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3253),U_3251)),
    inference(variable_rename,[status(thm)],[f_825_1]) ).

fof(f_825_3,plain,
    ! [U_3251,U_3253,U_3252] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3253),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3252),U_3251)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3253),U_3252)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3253),U_3251)),
    inference(definitional_conversion,[status(esa)],[f_825_2]) ).

cnf(f_825_4,plain,
    hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3253),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3252),U_3251)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3253),U_3252)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3253),U_3251)),
    inference(clausify,[status(thm)],[f_825_3]) ).

fof(f_826_1,plain,
    ! [V,W] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,number_number_of(int),V)),hAPP(int,int,number_number_of(int),W)) = hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),W)),
    inference(fof_nnf,[status(thm)],[fact_755_plus__numeral__code_I9_J]) ).

fof(f_826_2,plain,
    ! [U_3255,U_3254] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,number_number_of(int),U_3255)),hAPP(int,int,number_number_of(int),U_3254)) = hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3255),U_3254)),
    inference(variable_rename,[status(thm)],[f_826_1]) ).

fof(f_826_3,plain,
    ! [U_3254,U_3255] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,number_number_of(int),U_3255)),hAPP(int,int,number_number_of(int),U_3254)) = hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3255),U_3254)),
    inference(definitional_conversion,[status(esa)],[f_826_2]) ).

cnf(f_826_4,plain,
    hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,number_number_of(int),U_3255)),hAPP(int,int,number_number_of(int),U_3254)) = hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3255),U_3254)),
    inference(clausify,[status(thm)],[f_826_3]) ).

fof(f_827_1,plain,
    ! [Z1,Z2,W] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z1),Z2)),W) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z1),W)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z2),W)),
    inference(fof_nnf,[status(thm)],[fact_756_zadd__zmult__distrib]) ).

fof(f_827_2,plain,
    ! [U_3258,U_3257,U_3256] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3258),U_3257)),U_3256) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3258),U_3256)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3257),U_3256)),
    inference(variable_rename,[status(thm)],[f_827_1]) ).

fof(f_827_3,plain,
    ! [U_3256,U_3257,U_3258] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3258),U_3257)),U_3256) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3258),U_3256)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3257),U_3256)),
    inference(definitional_conversion,[status(esa)],[f_827_2]) ).

cnf(f_827_4,plain,
    hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3258),U_3257)),U_3256) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3258),U_3256)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3257),U_3256)),
    inference(clausify,[status(thm)],[f_827_3]) ).

fof(f_828_1,plain,
    ! [K_1,I_2,J] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_1),I_2)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_1),J)))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K_1))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_2),J)) ),
    inference(fof_nnf,[status(thm)],[fact_757_zmult__zless__mono2]) ).

fof(f_828_2,plain,
    ! [U_3261,U_3260,U_3259] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3261),U_3260)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3261),U_3259)))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3261))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3260),U_3259)) ),
    inference(variable_rename,[status(thm)],[f_828_1]) ).

fof(f_828_3,plain,
    ! [U_3260,U_3259,U_3261] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3261),U_3260)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3261),U_3259)))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3261))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3260),U_3259)) ),
    inference(definitional_conversion,[status(esa)],[f_828_2]) ).

cnf(f_828_4,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3261),U_3260)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3261),U_3259)))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3261))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3260),U_3259)) ),
    inference(clausify,[status(thm)],[f_828_3]) ).

fof(f_829_1,plain,
    ! [Na,M] :
      ( ( ( hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M),Na) = one_one(int)
          | Na != one_one(int)
          | M != one_one(int) )
        & ( ( Na = one_one(int)
            & M = one_one(int) )
          | hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M),Na) != one_one(int) ) )
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M)) ),
    inference(fof_nnf,[status(thm)],[fact_758_pos__zmult__eq__1__iff]) ).

fof(f_829_2,plain,
    ! [U_3263,U_3262] :
      ( ( ( hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3262),U_3263) = one_one(int)
          | U_3263 != one_one(int)
          | U_3262 != one_one(int) )
        & ( ( U_3263 = one_one(int)
            & U_3262 = one_one(int) )
          | hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3262),U_3263) != one_one(int) ) )
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3262)) ),
    inference(variable_rename,[status(thm)],[f_829_1]) ).

fof(f_829_3,plain,
    ( ! [U_3262,U_3263] :
        ( U_3263 = one_one(int)
        | ~ sP231(U_3262,U_3263) )
    & ! [U_3262,U_3263] :
        ( U_3262 = one_one(int)
        | ~ sP231(U_3262,U_3263) )
    & ! [U_3262,U_3263] :
        ( hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3262),U_3263) = one_one(int)
        | U_3263 != one_one(int)
        | U_3262 != one_one(int)
        | ~ sP232(U_3262,U_3263) )
    & ! [U_3262,U_3263] :
        ( sP231(U_3262,U_3263)
        | hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3262),U_3263) != one_one(int)
        | ~ sP232(U_3262,U_3263) )
    & ! [U_3262,U_3263] :
        ( sP232(U_3262,U_3263)
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3262)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP231,sP232])],[f_829_2]) ).

cnf(f_829_4,plain,
    ( sP232(U_3262,U_3263)
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3262)) ),
    inference(clausify,[status(thm)],[f_829_3]) ).

cnf(f_829_5,plain,
    ( sP231(U_3262,U_3263)
    | hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3262),U_3263) != one_one(int)
    | ~ sP232(U_3262,U_3263) ),
    inference(clausify,[status(thm)],[f_829_3]) ).

cnf(f_829_6,plain,
    ( hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3262),U_3263) = one_one(int)
    | U_3263 != one_one(int)
    | U_3262 != one_one(int)
    | ~ sP232(U_3262,U_3263) ),
    inference(clausify,[status(thm)],[f_829_3]) ).

cnf(f_829_7,plain,
    ( U_3262 = one_one(int)
    | ~ sP231(U_3262,U_3263) ),
    inference(clausify,[status(thm)],[f_829_3]) ).

cnf(f_829_8,plain,
    ( U_3263 = one_one(int)
    | ~ sP231(U_3262,U_3263) ),
    inference(clausify,[status(thm)],[f_829_3]) ).

fof(f_830_1,plain,
    ! [Z] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),Z)),Z) != zero_zero(int),
    inference(fof_nnf,[status(thm)],[fact_759_odd__nonzero]) ).

fof(f_830_2,plain,
    ! [U_3264] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),U_3264)),U_3264) != zero_zero(int),
    inference(variable_rename,[status(thm)],[f_830_1]) ).

fof(f_830_3,plain,
    ! [U_3264] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),U_3264)),U_3264) != zero_zero(int),
    inference(definitional_conversion,[status(esa)],[f_830_2]) ).

cnf(f_830_4,plain,
    hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),U_3264)),U_3264) != zero_zero(int),
    inference(clausify,[status(thm)],[f_830_3]) ).

fof(f_831_1,plain,
    ! [Z] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z),zero_zero(int)) = Z,
    inference(fof_nnf,[status(thm)],[fact_760_zadd__0__right]) ).

fof(f_831_2,plain,
    ! [U_3265] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3265),zero_zero(int)) = U_3265,
    inference(variable_rename,[status(thm)],[f_831_1]) ).

fof(f_831_3,plain,
    ! [U_3265] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3265),zero_zero(int)) = U_3265,
    inference(definitional_conversion,[status(esa)],[f_831_2]) ).

cnf(f_831_4,plain,
    hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3265),zero_zero(int)) = U_3265,
    inference(clausify,[status(thm)],[f_831_3]) ).

fof(f_832_1,plain,
    ! [Z] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),zero_zero(int)),Z) = Z,
    inference(fof_nnf,[status(thm)],[fact_761_zadd__0]) ).

fof(f_832_2,plain,
    ! [U_3266] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),zero_zero(int)),U_3266) = U_3266,
    inference(variable_rename,[status(thm)],[f_832_1]) ).

fof(f_832_3,plain,
    ! [U_3266] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),zero_zero(int)),U_3266) = U_3266,
    inference(definitional_conversion,[status(esa)],[f_832_2]) ).

cnf(f_832_4,plain,
    hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),zero_zero(int)),U_3266) = U_3266,
    inference(clausify,[status(thm)],[f_832_3]) ).

fof(f_833_1,plain,
    hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),one_one(int))),
    inference(fof_nnf,[status(thm)],[fact_762_int__0__less__1]) ).

fof(f_833_2,plain,
    hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),one_one(int))),
    inference(definitional_conversion,[status(esa)],[f_833_1]) ).

cnf(f_833_3,plain,
    hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),one_one(int))),
    inference(clausify,[status(thm)],[f_833_2]) ).

fof(f_834_1,plain,
    ! [Z_2] :
      ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),Z_2))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z_2)) )
      & ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z_2))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),Z_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_763_int__one__le__iff__zero__less]) ).

fof(f_834_2,plain,
    ! [U_3267] :
      ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),U_3267))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3267)) )
      & ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3267))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),U_3267)) ) ),
    inference(variable_rename,[status(thm)],[f_834_1]) ).

fof(f_834_3,plain,
    ( ! [U_3269] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),U_3269))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3269)) )
    & ! [U_3268] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3268))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),U_3268)) ) ),
    inference(miniscope,[status(thm)],[f_834_2]) ).

fof(f_834_4,plain,
    ( ! [U_3269] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),U_3269))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3269)) )
    & ! [U_3268] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3268))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),U_3268)) ) ),
    inference(definitional_conversion,[status(esa)],[f_834_3]) ).

cnf(f_834_5,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3268))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),U_3268)) ),
    inference(clausify,[status(thm)],[f_834_4]) ).

cnf(f_834_6,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),U_3269))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3269)) ),
    inference(clausify,[status(thm)],[f_834_4]) ).

fof(f_835_1,plain,
    ! [K,L] :
      ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K),L)),zero_zero(int))) )
      & ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K),L)),zero_zero(int)))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L)) ) ),
    inference(fof_nnf,[status(thm)],[fact_764_less__bin__lemma]) ).

fof(f_835_2,plain,
    ! [U_3271,U_3270] :
      ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3271),U_3270))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3271),U_3270)),zero_zero(int))) )
      & ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3271),U_3270)),zero_zero(int)))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3271),U_3270)) ) ),
    inference(variable_rename,[status(thm)],[f_835_1]) ).

fof(f_835_3,plain,
    ( ! [U_3275,U_3273] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3275),U_3273))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3275),U_3273)),zero_zero(int))) )
    & ! [U_3274,U_3272] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3274),U_3272)),zero_zero(int)))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3274),U_3272)) ) ),
    inference(miniscope,[status(thm)],[f_835_2]) ).

fof(f_835_4,plain,
    ( ! [U_3273,U_3275] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3275),U_3273))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3275),U_3273)),zero_zero(int))) )
    & ! [U_3274,U_3272] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3274),U_3272)),zero_zero(int)))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3274),U_3272)) ) ),
    inference(definitional_conversion,[status(esa)],[f_835_3]) ).

cnf(f_835_5,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3274),U_3272)),zero_zero(int)))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3274),U_3272)) ),
    inference(clausify,[status(thm)],[f_835_4]) ).

cnf(f_835_6,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3275),U_3273))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3275),U_3273)),zero_zero(int))) ),
    inference(clausify,[status(thm)],[f_835_4]) ).

fof(f_836_1,plain,
    ! [Z] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),Z)))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z)) ),
    inference(fof_nnf,[status(thm)],[fact_765_le__imp__0__less]) ).

fof(f_836_2,plain,
    ! [U_3276] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),U_3276)))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3276)) ),
    inference(variable_rename,[status(thm)],[f_836_1]) ).

fof(f_836_3,plain,
    ! [U_3276] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),U_3276)))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3276)) ),
    inference(definitional_conversion,[status(esa)],[f_836_2]) ).

cnf(f_836_4,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),U_3276)))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3276)) ),
    inference(clausify,[status(thm)],[f_836_3]) ).

fof(f_837_1,plain,
    ! [Z_2] :
      ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),Z_2)),Z_2)),zero_zero(int)))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),zero_zero(int))) )
      & ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),zero_zero(int)))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),Z_2)),Z_2)),zero_zero(int))) ) ),
    inference(fof_nnf,[status(thm)],[fact_766_odd__less__0]) ).

fof(f_837_2,plain,
    ! [U_3277] :
      ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),U_3277)),U_3277)),zero_zero(int)))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3277),zero_zero(int))) )
      & ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3277),zero_zero(int)))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),U_3277)),U_3277)),zero_zero(int))) ) ),
    inference(variable_rename,[status(thm)],[f_837_1]) ).

fof(f_837_3,plain,
    ( ! [U_3279] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),U_3279)),U_3279)),zero_zero(int)))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3279),zero_zero(int))) )
    & ! [U_3278] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3278),zero_zero(int)))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),U_3278)),U_3278)),zero_zero(int))) ) ),
    inference(miniscope,[status(thm)],[f_837_2]) ).

fof(f_837_4,plain,
    ( ! [U_3279] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),U_3279)),U_3279)),zero_zero(int)))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3279),zero_zero(int))) )
    & ! [U_3278] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3278),zero_zero(int)))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),U_3278)),U_3278)),zero_zero(int))) ) ),
    inference(definitional_conversion,[status(esa)],[f_837_3]) ).

cnf(f_837_5,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3278),zero_zero(int)))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),U_3278)),U_3278)),zero_zero(int))) ),
    inference(clausify,[status(thm)],[f_837_4]) ).

cnf(f_837_6,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),U_3279)),U_3279)),zero_zero(int)))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3279),zero_zero(int))) ),
    inference(clausify,[status(thm)],[f_837_4]) ).

fof(f_838_1,plain,
    ! [K_1,I_2,J] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_1),I_2)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_1),J)))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I_2),J)) ),
    inference(fof_nnf,[status(thm)],[fact_767_zadd__left__mono]) ).

fof(f_838_2,plain,
    ! [U_3282,U_3281,U_3280] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3282),U_3281)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3282),U_3280)))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3281),U_3280)) ),
    inference(variable_rename,[status(thm)],[f_838_1]) ).

fof(f_838_3,plain,
    ! [U_3280,U_3281,U_3282] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3282),U_3281)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3282),U_3280)))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3281),U_3280)) ),
    inference(definitional_conversion,[status(esa)],[f_838_2]) ).

cnf(f_838_4,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3282),U_3281)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3282),U_3280)))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3281),U_3280)) ),
    inference(clausify,[status(thm)],[f_838_3]) ).

fof(f_839_1,plain,
    ! [Z1,Z2,Z3] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z1),Z2)),Z3) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z2),Z3)),
    inference(fof_nnf,[status(thm)],[fact_768_zadd__assoc]) ).

fof(f_839_2,plain,
    ! [U_3285,U_3284,U_3283] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3285),U_3284)),U_3283) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3285),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3284),U_3283)),
    inference(variable_rename,[status(thm)],[f_839_1]) ).

fof(f_839_3,plain,
    ! [U_3283,U_3284,U_3285] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3285),U_3284)),U_3283) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3285),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3284),U_3283)),
    inference(definitional_conversion,[status(esa)],[f_839_2]) ).

cnf(f_839_4,plain,
    hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3285),U_3284)),U_3283) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3285),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3284),U_3283)),
    inference(clausify,[status(thm)],[f_839_3]) ).

fof(f_840_1,plain,
    ! [X,Y,Z] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Y),Z)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Y),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),Z)),
    inference(fof_nnf,[status(thm)],[fact_769_zadd__left__commute]) ).

fof(f_840_2,plain,
    ! [U_3288,U_3287,U_3286] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3288),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3287),U_3286)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3287),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3288),U_3286)),
    inference(variable_rename,[status(thm)],[f_840_1]) ).

fof(f_840_3,plain,
    ! [U_3286,U_3288,U_3287] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3288),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3287),U_3286)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3287),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3288),U_3286)),
    inference(definitional_conversion,[status(esa)],[f_840_2]) ).

cnf(f_840_4,plain,
    hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3288),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3287),U_3286)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3287),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3288),U_3286)),
    inference(clausify,[status(thm)],[f_840_3]) ).

fof(f_841_1,plain,
    ! [Z,W] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z),W) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W),Z),
    inference(fof_nnf,[status(thm)],[fact_770_zadd__commute]) ).

fof(f_841_2,plain,
    ! [U_3290,U_3289] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3290),U_3289) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3289),U_3290),
    inference(variable_rename,[status(thm)],[f_841_1]) ).

fof(f_841_3,plain,
    ! [U_3289,U_3290] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3290),U_3289) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3289),U_3290),
    inference(definitional_conversion,[status(esa)],[f_841_2]) ).

cnf(f_841_4,plain,
    hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3290),U_3289) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3289),U_3290),
    inference(clausify,[status(thm)],[f_841_3]) ).

fof(f_842_1,plain,
    ! [W] : hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W),W)),
    inference(fof_nnf,[status(thm)],[fact_771_zle__refl]) ).

fof(f_842_2,plain,
    ! [U_3291] : hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3291),U_3291)),
    inference(variable_rename,[status(thm)],[f_842_1]) ).

fof(f_842_3,plain,
    ! [U_3291] : hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3291),U_3291)),
    inference(definitional_conversion,[status(esa)],[f_842_2]) ).

cnf(f_842_4,plain,
    hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3291),U_3291)),
    inference(clausify,[status(thm)],[f_842_3]) ).

fof(f_843_1,plain,
    ! [Z,W] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W),Z))
      | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z),W)) ),
    inference(fof_nnf,[status(thm)],[fact_772_zle__linear]) ).

fof(f_843_2,plain,
    ! [U_3293,U_3292] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3292),U_3293))
      | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3293),U_3292)) ),
    inference(variable_rename,[status(thm)],[f_843_1]) ).

fof(f_843_3,plain,
    ! [U_3292,U_3293] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3292),U_3293))
      | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3293),U_3292)) ),
    inference(definitional_conversion,[status(esa)],[f_843_2]) ).

cnf(f_843_4,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3292),U_3293))
    | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3293),U_3292)) ),
    inference(clausify,[status(thm)],[f_843_3]) ).

fof(f_844_1,plain,
    ! [K_1,I_2,J] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I_2),K_1))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),J),K_1))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I_2),J)) ),
    inference(fof_nnf,[status(thm)],[fact_773_zle__trans]) ).

fof(f_844_2,plain,
    ! [U_3296,U_3295,U_3294] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3295),U_3296))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3294),U_3296))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3295),U_3294)) ),
    inference(variable_rename,[status(thm)],[f_844_1]) ).

fof(f_844_3,plain,
    ! [U_3294,U_3295,U_3296] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3295),U_3296))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3294),U_3296))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3295),U_3294)) ),
    inference(definitional_conversion,[status(esa)],[f_844_2]) ).

cnf(f_844_4,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3295),U_3296))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3294),U_3296))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3295),U_3294)) ),
    inference(clausify,[status(thm)],[f_844_3]) ).

fof(f_845_1,plain,
    ! [Z,W] :
      ( Z = W
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W),Z))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z),W)) ),
    inference(fof_nnf,[status(thm)],[fact_774_zle__antisym]) ).

fof(f_845_2,plain,
    ! [U_3298,U_3297] :
      ( U_3298 = U_3297
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3297),U_3298))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3298),U_3297)) ),
    inference(variable_rename,[status(thm)],[f_845_1]) ).

fof(f_845_3,plain,
    ! [U_3298,U_3297] :
      ( U_3298 = U_3297
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3297),U_3298))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3298),U_3297)) ),
    inference(definitional_conversion,[status(esa)],[f_845_2]) ).

cnf(f_845_4,plain,
    ( U_3298 = U_3297
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3297),U_3298))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3298),U_3297)) ),
    inference(clausify,[status(thm)],[f_845_3]) ).

fof(f_846_1,plain,
    ! [W_1,Z_2] :
      ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z_2),one_one(int))))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_2)) )
      & ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_2))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z_2),one_one(int)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_775_zle__diff1__eq]) ).

fof(f_846_2,plain,
    ! [U_3300,U_3299] :
      ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3300),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3299),one_one(int))))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3300),U_3299)) )
      & ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3300),U_3299))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3300),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3299),one_one(int)))) ) ),
    inference(variable_rename,[status(thm)],[f_846_1]) ).

fof(f_846_3,plain,
    ( ! [U_3304,U_3302] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3304),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3302),one_one(int))))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3304),U_3302)) )
    & ! [U_3303,U_3301] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3303),U_3301))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3303),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3301),one_one(int)))) ) ),
    inference(miniscope,[status(thm)],[f_846_2]) ).

fof(f_846_4,plain,
    ( ! [U_3304,U_3302] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3304),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3302),one_one(int))))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3304),U_3302)) )
    & ! [U_3301,U_3303] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3303),U_3301))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3303),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3301),one_one(int)))) ) ),
    inference(definitional_conversion,[status(esa)],[f_846_3]) ).

cnf(f_846_5,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3303),U_3301))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3303),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3301),one_one(int)))) ),
    inference(clausify,[status(thm)],[f_846_4]) ).

cnf(f_846_6,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3304),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3302),one_one(int))))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3304),U_3302)) ),
    inference(clausify,[status(thm)],[f_846_4]) ).

fof(f_847_1,plain,
    ! [X,Y] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y),X))
      | X = Y
      | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),Y)) ),
    inference(fof_nnf,[status(thm)],[fact_776_zless__linear]) ).

fof(f_847_2,plain,
    ! [U_3306,U_3305] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3305),U_3306))
      | U_3306 = U_3305
      | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3306),U_3305)) ),
    inference(variable_rename,[status(thm)],[f_847_1]) ).

fof(f_847_3,plain,
    ! [U_3305,U_3306] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3305),U_3306))
      | U_3306 = U_3305
      | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3306),U_3305)) ),
    inference(definitional_conversion,[status(esa)],[f_847_2]) ).

cnf(f_847_4,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3305),U_3306))
    | U_3306 = U_3305
    | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3306),U_3305)) ),
    inference(clausify,[status(thm)],[f_847_3]) ).

fof(f_848_1,plain,
    ! [Z_2,W_1] :
      ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),W_1))
        | Z_2 = W_1
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_2),W_1)) )
      & ( ( Z_2 != W_1
          & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_2),W_1)) )
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),W_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_777_zless__le]) ).

fof(f_848_2,plain,
    ! [U_3308,U_3307] :
      ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3308),U_3307))
        | U_3308 = U_3307
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3308),U_3307)) )
      & ( ( U_3308 != U_3307
          & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3308),U_3307)) )
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3308),U_3307)) ) ),
    inference(variable_rename,[status(thm)],[f_848_1]) ).

fof(f_848_3,plain,
    ( ! [U_3312,U_3310] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3312),U_3310))
        | U_3312 = U_3310
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3312),U_3310)) )
    & ! [U_3311,U_3309] :
        ( ( U_3311 != U_3309
          & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3311),U_3309)) )
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3311),U_3309)) ) ),
    inference(miniscope,[status(thm)],[f_848_2]) ).

fof(f_848_4,plain,
    ( ! [U_3309,U_3311] :
        ( U_3311 != U_3309
        | ~ sP233(U_3309,U_3311) )
    & ! [U_3309,U_3311] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3311),U_3309))
        | ~ sP233(U_3309,U_3311) )
    & ! [U_3312,U_3310] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3312),U_3310))
        | U_3312 = U_3310
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3312),U_3310)) )
    & ! [U_3309,U_3311] :
        ( sP233(U_3309,U_3311)
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3311),U_3309)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP233])],[f_848_3]) ).

cnf(f_848_5,plain,
    ( sP233(U_3309,U_3311)
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3311),U_3309)) ),
    inference(clausify,[status(thm)],[f_848_4]) ).

cnf(f_848_6,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3312),U_3310))
    | U_3312 = U_3310
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3312),U_3310)) ),
    inference(clausify,[status(thm)],[f_848_4]) ).

cnf(f_848_7,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3311),U_3309))
    | ~ sP233(U_3309,U_3311) ),
    inference(clausify,[status(thm)],[f_848_4]) ).

cnf(f_848_8,plain,
    ( U_3311 != U_3309
    | ~ sP233(U_3309,U_3311) ),
    inference(clausify,[status(thm)],[f_848_4]) ).

fof(f_849_1,plain,
    ! [K_1,I_2,J] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I_2),K_1)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),J),K_1)))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_2),J)) ),
    inference(fof_nnf,[status(thm)],[fact_778_zadd__strict__right__mono]) ).

fof(f_849_2,plain,
    ! [U_3315,U_3314,U_3313] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3314),U_3315)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3313),U_3315)))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3314),U_3313)) ),
    inference(variable_rename,[status(thm)],[f_849_1]) ).

fof(f_849_3,plain,
    ! [U_3314,U_3313,U_3315] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3314),U_3315)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3313),U_3315)))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3314),U_3313)) ),
    inference(definitional_conversion,[status(esa)],[f_849_2]) ).

cnf(f_849_4,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3314),U_3315)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3313),U_3315)))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3314),U_3313)) ),
    inference(clausify,[status(thm)],[f_849_3]) ).

fof(f_850_1,plain,
    ! [Z_4,Z,W_2,W] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_2),Z_4)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W),Z)))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_4),Z))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_2),W)) ),
    inference(fof_nnf,[status(thm)],[fact_779_zadd__zless__mono]) ).

fof(f_850_2,plain,
    ! [U_3319,U_3318,U_3317,U_3316] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3317),U_3319)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3316),U_3318)))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3319),U_3318))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3317),U_3316)) ),
    inference(variable_rename,[status(thm)],[f_850_1]) ).

fof(f_850_3,plain,
    ! [U_3317,U_3316,U_3318,U_3319] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3317),U_3319)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3316),U_3318)))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3319),U_3318))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3317),U_3316)) ),
    inference(definitional_conversion,[status(esa)],[f_850_2]) ).

cnf(f_850_4,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3317),U_3319)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3316),U_3318)))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3319),U_3318))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3317),U_3316)) ),
    inference(clausify,[status(thm)],[f_850_3]) ).

fof(f_851_1,plain,
    ! [W_1,Z_2] :
      ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_2),one_one(int))))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W_1),Z_2)) )
      & ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W_1),Z_2))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_2),one_one(int)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_780_zle__add1__eq__le]) ).

fof(f_851_2,plain,
    ! [U_3321,U_3320] :
      ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3321),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3320),one_one(int))))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3321),U_3320)) )
      & ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3321),U_3320))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3321),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3320),one_one(int)))) ) ),
    inference(variable_rename,[status(thm)],[f_851_1]) ).

fof(f_851_3,plain,
    ( ! [U_3325,U_3323] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3325),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3323),one_one(int))))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3325),U_3323)) )
    & ! [U_3324,U_3322] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3324),U_3322))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3324),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3322),one_one(int)))) ) ),
    inference(miniscope,[status(thm)],[f_851_2]) ).

fof(f_851_4,plain,
    ( ! [U_3325,U_3323] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3325),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3323),one_one(int))))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3325),U_3323)) )
    & ! [U_3322,U_3324] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3324),U_3322))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3324),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3322),one_one(int)))) ) ),
    inference(definitional_conversion,[status(esa)],[f_851_3]) ).

cnf(f_851_5,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3324),U_3322))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3324),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3322),one_one(int)))) ),
    inference(clausify,[status(thm)],[f_851_4]) ).

cnf(f_851_6,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3325),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3323),one_one(int))))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3325),U_3323)) ),
    inference(clausify,[status(thm)],[f_851_4]) ).

fof(f_852_1,plain,
    ! [W_1,Z_2] :
      ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_1),one_one(int))),Z_2))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_2)) )
      & ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_2))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_1),one_one(int))),Z_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_781_add1__zle__eq]) ).

fof(f_852_2,plain,
    ! [U_3327,U_3326] :
      ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3327),one_one(int))),U_3326))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3327),U_3326)) )
      & ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3327),U_3326))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3327),one_one(int))),U_3326)) ) ),
    inference(variable_rename,[status(thm)],[f_852_1]) ).

fof(f_852_3,plain,
    ( ! [U_3331,U_3329] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3331),one_one(int))),U_3329))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3331),U_3329)) )
    & ! [U_3330,U_3328] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3330),U_3328))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3330),one_one(int))),U_3328)) ) ),
    inference(miniscope,[status(thm)],[f_852_2]) ).

fof(f_852_4,plain,
    ( ! [U_3329,U_3331] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3331),one_one(int))),U_3329))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3331),U_3329)) )
    & ! [U_3330,U_3328] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3330),U_3328))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3330),one_one(int))),U_3328)) ) ),
    inference(definitional_conversion,[status(esa)],[f_852_3]) ).

cnf(f_852_5,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3330),U_3328))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3330),one_one(int))),U_3328)) ),
    inference(clausify,[status(thm)],[f_852_4]) ).

cnf(f_852_6,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3331),one_one(int))),U_3329))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3331),U_3329)) ),
    inference(clausify,[status(thm)],[f_852_4]) ).

fof(f_853_1,plain,
    ! [W,Z] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W),one_one(int))),Z))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W),Z)) ),
    inference(fof_nnf,[status(thm)],[fact_782_zless__imp__add1__zle]) ).

fof(f_853_2,plain,
    ! [U_3333,U_3332] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3333),one_one(int))),U_3332))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3333),U_3332)) ),
    inference(variable_rename,[status(thm)],[f_853_1]) ).

fof(f_853_3,plain,
    ! [U_3332,U_3333] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3333),one_one(int))),U_3332))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3333),U_3332)) ),
    inference(definitional_conversion,[status(esa)],[f_853_2]) ).

cnf(f_853_4,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3333),one_one(int))),U_3332))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3333),U_3332)) ),
    inference(clausify,[status(thm)],[f_853_3]) ).

fof(f_854_1,plain,
    ! [W_1,Z_2] :
      ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_2),one_one(int))))
        | ( W_1 != Z_2
          & ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_2)) ) )
      & ( W_1 = Z_2
        | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_2))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_2),one_one(int)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_783_zless__add1__eq]) ).

fof(f_854_2,plain,
    ! [U_3335,U_3334] :
      ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3335),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3334),one_one(int))))
        | ( U_3335 != U_3334
          & ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3335),U_3334)) ) )
      & ( U_3335 = U_3334
        | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3335),U_3334))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3335),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3334),one_one(int)))) ) ),
    inference(variable_rename,[status(thm)],[f_854_1]) ).

fof(f_854_3,plain,
    ( ! [U_3339,U_3337] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3339),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3337),one_one(int))))
        | ( U_3339 != U_3337
          & ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3339),U_3337)) ) )
    & ! [U_3338,U_3336] :
        ( U_3338 = U_3336
        | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3338),U_3336))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3338),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3336),one_one(int)))) ) ),
    inference(miniscope,[status(thm)],[f_854_2]) ).

fof(f_854_4,plain,
    ( ! [U_3339,U_3337] :
        ( U_3339 != U_3337
        | ~ sP234(U_3339,U_3337) )
    & ! [U_3339,U_3337] :
        ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3339),U_3337))
        | ~ sP234(U_3339,U_3337) )
    & ! [U_3339,U_3337] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3339),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3337),one_one(int))))
        | sP234(U_3339,U_3337) )
    & ! [U_3336,U_3338] :
        ( U_3338 = U_3336
        | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3338),U_3336))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3338),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3336),one_one(int)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP234])],[f_854_3]) ).

cnf(f_854_5,plain,
    ( U_3338 = U_3336
    | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3338),U_3336))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3338),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3336),one_one(int)))) ),
    inference(clausify,[status(thm)],[f_854_4]) ).

cnf(f_854_6,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3339),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3337),one_one(int))))
    | sP234(U_3339,U_3337) ),
    inference(clausify,[status(thm)],[f_854_4]) ).

cnf(f_854_7,plain,
    ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3339),U_3337))
    | ~ sP234(U_3339,U_3337) ),
    inference(clausify,[status(thm)],[f_854_4]) ).

cnf(f_854_8,plain,
    ( U_3339 != U_3337
    | ~ sP234(U_3339,U_3337) ),
    inference(clausify,[status(thm)],[f_854_4]) ).

fof(f_855_1,plain,
    ! [K,M,Na] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na)
        | ( M != Na
          & K != zero_zero(nat) ) )
      & ( M = Na
        | K = zero_zero(nat)
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na) ) ),
    inference(fof_nnf,[status(thm)],[fact_784_nat__mult__eq__cancel__disj]) ).

fof(f_855_2,plain,
    ! [U_3342,U_3341,U_3340] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3342),U_3341) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3342),U_3340)
        | ( U_3341 != U_3340
          & U_3342 != zero_zero(nat) ) )
      & ( U_3341 = U_3340
        | U_3342 = zero_zero(nat)
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3342),U_3341) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3342),U_3340) ) ),
    inference(variable_rename,[status(thm)],[f_855_1]) ).

fof(f_855_3,plain,
    ( ! [U_3348,U_3346,U_3344] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3348),U_3346) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3348),U_3344)
        | ( U_3346 != U_3344
          & U_3348 != zero_zero(nat) ) )
    & ! [U_3347,U_3345,U_3343] :
        ( U_3345 = U_3343
        | U_3347 = zero_zero(nat)
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3347),U_3345) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3347),U_3343) ) ),
    inference(miniscope,[status(thm)],[f_855_2]) ).

fof(f_855_4,plain,
    ( ! [U_3348,U_3346,U_3344] :
        ( U_3346 != U_3344
        | ~ sP235(U_3348,U_3346,U_3344) )
    & ! [U_3348,U_3346,U_3344] :
        ( U_3348 != zero_zero(nat)
        | ~ sP235(U_3348,U_3346,U_3344) )
    & ! [U_3348,U_3346,U_3344] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3348),U_3346) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3348),U_3344)
        | sP235(U_3348,U_3346,U_3344) )
    & ! [U_3343,U_3347,U_3345] :
        ( U_3345 = U_3343
        | U_3347 = zero_zero(nat)
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3347),U_3345) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3347),U_3343) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP235])],[f_855_3]) ).

cnf(f_855_5,plain,
    ( U_3345 = U_3343
    | U_3347 = zero_zero(nat)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3347),U_3345) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3347),U_3343) ),
    inference(clausify,[status(thm)],[f_855_4]) ).

cnf(f_855_6,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3348),U_3346) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3348),U_3344)
    | sP235(U_3348,U_3346,U_3344) ),
    inference(clausify,[status(thm)],[f_855_4]) ).

cnf(f_855_7,plain,
    ( U_3348 != zero_zero(nat)
    | ~ sP235(U_3348,U_3346,U_3344) ),
    inference(clausify,[status(thm)],[f_855_4]) ).

cnf(f_855_8,plain,
    ( U_3346 != U_3344
    | ~ sP235(U_3348,U_3346,U_3344) ),
    inference(clausify,[status(thm)],[f_855_4]) ).

fof(f_856_1,plain,
    ! [I_2,U_1,J,K_1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_2),U_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),U_1)),K_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),J)),U_1)),K_1),
    inference(fof_nnf,[status(thm)],[fact_785_left__add__mult__distrib]) ).

fof(f_856_2,plain,
    ! [U_3352,U_3351,U_3350,U_3349] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3352),U_3351)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3350),U_3351)),U_3349)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_3352),U_3350)),U_3351)),U_3349),
    inference(variable_rename,[status(thm)],[f_856_1]) ).

fof(f_856_3,plain,
    ! [U_3349,U_3350,U_3351,U_3352] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3352),U_3351)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3350),U_3351)),U_3349)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_3352),U_3350)),U_3351)),U_3349),
    inference(definitional_conversion,[status(esa)],[f_856_2]) ).

cnf(f_856_4,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3352),U_3351)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3350),U_3351)),U_3349)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_3352),U_3350)),U_3351)),U_3349),
    inference(clausify,[status(thm)],[f_856_3]) ).

fof(f_857_1,plain,
    ! [M,Na,K] :
      ( ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na)
          | M != Na )
        & ( M = Na
          | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na) ) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) ),
    inference(fof_nnf,[status(thm)],[fact_786_nat__mult__eq__cancel1]) ).

fof(f_857_2,plain,
    ! [U_3355,U_3354,U_3353] :
      ( ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3353),U_3355) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3353),U_3354)
          | U_3355 != U_3354 )
        & ( U_3355 = U_3354
          | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3353),U_3355) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3353),U_3354) ) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_3353)) ),
    inference(variable_rename,[status(thm)],[f_857_1]) ).

fof(f_857_3,plain,
    ( ! [U_3355,U_3354,U_3353] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3353),U_3355) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3353),U_3354)
        | U_3355 != U_3354
        | ~ sP236(U_3355,U_3354,U_3353) )
    & ! [U_3355,U_3354,U_3353] :
        ( U_3355 = U_3354
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3353),U_3355) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3353),U_3354)
        | ~ sP236(U_3355,U_3354,U_3353) )
    & ! [U_3355,U_3354,U_3353] :
        ( sP236(U_3355,U_3354,U_3353)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_3353)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP236])],[f_857_2]) ).

cnf(f_857_4,plain,
    ( sP236(U_3355,U_3354,U_3353)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_3353)) ),
    inference(clausify,[status(thm)],[f_857_3]) ).

cnf(f_857_5,plain,
    ( U_3355 = U_3354
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3353),U_3355) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3353),U_3354)
    | ~ sP236(U_3355,U_3354,U_3353) ),
    inference(clausify,[status(thm)],[f_857_3]) ).

cnf(f_857_6,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3353),U_3355) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3353),U_3354)
    | U_3355 != U_3354
    | ~ sP236(U_3355,U_3354,U_3353) ),
    inference(clausify,[status(thm)],[f_857_3]) ).

fof(f_858_1,plain,
    ! [M,Na,K] :
      ( ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na)))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)) )
        & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na))) ) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) ),
    inference(fof_nnf,[status(thm)],[fact_787_nat__mult__less__cancel1]) ).

fof(f_858_2,plain,
    ! [U_3358,U_3357,U_3356] :
      ( ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3356),U_3358)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3356),U_3357)))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3358),U_3357)) )
        & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3358),U_3357))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3356),U_3358)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3356),U_3357))) ) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_3356)) ),
    inference(variable_rename,[status(thm)],[f_858_1]) ).

fof(f_858_3,plain,
    ( ! [U_3357,U_3358,U_3356] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3356),U_3358)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3356),U_3357)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3358),U_3357))
        | ~ sP237(U_3357,U_3358,U_3356) )
    & ! [U_3357,U_3358,U_3356] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3358),U_3357))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3356),U_3358)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3356),U_3357)))
        | ~ sP237(U_3357,U_3358,U_3356) )
    & ! [U_3357,U_3358,U_3356] :
        ( sP237(U_3357,U_3358,U_3356)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_3356)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP237])],[f_858_2]) ).

cnf(f_858_4,plain,
    ( sP237(U_3357,U_3358,U_3356)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_3356)) ),
    inference(clausify,[status(thm)],[f_858_3]) ).

cnf(f_858_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3358),U_3357))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3356),U_3358)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3356),U_3357)))
    | ~ sP237(U_3357,U_3358,U_3356) ),
    inference(clausify,[status(thm)],[f_858_3]) ).

cnf(f_858_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3356),U_3358)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3356),U_3357)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3358),U_3357))
    | ~ sP237(U_3357,U_3358,U_3356) ),
    inference(clausify,[status(thm)],[f_858_3]) ).

fof(f_859_1,plain,
    ! [M,Na,K] :
      ( ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na)))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)) )
        & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na))) ) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) ),
    inference(fof_nnf,[status(thm)],[fact_788_nat__mult__le__cancel1]) ).

fof(f_859_2,plain,
    ! [U_3361,U_3360,U_3359] :
      ( ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3359),U_3361)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3359),U_3360)))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3361),U_3360)) )
        & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3361),U_3360))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3359),U_3361)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3359),U_3360))) ) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_3359)) ),
    inference(variable_rename,[status(thm)],[f_859_1]) ).

fof(f_859_3,plain,
    ( ! [U_3360,U_3361,U_3359] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3359),U_3361)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3359),U_3360)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3361),U_3360))
        | ~ sP238(U_3360,U_3361,U_3359) )
    & ! [U_3360,U_3361,U_3359] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3361),U_3360))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3359),U_3361)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3359),U_3360)))
        | ~ sP238(U_3360,U_3361,U_3359) )
    & ! [U_3360,U_3361,U_3359] :
        ( sP238(U_3360,U_3361,U_3359)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_3359)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP238])],[f_859_2]) ).

cnf(f_859_4,plain,
    ( sP238(U_3360,U_3361,U_3359)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_3359)) ),
    inference(clausify,[status(thm)],[f_859_3]) ).

cnf(f_859_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3361),U_3360))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3359),U_3361)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3359),U_3360)))
    | ~ sP238(U_3360,U_3361,U_3359) ),
    inference(clausify,[status(thm)],[f_859_3]) ).

cnf(f_859_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3359),U_3361)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3359),U_3360)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3361),U_3360))
    | ~ sP238(U_3360,U_3361,U_3359) ),
    inference(clausify,[status(thm)],[f_859_3]) ).

fof(f_860_1,plain,
    ! [U,M,Na,J_1,I_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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),Na)))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J_1)),U)),M)),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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J_1)),U)),M)),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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),Na))) ) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J_1),I_1)) ),
    inference(fof_nnf,[status(thm)],[fact_789_nat__le__add__iff1]) ).

fof(f_860_2,plain,
    ! [U_3366,U_3365,U_3364,U_3363,U_3362] :
      ( ( ( 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,hAPP(nat,fun(nat,nat),times_times(nat),U_3362),U_3366)),U_3365)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3363),U_3366)),U_3364)))
          | ~ 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,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3362),U_3363)),U_3366)),U_3365)),U_3364)) )
        & ( 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,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3362),U_3363)),U_3366)),U_3365)),U_3364))
          | ~ 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,hAPP(nat,fun(nat,nat),times_times(nat),U_3362),U_3366)),U_3365)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3363),U_3366)),U_3364))) ) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3363),U_3362)) ),
    inference(variable_rename,[status(thm)],[f_860_1]) ).

fof(f_860_3,plain,
    ( ! [U_3362,U_3363,U_3364,U_3365,U_3366] :
        ( 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,hAPP(nat,fun(nat,nat),times_times(nat),U_3362),U_3366)),U_3365)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3363),U_3366)),U_3364)))
        | ~ 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,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3362),U_3363)),U_3366)),U_3365)),U_3364))
        | ~ sP239(U_3362,U_3363,U_3364,U_3365,U_3366) )
    & ! [U_3362,U_3363,U_3364,U_3365,U_3366] :
        ( 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,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3362),U_3363)),U_3366)),U_3365)),U_3364))
        | ~ 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,hAPP(nat,fun(nat,nat),times_times(nat),U_3362),U_3366)),U_3365)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3363),U_3366)),U_3364)))
        | ~ sP239(U_3362,U_3363,U_3364,U_3365,U_3366) )
    & ! [U_3362,U_3363,U_3364,U_3365,U_3366] :
        ( sP239(U_3362,U_3363,U_3364,U_3365,U_3366)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3363),U_3362)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP239])],[f_860_2]) ).

cnf(f_860_4,plain,
    ( sP239(U_3362,U_3363,U_3364,U_3365,U_3366)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3363),U_3362)) ),
    inference(clausify,[status(thm)],[f_860_3]) ).

cnf(f_860_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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3362),U_3363)),U_3366)),U_3365)),U_3364))
    | ~ 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,hAPP(nat,fun(nat,nat),times_times(nat),U_3362),U_3366)),U_3365)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3363),U_3366)),U_3364)))
    | ~ sP239(U_3362,U_3363,U_3364,U_3365,U_3366) ),
    inference(clausify,[status(thm)],[f_860_3]) ).

cnf(f_860_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,hAPP(nat,fun(nat,nat),times_times(nat),U_3362),U_3366)),U_3365)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3363),U_3366)),U_3364)))
    | ~ 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,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3362),U_3363)),U_3366)),U_3365)),U_3364))
    | ~ sP239(U_3362,U_3363,U_3364,U_3365,U_3366) ),
    inference(clausify,[status(thm)],[f_860_3]) ).

fof(f_861_1,plain,
    ! [U_1,M_1,N,J,I_2] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_2),U_1)),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),U_1)),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_2),J)),U_1)),M_1)),N)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J),I_2)) ),
    inference(fof_nnf,[status(thm)],[fact_790_nat__diff__add__eq1]) ).

fof(f_861_2,plain,
    ! [U_3371,U_3370,U_3369,U_3368,U_3367] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3367),U_3371)),U_3370)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3368),U_3371)),U_3369)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3367),U_3368)),U_3371)),U_3370)),U_3369)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3368),U_3367)) ),
    inference(variable_rename,[status(thm)],[f_861_1]) ).

fof(f_861_3,plain,
    ! [U_3367,U_3368,U_3369,U_3370,U_3371] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3367),U_3371)),U_3370)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3368),U_3371)),U_3369)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3367),U_3368)),U_3371)),U_3370)),U_3369)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3368),U_3367)) ),
    inference(definitional_conversion,[status(esa)],[f_861_2]) ).

cnf(f_861_4,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3367),U_3371)),U_3370)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3368),U_3371)),U_3369)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3367),U_3368)),U_3371)),U_3370)),U_3369)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3368),U_3367)) ),
    inference(clausify,[status(thm)],[f_861_3]) ).

fof(f_862_1,plain,
    ! [U,M,Na,J_1,I_1] :
      ( ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),Na)
          | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J_1)),U)),M) != Na )
        & ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J_1)),U)),M) = Na
          | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),Na) ) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J_1),I_1)) ),
    inference(fof_nnf,[status(thm)],[fact_791_nat__eq__add__iff1]) ).

fof(f_862_2,plain,
    ! [U_3376,U_3375,U_3374,U_3373,U_3372] :
      ( ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3372),U_3376)),U_3375) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3373),U_3376)),U_3374)
          | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3372),U_3373)),U_3376)),U_3375) != U_3374 )
        & ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3372),U_3373)),U_3376)),U_3375) = U_3374
          | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3372),U_3376)),U_3375) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3373),U_3376)),U_3374) ) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3373),U_3372)) ),
    inference(variable_rename,[status(thm)],[f_862_1]) ).

fof(f_862_3,plain,
    ( ! [U_3373,U_3372,U_3374,U_3375,U_3376] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3372),U_3376)),U_3375) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3373),U_3376)),U_3374)
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3372),U_3373)),U_3376)),U_3375) != U_3374
        | ~ sP240(U_3373,U_3372,U_3374,U_3375,U_3376) )
    & ! [U_3373,U_3372,U_3374,U_3375,U_3376] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3372),U_3373)),U_3376)),U_3375) = U_3374
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3372),U_3376)),U_3375) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3373),U_3376)),U_3374)
        | ~ sP240(U_3373,U_3372,U_3374,U_3375,U_3376) )
    & ! [U_3373,U_3372,U_3374,U_3375,U_3376] :
        ( sP240(U_3373,U_3372,U_3374,U_3375,U_3376)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3373),U_3372)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP240])],[f_862_2]) ).

cnf(f_862_4,plain,
    ( sP240(U_3373,U_3372,U_3374,U_3375,U_3376)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3373),U_3372)) ),
    inference(clausify,[status(thm)],[f_862_3]) ).

cnf(f_862_5,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3372),U_3373)),U_3376)),U_3375) = U_3374
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3372),U_3376)),U_3375) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3373),U_3376)),U_3374)
    | ~ sP240(U_3373,U_3372,U_3374,U_3375,U_3376) ),
    inference(clausify,[status(thm)],[f_862_3]) ).

cnf(f_862_6,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3372),U_3376)),U_3375) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3373),U_3376)),U_3374)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3372),U_3373)),U_3376)),U_3375) != U_3374
    | ~ sP240(U_3373,U_3372,U_3374,U_3375,U_3376) ),
    inference(clausify,[status(thm)],[f_862_3]) ).

fof(f_863_1,plain,
    ! [U,M,Na,I_1,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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),Na)))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),I_1)),U)),Na))) )
        & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),I_1)),U)),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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),Na))) ) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_1)) ),
    inference(fof_nnf,[status(thm)],[fact_792_nat__le__add__iff2]) ).

fof(f_863_2,plain,
    ! [U_3381,U_3380,U_3379,U_3378,U_3377] :
      ( ( ( 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,hAPP(nat,fun(nat,nat),times_times(nat),U_3378),U_3381)),U_3380)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3377),U_3381)),U_3379)))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3380),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3377),U_3378)),U_3381)),U_3379))) )
        & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3380),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3377),U_3378)),U_3381)),U_3379)))
          | ~ 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,hAPP(nat,fun(nat,nat),times_times(nat),U_3378),U_3381)),U_3380)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3377),U_3381)),U_3379))) ) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3378),U_3377)) ),
    inference(variable_rename,[status(thm)],[f_863_1]) ).

fof(f_863_3,plain,
    ( ! [U_3378,U_3377,U_3379,U_3380,U_3381] :
        ( 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,hAPP(nat,fun(nat,nat),times_times(nat),U_3378),U_3381)),U_3380)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3377),U_3381)),U_3379)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3380),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3377),U_3378)),U_3381)),U_3379)))
        | ~ sP241(U_3378,U_3377,U_3379,U_3380,U_3381) )
    & ! [U_3378,U_3377,U_3379,U_3380,U_3381] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3380),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3377),U_3378)),U_3381)),U_3379)))
        | ~ 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,hAPP(nat,fun(nat,nat),times_times(nat),U_3378),U_3381)),U_3380)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3377),U_3381)),U_3379)))
        | ~ sP241(U_3378,U_3377,U_3379,U_3380,U_3381) )
    & ! [U_3378,U_3377,U_3379,U_3380,U_3381] :
        ( sP241(U_3378,U_3377,U_3379,U_3380,U_3381)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3378),U_3377)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP241])],[f_863_2]) ).

cnf(f_863_4,plain,
    ( sP241(U_3378,U_3377,U_3379,U_3380,U_3381)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3378),U_3377)) ),
    inference(clausify,[status(thm)],[f_863_3]) ).

cnf(f_863_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3380),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3377),U_3378)),U_3381)),U_3379)))
    | ~ 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,hAPP(nat,fun(nat,nat),times_times(nat),U_3378),U_3381)),U_3380)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3377),U_3381)),U_3379)))
    | ~ sP241(U_3378,U_3377,U_3379,U_3380,U_3381) ),
    inference(clausify,[status(thm)],[f_863_3]) ).

cnf(f_863_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,hAPP(nat,fun(nat,nat),times_times(nat),U_3378),U_3381)),U_3380)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3377),U_3381)),U_3379)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3380),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3377),U_3378)),U_3381)),U_3379)))
    | ~ sP241(U_3378,U_3377,U_3379,U_3380,U_3381) ),
    inference(clausify,[status(thm)],[f_863_3]) ).

fof(f_864_1,plain,
    ! [U_1,M_1,N,I_2,J] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_2),U_1)),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),U_1)),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),I_2)),U_1)),N))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),J)) ),
    inference(fof_nnf,[status(thm)],[fact_793_nat__diff__add__eq2]) ).

fof(f_864_2,plain,
    ! [U_3386,U_3385,U_3384,U_3383,U_3382] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3383),U_3386)),U_3385)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3382),U_3386)),U_3384)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3385),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3382),U_3383)),U_3386)),U_3384))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3383),U_3382)) ),
    inference(variable_rename,[status(thm)],[f_864_1]) ).

fof(f_864_3,plain,
    ! [U_3383,U_3384,U_3382,U_3385,U_3386] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3383),U_3386)),U_3385)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3382),U_3386)),U_3384)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3385),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3382),U_3383)),U_3386)),U_3384))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3383),U_3382)) ),
    inference(definitional_conversion,[status(esa)],[f_864_2]) ).

cnf(f_864_4,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3383),U_3386)),U_3385)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3382),U_3386)),U_3384)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3385),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3382),U_3383)),U_3386)),U_3384))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3383),U_3382)) ),
    inference(clausify,[status(thm)],[f_864_3]) ).

fof(f_865_1,plain,
    ! [U,M,Na,I_1,J_1] :
      ( ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),Na)
          | M != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),I_1)),U)),Na) )
        & ( M = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),I_1)),U)),Na)
          | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),Na) ) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_1)) ),
    inference(fof_nnf,[status(thm)],[fact_794_nat__eq__add__iff2]) ).

fof(f_865_2,plain,
    ! [U_3391,U_3390,U_3389,U_3388,U_3387] :
      ( ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3388),U_3391)),U_3390) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3387),U_3391)),U_3389)
          | U_3390 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3387),U_3388)),U_3391)),U_3389) )
        & ( U_3390 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3387),U_3388)),U_3391)),U_3389)
          | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3388),U_3391)),U_3390) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3387),U_3391)),U_3389) ) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3388),U_3387)) ),
    inference(variable_rename,[status(thm)],[f_865_1]) ).

fof(f_865_3,plain,
    ( ! [U_3387,U_3388,U_3389,U_3390,U_3391] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3388),U_3391)),U_3390) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3387),U_3391)),U_3389)
        | U_3390 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3387),U_3388)),U_3391)),U_3389)
        | ~ sP242(U_3387,U_3388,U_3389,U_3390,U_3391) )
    & ! [U_3387,U_3388,U_3389,U_3390,U_3391] :
        ( U_3390 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3387),U_3388)),U_3391)),U_3389)
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3388),U_3391)),U_3390) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3387),U_3391)),U_3389)
        | ~ sP242(U_3387,U_3388,U_3389,U_3390,U_3391) )
    & ! [U_3387,U_3388,U_3389,U_3390,U_3391] :
        ( sP242(U_3387,U_3388,U_3389,U_3390,U_3391)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3388),U_3387)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP242])],[f_865_2]) ).

cnf(f_865_4,plain,
    ( sP242(U_3387,U_3388,U_3389,U_3390,U_3391)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3388),U_3387)) ),
    inference(clausify,[status(thm)],[f_865_3]) ).

cnf(f_865_5,plain,
    ( U_3390 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3387),U_3388)),U_3391)),U_3389)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3388),U_3391)),U_3390) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3387),U_3391)),U_3389)
    | ~ sP242(U_3387,U_3388,U_3389,U_3390,U_3391) ),
    inference(clausify,[status(thm)],[f_865_3]) ).

cnf(f_865_6,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3388),U_3391)),U_3390) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3387),U_3391)),U_3389)
    | U_3390 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3387),U_3388)),U_3391)),U_3389)
    | ~ sP242(U_3387,U_3388,U_3389,U_3390,U_3391) ),
    inference(clausify,[status(thm)],[f_865_3]) ).

fof(f_866_1,plain,
    ! [U,M,Na,J_1,I_1] :
      ( ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),Na)))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J_1)),U)),M)),Na)) )
        & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J_1)),U)),M)),Na))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),Na))) ) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J_1),I_1)) ),
    inference(fof_nnf,[status(thm)],[fact_795_nat__less__add__iff1]) ).

fof(f_866_2,plain,
    ! [U_3396,U_3395,U_3394,U_3393,U_3392] :
      ( ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3392),U_3396)),U_3395)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3393),U_3396)),U_3394)))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3392),U_3393)),U_3396)),U_3395)),U_3394)) )
        & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3392),U_3393)),U_3396)),U_3395)),U_3394))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3392),U_3396)),U_3395)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3393),U_3396)),U_3394))) ) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3393),U_3392)) ),
    inference(variable_rename,[status(thm)],[f_866_1]) ).

fof(f_866_3,plain,
    ( ! [U_3392,U_3393,U_3394,U_3395,U_3396] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3392),U_3396)),U_3395)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3393),U_3396)),U_3394)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3392),U_3393)),U_3396)),U_3395)),U_3394))
        | ~ sP243(U_3392,U_3393,U_3394,U_3395,U_3396) )
    & ! [U_3392,U_3393,U_3394,U_3395,U_3396] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3392),U_3393)),U_3396)),U_3395)),U_3394))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3392),U_3396)),U_3395)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3393),U_3396)),U_3394)))
        | ~ sP243(U_3392,U_3393,U_3394,U_3395,U_3396) )
    & ! [U_3392,U_3393,U_3394,U_3395,U_3396] :
        ( sP243(U_3392,U_3393,U_3394,U_3395,U_3396)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3393),U_3392)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP243])],[f_866_2]) ).

cnf(f_866_4,plain,
    ( sP243(U_3392,U_3393,U_3394,U_3395,U_3396)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3393),U_3392)) ),
    inference(clausify,[status(thm)],[f_866_3]) ).

cnf(f_866_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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3392),U_3393)),U_3396)),U_3395)),U_3394))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3392),U_3396)),U_3395)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3393),U_3396)),U_3394)))
    | ~ sP243(U_3392,U_3393,U_3394,U_3395,U_3396) ),
    inference(clausify,[status(thm)],[f_866_3]) ).

cnf(f_866_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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3392),U_3396)),U_3395)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3393),U_3396)),U_3394)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3392),U_3393)),U_3396)),U_3395)),U_3394))
    | ~ sP243(U_3392,U_3393,U_3394,U_3395,U_3396) ),
    inference(clausify,[status(thm)],[f_866_3]) ).

fof(f_867_1,plain,
    ! [B,Q_2,R_3,B_2,Q_1,R_2] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Q_1),Q_2))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_2),B))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_2))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R_2))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_3),B))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_2),Q_1)),R_2)),zero_zero(int)))
      | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q_2)),R_3) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_2),Q_1)),R_2) ),
    inference(fof_nnf,[status(thm)],[fact_796_zdiv__mono2__neg__lemma]) ).

fof(f_867_2,plain,
    ! [U_3402,U_3401,U_3400,U_3399,U_3398,U_3397] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3398),U_3401))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3399),U_3402))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3399))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3397))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3400),U_3402))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3399),U_3398)),U_3397)),zero_zero(int)))
      | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3402),U_3401)),U_3400) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3399),U_3398)),U_3397) ),
    inference(variable_rename,[status(thm)],[f_867_1]) ).

fof(f_867_3,plain,
    ! [U_3398,U_3400,U_3399,U_3397,U_3401,U_3402] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3398),U_3401))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3399),U_3402))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3399))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3397))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3400),U_3402))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3399),U_3398)),U_3397)),zero_zero(int)))
      | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3402),U_3401)),U_3400) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3399),U_3398)),U_3397) ),
    inference(definitional_conversion,[status(esa)],[f_867_2]) ).

cnf(f_867_4,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3398),U_3401))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3399),U_3402))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3399))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3397))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3400),U_3402))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3399),U_3398)),U_3397)),zero_zero(int)))
    | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3402),U_3401)),U_3400) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3399),U_3398)),U_3397) ),
    inference(clausify,[status(thm)],[f_867_3]) ).

fof(f_868_1,plain,
    ! [B,Q_1,R_2,Q_2,R_3] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Q_2),Q_1))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R_2))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R_3))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),R_3),zero_zero(int)))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q_1)),R_2)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q_2)),R_3))) ),
    inference(fof_nnf,[status(thm)],[fact_797_unique__quotient__lemma__neg]) ).

fof(f_868_2,plain,
    ! [U_3407,U_3406,U_3405,U_3404,U_3403] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3404),U_3406))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3407),U_3405))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3407),U_3403))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3403),zero_zero(int)))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3407),U_3406)),U_3405)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3407),U_3404)),U_3403))) ),
    inference(variable_rename,[status(thm)],[f_868_1]) ).

fof(f_868_3,plain,
    ! [U_3405,U_3407,U_3406,U_3404,U_3403] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3404),U_3406))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3407),U_3405))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3407),U_3403))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3403),zero_zero(int)))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3407),U_3406)),U_3405)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3407),U_3404)),U_3403))) ),
    inference(definitional_conversion,[status(esa)],[f_868_2]) ).

cnf(f_868_4,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3404),U_3406))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3407),U_3405))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3407),U_3403))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3403),zero_zero(int)))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3407),U_3406)),U_3405)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3407),U_3404)),U_3403))) ),
    inference(clausify,[status(thm)],[f_868_3]) ).

fof(f_869_1,plain,
    ! [K_1] : hAPP(int,int,number_number_of(int),K_1) = K_1,
    inference(fof_nnf,[status(thm)],[fact_798_number__of__is__id]) ).

fof(f_869_2,plain,
    ! [U_3408] : hAPP(int,int,number_number_of(int),U_3408) = U_3408,
    inference(variable_rename,[status(thm)],[f_869_1]) ).

fof(f_869_3,plain,
    ! [U_3408] : hAPP(int,int,number_number_of(int),U_3408) = U_3408,
    inference(definitional_conversion,[status(esa)],[f_869_2]) ).

cnf(f_869_4,plain,
    hAPP(int,int,number_number_of(int),U_3408) = U_3408,
    inference(clausify,[status(thm)],[f_869_3]) ).

fof(f_870_1,plain,
    zero_zero(int) != one_one(int),
    inference(fof_nnf,[status(thm)],[fact_799_int__0__neq__1]) ).

fof(f_870_2,plain,
    zero_zero(int) != one_one(int),
    inference(definitional_conversion,[status(esa)],[f_870_1]) ).

cnf(f_870_3,plain,
    zero_zero(int) != one_one(int),
    inference(clausify,[status(thm)],[f_870_2]) ).

fof(f_871_1,plain,
    ! [R_3,Q_2,A_1] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),Q_2))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_3),A_1))
      | A_1 != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),R_3),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),Q_2))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_800_self__quotient__aux1]) ).

fof(f_871_2,plain,
    ! [U_3411,U_3410,U_3409] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),U_3410))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3411),U_3409))
      | U_3409 != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3411),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3409),U_3410))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3409)) ),
    inference(variable_rename,[status(thm)],[f_871_1]) ).

fof(f_871_3,plain,
    ! [U_3409,U_3411,U_3410] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),U_3410))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3411),U_3409))
      | U_3409 != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3411),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3409),U_3410))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3409)) ),
    inference(definitional_conversion,[status(esa)],[f_871_2]) ).

cnf(f_871_4,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),U_3410))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3411),U_3409))
    | U_3409 != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3411),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3409),U_3410))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3409)) ),
    inference(clausify,[status(thm)],[f_871_3]) ).

fof(f_872_1,plain,
    ! [R_3,Q_2,A_1] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Q_2),one_one(int)))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R_3))
      | A_1 != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),R_3),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),Q_2))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_801_self__quotient__aux2]) ).

fof(f_872_2,plain,
    ! [U_3414,U_3413,U_3412] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3413),one_one(int)))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3414))
      | U_3412 != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3414),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3412),U_3413))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3412)) ),
    inference(variable_rename,[status(thm)],[f_872_1]) ).

fof(f_872_3,plain,
    ! [U_3412,U_3414,U_3413] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3413),one_one(int)))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3414))
      | U_3412 != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3414),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3412),U_3413))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3412)) ),
    inference(definitional_conversion,[status(esa)],[f_872_2]) ).

cnf(f_872_4,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3413),one_one(int)))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3414))
    | U_3412 != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3414),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3412),U_3413))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3412)) ),
    inference(clausify,[status(thm)],[f_872_3]) ).

fof(f_873_1,plain,
    ! [B_2,Q_1,R_2] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Q_1))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_2))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_2),B_2))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_2),Q_1)),R_2))) ),
    inference(fof_nnf,[status(thm)],[fact_802_q__pos__lemma]) ).

fof(f_873_2,plain,
    ! [U_3417,U_3416,U_3415] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3416))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3417))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3415),U_3417))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3417),U_3416)),U_3415))) ),
    inference(variable_rename,[status(thm)],[f_873_1]) ).

fof(f_873_3,plain,
    ! [U_3416,U_3415,U_3417] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3416))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3417))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3415),U_3417))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3417),U_3416)),U_3415))) ),
    inference(definitional_conversion,[status(esa)],[f_873_2]) ).

cnf(f_873_4,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3416))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3417))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3415),U_3417))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3417),U_3416)),U_3415))) ),
    inference(clausify,[status(thm)],[f_873_3]) ).

fof(f_874_1,plain,
    ! [B_2,Q_1,R_2] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Q_1),zero_zero(int)))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_2))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R_2))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_2),Q_1)),R_2)),zero_zero(int))) ),
    inference(fof_nnf,[status(thm)],[fact_803_q__neg__lemma]) ).

fof(f_874_2,plain,
    ! [U_3420,U_3419,U_3418] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3419),zero_zero(int)))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3420))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3418))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3420),U_3419)),U_3418)),zero_zero(int))) ),
    inference(variable_rename,[status(thm)],[f_874_1]) ).

fof(f_874_3,plain,
    ! [U_3418,U_3419,U_3420] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3419),zero_zero(int)))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3420))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3418))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3420),U_3419)),U_3418)),zero_zero(int))) ),
    inference(definitional_conversion,[status(esa)],[f_874_2]) ).

cnf(f_874_4,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3419),zero_zero(int)))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3420))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3418))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3420),U_3419)),U_3418)),zero_zero(int))) ),
    inference(clausify,[status(thm)],[f_874_3]) ).

fof(f_875_1,plain,
    ! [B,Q_1,R_2,Q_2,R_3] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Q_1),Q_2))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_3),B))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_2),B))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R_2))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q_1)),R_2)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q_2)),R_3))) ),
    inference(fof_nnf,[status(thm)],[fact_804_unique__quotient__lemma]) ).

fof(f_875_2,plain,
    ! [U_3425,U_3424,U_3423,U_3422,U_3421] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3424),U_3422))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3421),U_3425))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3423),U_3425))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3423))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3425),U_3424)),U_3423)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3425),U_3422)),U_3421))) ),
    inference(variable_rename,[status(thm)],[f_875_1]) ).

fof(f_875_3,plain,
    ! [U_3421,U_3423,U_3422,U_3424,U_3425] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3424),U_3422))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3421),U_3425))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3423),U_3425))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3423))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3425),U_3424)),U_3423)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3425),U_3422)),U_3421))) ),
    inference(definitional_conversion,[status(esa)],[f_875_2]) ).

cnf(f_875_4,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3424),U_3422))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3421),U_3425))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3423),U_3425))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3423))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3425),U_3424)),U_3423)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3425),U_3422)),U_3421))) ),
    inference(clausify,[status(thm)],[f_875_3]) ).

fof(f_876_1,plain,
    ! [B,Q_2,R_3,B_2,Q_1,R_2] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Q_2),Q_1))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_2),B))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_2))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R_3))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_2),B_2))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_2),Q_1)),R_2)))
      | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q_2)),R_3) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_2),Q_1)),R_2) ),
    inference(fof_nnf,[status(thm)],[fact_805_zdiv__mono2__lemma]) ).

fof(f_876_2,plain,
    ! [U_3431,U_3430,U_3429,U_3428,U_3427,U_3426] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3430),U_3427))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3428),U_3431))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3428))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3429))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3426),U_3428))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3428),U_3427)),U_3426)))
      | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3431),U_3430)),U_3429) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3428),U_3427)),U_3426) ),
    inference(variable_rename,[status(thm)],[f_876_1]) ).

fof(f_876_3,plain,
    ! [U_3429,U_3427,U_3428,U_3426,U_3430,U_3431] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3430),U_3427))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3428),U_3431))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3428))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3429))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3426),U_3428))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3428),U_3427)),U_3426)))
      | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3431),U_3430)),U_3429) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3428),U_3427)),U_3426) ),
    inference(definitional_conversion,[status(esa)],[f_876_2]) ).

cnf(f_876_4,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3430),U_3427))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3428),U_3431))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3428))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3429))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3426),U_3428))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3428),U_3427)),U_3426)))
    | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3431),U_3430)),U_3429) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3428),U_3427)),U_3426) ),
    inference(clausify,[status(thm)],[f_876_3]) ).

fof(f_877_1,plain,
    ! [Pa,I_1,K] :
      ( hBOOL(hAPP(int,bool,Pa,I_1))
      | ? [I] :
          ( ~ hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),I),one_one(int))))
          & hBOOL(hAPP(int,bool,Pa,I))
          & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I),K)) )
      | ~ hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K),one_one(int))))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_1),K)) ),
    inference(fof_nnf,[status(thm)],[fact_806_int__less__induct]) ).

fof(f_877_2,plain,
    ! [U_3435,U_3434,U_3433] :
      ( hBOOL(hAPP(int,bool,U_3435,U_3434))
      | ? [U_3432] :
          ( ~ hBOOL(hAPP(int,bool,U_3435,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3432),one_one(int))))
          & hBOOL(hAPP(int,bool,U_3435,U_3432))
          & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3432),U_3433)) )
      | ~ hBOOL(hAPP(int,bool,U_3435,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3433),one_one(int))))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3434),U_3433)) ),
    inference(variable_rename,[status(thm)],[f_877_1]) ).

fof(f_877_3,plain,
    ! [U_3435,U_3434,U_3433] :
      ( hBOOL(hAPP(int,bool,U_3435,U_3434))
      | ( ~ hBOOL(hAPP(int,bool,U_3435,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),sK102(U_3435,U_3434,U_3433)),one_one(int))))
        & hBOOL(hAPP(int,bool,U_3435,sK102(U_3435,U_3434,U_3433)))
        & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),sK102(U_3435,U_3434,U_3433)),U_3433)) )
      | ~ hBOOL(hAPP(int,bool,U_3435,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3433),one_one(int))))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3434),U_3433)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK102]),skolemize(U_3432,sK102(U_3435,U_3434,U_3433))],[f_877_2]) ).

fof(f_877_4,plain,
    ( ! [U_3435,U_3434,U_3433] :
        ( ~ hBOOL(hAPP(int,bool,U_3435,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),sK102(U_3435,U_3434,U_3433)),one_one(int))))
        | ~ sP244(U_3435,U_3434,U_3433) )
    & ! [U_3435,U_3434,U_3433] :
        ( hBOOL(hAPP(int,bool,U_3435,sK102(U_3435,U_3434,U_3433)))
        | ~ sP244(U_3435,U_3434,U_3433) )
    & ! [U_3435,U_3434,U_3433] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),sK102(U_3435,U_3434,U_3433)),U_3433))
        | ~ sP244(U_3435,U_3434,U_3433) )
    & ! [U_3435,U_3434,U_3433] :
        ( hBOOL(hAPP(int,bool,U_3435,U_3434))
        | sP244(U_3435,U_3434,U_3433)
        | ~ hBOOL(hAPP(int,bool,U_3435,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3433),one_one(int))))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3434),U_3433)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP244])],[f_877_3]) ).

cnf(f_877_5,plain,
    ( hBOOL(hAPP(int,bool,U_3435,U_3434))
    | sP244(U_3435,U_3434,U_3433)
    | ~ hBOOL(hAPP(int,bool,U_3435,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3433),one_one(int))))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3434),U_3433)) ),
    inference(clausify,[status(thm)],[f_877_4]) ).

cnf(f_877_6,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),sK102(U_3435,U_3434,U_3433)),U_3433))
    | ~ sP244(U_3435,U_3434,U_3433) ),
    inference(clausify,[status(thm)],[f_877_4]) ).

cnf(f_877_7,plain,
    ( hBOOL(hAPP(int,bool,U_3435,sK102(U_3435,U_3434,U_3433)))
    | ~ sP244(U_3435,U_3434,U_3433) ),
    inference(clausify,[status(thm)],[f_877_4]) ).

cnf(f_877_8,plain,
    ( ~ hBOOL(hAPP(int,bool,U_3435,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),sK102(U_3435,U_3434,U_3433)),one_one(int))))
    | ~ sP244(U_3435,U_3434,U_3433) ),
    inference(clausify,[status(thm)],[f_877_4]) ).

fof(f_878_1,plain,
    ! [Pa,I_1,K] :
      ( hBOOL(hAPP(int,bool,Pa,I_1))
      | ? [I] :
          ( ~ hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),I),one_one(int))))
          & hBOOL(hAPP(int,bool,Pa,I))
          & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I),K)) )
      | ~ hBOOL(hAPP(int,bool,Pa,K))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I_1),K)) ),
    inference(fof_nnf,[status(thm)],[fact_807_int__le__induct]) ).

fof(f_878_2,plain,
    ! [U_3439,U_3438,U_3437] :
      ( hBOOL(hAPP(int,bool,U_3439,U_3438))
      | ? [U_3436] :
          ( ~ hBOOL(hAPP(int,bool,U_3439,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3436),one_one(int))))
          & hBOOL(hAPP(int,bool,U_3439,U_3436))
          & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3436),U_3437)) )
      | ~ hBOOL(hAPP(int,bool,U_3439,U_3437))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3438),U_3437)) ),
    inference(variable_rename,[status(thm)],[f_878_1]) ).

fof(f_878_3,plain,
    ! [U_3439,U_3438,U_3437] :
      ( hBOOL(hAPP(int,bool,U_3439,U_3438))
      | ( ~ hBOOL(hAPP(int,bool,U_3439,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),sK103(U_3439,U_3438,U_3437)),one_one(int))))
        & hBOOL(hAPP(int,bool,U_3439,sK103(U_3439,U_3438,U_3437)))
        & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),sK103(U_3439,U_3438,U_3437)),U_3437)) )
      | ~ hBOOL(hAPP(int,bool,U_3439,U_3437))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3438),U_3437)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK103]),skolemize(U_3436,sK103(U_3439,U_3438,U_3437))],[f_878_2]) ).

fof(f_878_4,plain,
    ( ! [U_3439,U_3438,U_3437] :
        ( ~ hBOOL(hAPP(int,bool,U_3439,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),sK103(U_3439,U_3438,U_3437)),one_one(int))))
        | ~ sP245(U_3439,U_3438,U_3437) )
    & ! [U_3439,U_3438,U_3437] :
        ( hBOOL(hAPP(int,bool,U_3439,sK103(U_3439,U_3438,U_3437)))
        | ~ sP245(U_3439,U_3438,U_3437) )
    & ! [U_3439,U_3438,U_3437] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),sK103(U_3439,U_3438,U_3437)),U_3437))
        | ~ sP245(U_3439,U_3438,U_3437) )
    & ! [U_3439,U_3438,U_3437] :
        ( hBOOL(hAPP(int,bool,U_3439,U_3438))
        | sP245(U_3439,U_3438,U_3437)
        | ~ hBOOL(hAPP(int,bool,U_3439,U_3437))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3438),U_3437)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP245])],[f_878_3]) ).

cnf(f_878_5,plain,
    ( hBOOL(hAPP(int,bool,U_3439,U_3438))
    | sP245(U_3439,U_3438,U_3437)
    | ~ hBOOL(hAPP(int,bool,U_3439,U_3437))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3438),U_3437)) ),
    inference(clausify,[status(thm)],[f_878_4]) ).

cnf(f_878_6,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),sK103(U_3439,U_3438,U_3437)),U_3437))
    | ~ sP245(U_3439,U_3438,U_3437) ),
    inference(clausify,[status(thm)],[f_878_4]) ).

cnf(f_878_7,plain,
    ( hBOOL(hAPP(int,bool,U_3439,sK103(U_3439,U_3438,U_3437)))
    | ~ sP245(U_3439,U_3438,U_3437) ),
    inference(clausify,[status(thm)],[f_878_4]) ).

cnf(f_878_8,plain,
    ( ~ hBOOL(hAPP(int,bool,U_3439,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),sK103(U_3439,U_3438,U_3437)),one_one(int))))
    | ~ sP245(U_3439,U_3438,U_3437) ),
    inference(clausify,[status(thm)],[f_878_4]) ).

fof(f_879_1,plain,
    ! [X_b,X_c] :
      ( ! [Z_2,G,H,A_3] :
          ( hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),G),Z_2),A_3) = hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),H),Z_2),A_3)
          | ? [X_2] :
              ( hAPP(X_b,X_c,G,X_2) != hAPP(X_b,X_c,H,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,finite_finite(X_b),A_3)) )
      | ~ ab_semigroup_mult(X_c) ),
    inference(fof_nnf,[status(thm)],[fact_808_fold__image__cong]) ).

fof(f_879_2,plain,
    ! [U_3446,U_3445] :
      ( ! [U_3444,U_3443,U_3442,U_3441] :
          ( hAPP(fun(U_3446,bool),U_3445,hAPP(U_3445,fun(fun(U_3446,bool),U_3445),hAPP(fun(U_3446,U_3445),fun(U_3445,fun(fun(U_3446,bool),U_3445)),hAPP(fun(U_3445,fun(U_3445,U_3445)),fun(fun(U_3446,U_3445),fun(U_3445,fun(fun(U_3446,bool),U_3445))),finite_fold_image(U_3445,U_3446),times_times(U_3445)),U_3443),U_3444),U_3441) = hAPP(fun(U_3446,bool),U_3445,hAPP(U_3445,fun(fun(U_3446,bool),U_3445),hAPP(fun(U_3446,U_3445),fun(U_3445,fun(fun(U_3446,bool),U_3445)),hAPP(fun(U_3445,fun(U_3445,U_3445)),fun(fun(U_3446,U_3445),fun(U_3445,fun(fun(U_3446,bool),U_3445))),finite_fold_image(U_3445,U_3446),times_times(U_3445)),U_3442),U_3444),U_3441)
          | ? [U_3440] :
              ( hAPP(U_3446,U_3445,U_3443,U_3440) != hAPP(U_3446,U_3445,U_3442,U_3440)
              & hBOOL(hAPP(fun(U_3446,bool),bool,hAPP(U_3446,fun(fun(U_3446,bool),bool),member(U_3446),U_3440),U_3441)) )
          | ~ hBOOL(hAPP(fun(U_3446,bool),bool,finite_finite(U_3446),U_3441)) )
      | ~ ab_semigroup_mult(U_3445) ),
    inference(variable_rename,[status(thm)],[f_879_1]) ).

fof(f_879_3,plain,
    ! [U_3446,U_3445] :
      ( ! [U_3444,U_3443,U_3442,U_3441] :
          ( hAPP(fun(U_3446,bool),U_3445,hAPP(U_3445,fun(fun(U_3446,bool),U_3445),hAPP(fun(U_3446,U_3445),fun(U_3445,fun(fun(U_3446,bool),U_3445)),hAPP(fun(U_3445,fun(U_3445,U_3445)),fun(fun(U_3446,U_3445),fun(U_3445,fun(fun(U_3446,bool),U_3445))),finite_fold_image(U_3445,U_3446),times_times(U_3445)),U_3443),U_3444),U_3441) = hAPP(fun(U_3446,bool),U_3445,hAPP(U_3445,fun(fun(U_3446,bool),U_3445),hAPP(fun(U_3446,U_3445),fun(U_3445,fun(fun(U_3446,bool),U_3445)),hAPP(fun(U_3445,fun(U_3445,U_3445)),fun(fun(U_3446,U_3445),fun(U_3445,fun(fun(U_3446,bool),U_3445))),finite_fold_image(U_3445,U_3446),times_times(U_3445)),U_3442),U_3444),U_3441)
          | ( hAPP(U_3446,U_3445,U_3443,sK104(U_3446,U_3445,U_3444,U_3443,U_3442,U_3441)) != hAPP(U_3446,U_3445,U_3442,sK104(U_3446,U_3445,U_3444,U_3443,U_3442,U_3441))
            & hBOOL(hAPP(fun(U_3446,bool),bool,hAPP(U_3446,fun(fun(U_3446,bool),bool),member(U_3446),sK104(U_3446,U_3445,U_3444,U_3443,U_3442,U_3441)),U_3441)) )
          | ~ hBOOL(hAPP(fun(U_3446,bool),bool,finite_finite(U_3446),U_3441)) )
      | ~ ab_semigroup_mult(U_3445) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK104]),skolemize(U_3440,sK104(U_3446,U_3445,U_3444,U_3443,U_3442,U_3441))],[f_879_2]) ).

fof(f_879_4,plain,
    ( ! [U_3443,U_3445,U_3441,U_3444,U_3442,U_3446] :
        ( hAPP(U_3446,U_3445,U_3443,sK104(U_3446,U_3445,U_3444,U_3443,U_3442,U_3441)) != hAPP(U_3446,U_3445,U_3442,sK104(U_3446,U_3445,U_3444,U_3443,U_3442,U_3441))
        | ~ sP246(U_3443,U_3445,U_3441,U_3444,U_3442,U_3446) )
    & ! [U_3443,U_3445,U_3441,U_3444,U_3442,U_3446] :
        ( hBOOL(hAPP(fun(U_3446,bool),bool,hAPP(U_3446,fun(fun(U_3446,bool),bool),member(U_3446),sK104(U_3446,U_3445,U_3444,U_3443,U_3442,U_3441)),U_3441))
        | ~ sP246(U_3443,U_3445,U_3441,U_3444,U_3442,U_3446) )
    & ! [U_3443,U_3445,U_3441,U_3444,U_3442,U_3446] :
        ( hAPP(fun(U_3446,bool),U_3445,hAPP(U_3445,fun(fun(U_3446,bool),U_3445),hAPP(fun(U_3446,U_3445),fun(U_3445,fun(fun(U_3446,bool),U_3445)),hAPP(fun(U_3445,fun(U_3445,U_3445)),fun(fun(U_3446,U_3445),fun(U_3445,fun(fun(U_3446,bool),U_3445))),finite_fold_image(U_3445,U_3446),times_times(U_3445)),U_3443),U_3444),U_3441) = hAPP(fun(U_3446,bool),U_3445,hAPP(U_3445,fun(fun(U_3446,bool),U_3445),hAPP(fun(U_3446,U_3445),fun(U_3445,fun(fun(U_3446,bool),U_3445)),hAPP(fun(U_3445,fun(U_3445,U_3445)),fun(fun(U_3446,U_3445),fun(U_3445,fun(fun(U_3446,bool),U_3445))),finite_fold_image(U_3445,U_3446),times_times(U_3445)),U_3442),U_3444),U_3441)
        | sP246(U_3443,U_3445,U_3441,U_3444,U_3442,U_3446)
        | ~ hBOOL(hAPP(fun(U_3446,bool),bool,finite_finite(U_3446),U_3441))
        | ~ ab_semigroup_mult(U_3445) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP246])],[f_879_3]) ).

cnf(f_879_5,plain,
    ( hAPP(fun(U_3446,bool),U_3445,hAPP(U_3445,fun(fun(U_3446,bool),U_3445),hAPP(fun(U_3446,U_3445),fun(U_3445,fun(fun(U_3446,bool),U_3445)),hAPP(fun(U_3445,fun(U_3445,U_3445)),fun(fun(U_3446,U_3445),fun(U_3445,fun(fun(U_3446,bool),U_3445))),finite_fold_image(U_3445,U_3446),times_times(U_3445)),U_3443),U_3444),U_3441) = hAPP(fun(U_3446,bool),U_3445,hAPP(U_3445,fun(fun(U_3446,bool),U_3445),hAPP(fun(U_3446,U_3445),fun(U_3445,fun(fun(U_3446,bool),U_3445)),hAPP(fun(U_3445,fun(U_3445,U_3445)),fun(fun(U_3446,U_3445),fun(U_3445,fun(fun(U_3446,bool),U_3445))),finite_fold_image(U_3445,U_3446),times_times(U_3445)),U_3442),U_3444),U_3441)
    | sP246(U_3443,U_3445,U_3441,U_3444,U_3442,U_3446)
    | ~ hBOOL(hAPP(fun(U_3446,bool),bool,finite_finite(U_3446),U_3441))
    | ~ ab_semigroup_mult(U_3445) ),
    inference(clausify,[status(thm)],[f_879_4]) ).

cnf(f_879_6,plain,
    ( hBOOL(hAPP(fun(U_3446,bool),bool,hAPP(U_3446,fun(fun(U_3446,bool),bool),member(U_3446),sK104(U_3446,U_3445,U_3444,U_3443,U_3442,U_3441)),U_3441))
    | ~ sP246(U_3443,U_3445,U_3441,U_3444,U_3442,U_3446) ),
    inference(clausify,[status(thm)],[f_879_4]) ).

cnf(f_879_7,plain,
    ( hAPP(U_3446,U_3445,U_3443,sK104(U_3446,U_3445,U_3444,U_3443,U_3442,U_3441)) != hAPP(U_3446,U_3445,U_3442,sK104(U_3446,U_3445,U_3444,U_3443,U_3442,U_3441))
    | ~ sP246(U_3443,U_3445,U_3441,U_3444,U_3442,U_3446) ),
    inference(clausify,[status(thm)],[f_879_4]) ).

fof(f_880_1,plain,
    ! [Pa,K,I_1] :
      ( hBOOL(hAPP(int,bool,Pa,I_1))
      | ? [I] :
          ( ~ hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I),one_one(int))))
          & hBOOL(hAPP(int,bool,Pa,I))
          & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),I)) )
      | ~ hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K),one_one(int))))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),I_1)) ),
    inference(fof_nnf,[status(thm)],[fact_809_int__gr__induct]) ).

fof(f_880_2,plain,
    ! [U_3450,U_3449,U_3448] :
      ( hBOOL(hAPP(int,bool,U_3450,U_3448))
      | ? [U_3447] :
          ( ~ hBOOL(hAPP(int,bool,U_3450,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3447),one_one(int))))
          & hBOOL(hAPP(int,bool,U_3450,U_3447))
          & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3449),U_3447)) )
      | ~ hBOOL(hAPP(int,bool,U_3450,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3449),one_one(int))))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3449),U_3448)) ),
    inference(variable_rename,[status(thm)],[f_880_1]) ).

fof(f_880_3,plain,
    ! [U_3450,U_3449,U_3448] :
      ( hBOOL(hAPP(int,bool,U_3450,U_3448))
      | ( ~ hBOOL(hAPP(int,bool,U_3450,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),sK105(U_3450,U_3449,U_3448)),one_one(int))))
        & hBOOL(hAPP(int,bool,U_3450,sK105(U_3450,U_3449,U_3448)))
        & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3449),sK105(U_3450,U_3449,U_3448))) )
      | ~ hBOOL(hAPP(int,bool,U_3450,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3449),one_one(int))))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3449),U_3448)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK105]),skolemize(U_3447,sK105(U_3450,U_3449,U_3448))],[f_880_2]) ).

fof(f_880_4,plain,
    ( ! [U_3449,U_3450,U_3448] :
        ( ~ hBOOL(hAPP(int,bool,U_3450,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),sK105(U_3450,U_3449,U_3448)),one_one(int))))
        | ~ sP247(U_3449,U_3450,U_3448) )
    & ! [U_3449,U_3450,U_3448] :
        ( hBOOL(hAPP(int,bool,U_3450,sK105(U_3450,U_3449,U_3448)))
        | ~ sP247(U_3449,U_3450,U_3448) )
    & ! [U_3449,U_3450,U_3448] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3449),sK105(U_3450,U_3449,U_3448)))
        | ~ sP247(U_3449,U_3450,U_3448) )
    & ! [U_3449,U_3450,U_3448] :
        ( hBOOL(hAPP(int,bool,U_3450,U_3448))
        | sP247(U_3449,U_3450,U_3448)
        | ~ hBOOL(hAPP(int,bool,U_3450,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3449),one_one(int))))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3449),U_3448)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP247])],[f_880_3]) ).

cnf(f_880_5,plain,
    ( hBOOL(hAPP(int,bool,U_3450,U_3448))
    | sP247(U_3449,U_3450,U_3448)
    | ~ hBOOL(hAPP(int,bool,U_3450,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3449),one_one(int))))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3449),U_3448)) ),
    inference(clausify,[status(thm)],[f_880_4]) ).

cnf(f_880_6,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3449),sK105(U_3450,U_3449,U_3448)))
    | ~ sP247(U_3449,U_3450,U_3448) ),
    inference(clausify,[status(thm)],[f_880_4]) ).

cnf(f_880_7,plain,
    ( hBOOL(hAPP(int,bool,U_3450,sK105(U_3450,U_3449,U_3448)))
    | ~ sP247(U_3449,U_3450,U_3448) ),
    inference(clausify,[status(thm)],[f_880_4]) ).

cnf(f_880_8,plain,
    ( ~ hBOOL(hAPP(int,bool,U_3450,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),sK105(U_3450,U_3449,U_3448)),one_one(int))))
    | ~ sP247(U_3449,U_3450,U_3448) ),
    inference(clausify,[status(thm)],[f_880_4]) ).

fof(f_881_1,plain,
    ! [Pa,K,I_1] :
      ( hBOOL(hAPP(int,bool,Pa,I_1))
      | ? [I] :
          ( ~ hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I),one_one(int))))
          & hBOOL(hAPP(int,bool,Pa,I))
          & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),I)) )
      | ~ hBOOL(hAPP(int,bool,Pa,K))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),I_1)) ),
    inference(fof_nnf,[status(thm)],[fact_810_int__ge__induct]) ).

fof(f_881_2,plain,
    ! [U_3454,U_3453,U_3452] :
      ( hBOOL(hAPP(int,bool,U_3454,U_3452))
      | ? [U_3451] :
          ( ~ hBOOL(hAPP(int,bool,U_3454,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3451),one_one(int))))
          & hBOOL(hAPP(int,bool,U_3454,U_3451))
          & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3453),U_3451)) )
      | ~ hBOOL(hAPP(int,bool,U_3454,U_3453))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3453),U_3452)) ),
    inference(variable_rename,[status(thm)],[f_881_1]) ).

fof(f_881_3,plain,
    ! [U_3454,U_3453,U_3452] :
      ( hBOOL(hAPP(int,bool,U_3454,U_3452))
      | ( ~ hBOOL(hAPP(int,bool,U_3454,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),sK106(U_3454,U_3453,U_3452)),one_one(int))))
        & hBOOL(hAPP(int,bool,U_3454,sK106(U_3454,U_3453,U_3452)))
        & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3453),sK106(U_3454,U_3453,U_3452))) )
      | ~ hBOOL(hAPP(int,bool,U_3454,U_3453))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3453),U_3452)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK106]),skolemize(U_3451,sK106(U_3454,U_3453,U_3452))],[f_881_2]) ).

fof(f_881_4,plain,
    ( ! [U_3452,U_3454,U_3453] :
        ( ~ hBOOL(hAPP(int,bool,U_3454,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),sK106(U_3454,U_3453,U_3452)),one_one(int))))
        | ~ sP248(U_3452,U_3454,U_3453) )
    & ! [U_3452,U_3454,U_3453] :
        ( hBOOL(hAPP(int,bool,U_3454,sK106(U_3454,U_3453,U_3452)))
        | ~ sP248(U_3452,U_3454,U_3453) )
    & ! [U_3452,U_3454,U_3453] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3453),sK106(U_3454,U_3453,U_3452)))
        | ~ sP248(U_3452,U_3454,U_3453) )
    & ! [U_3452,U_3454,U_3453] :
        ( hBOOL(hAPP(int,bool,U_3454,U_3452))
        | sP248(U_3452,U_3454,U_3453)
        | ~ hBOOL(hAPP(int,bool,U_3454,U_3453))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3453),U_3452)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP248])],[f_881_3]) ).

cnf(f_881_5,plain,
    ( hBOOL(hAPP(int,bool,U_3454,U_3452))
    | sP248(U_3452,U_3454,U_3453)
    | ~ hBOOL(hAPP(int,bool,U_3454,U_3453))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3453),U_3452)) ),
    inference(clausify,[status(thm)],[f_881_4]) ).

cnf(f_881_6,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3453),sK106(U_3454,U_3453,U_3452)))
    | ~ sP248(U_3452,U_3454,U_3453) ),
    inference(clausify,[status(thm)],[f_881_4]) ).

cnf(f_881_7,plain,
    ( hBOOL(hAPP(int,bool,U_3454,sK106(U_3454,U_3453,U_3452)))
    | ~ sP248(U_3452,U_3454,U_3453) ),
    inference(clausify,[status(thm)],[f_881_4]) ).

cnf(f_881_8,plain,
    ( ~ hBOOL(hAPP(int,bool,U_3454,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),sK106(U_3454,U_3453,U_3452)),one_one(int))))
    | ~ sP248(U_3452,U_3454,U_3453) ),
    inference(clausify,[status(thm)],[f_881_4]) ).

fof(f_882_1,plain,
    ! [Y,X] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),Y)))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) ),
    inference(fof_nnf,[status(thm)],[fact_811_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J]) ).

fof(f_882_2,plain,
    ! [U_3456,U_3455] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3455),U_3456)))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3456))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3455)) ),
    inference(variable_rename,[status(thm)],[f_882_1]) ).

fof(f_882_3,plain,
    ! [U_3456,U_3455] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3455),U_3456)))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3456))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3455)) ),
    inference(definitional_conversion,[status(esa)],[f_882_2]) ).

cnf(f_882_4,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3455),U_3456)))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3456))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3455)) ),
    inference(clausify,[status(thm)],[f_882_3]) ).

fof(f_883_1,plain,
    hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),zero_zero(int))),
    inference(fof_nnf,[status(thm)],[fact_812_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J]) ).

fof(f_883_2,plain,
    hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),zero_zero(int))),
    inference(definitional_conversion,[status(esa)],[f_883_1]) ).

cnf(f_883_3,plain,
    hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),zero_zero(int))),
    inference(clausify,[status(thm)],[f_883_2]) ).

fof(f_884_1,plain,
    ! [Y,X] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),Y)))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) ),
    inference(fof_nnf,[status(thm)],[fact_813_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J]) ).

fof(f_884_2,plain,
    ! [U_3458,U_3457] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3457),U_3458)))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3458))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3457)) ),
    inference(variable_rename,[status(thm)],[f_884_1]) ).

fof(f_884_3,plain,
    ! [U_3458,U_3457] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3457),U_3458)))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3458))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3457)) ),
    inference(definitional_conversion,[status(esa)],[f_884_2]) ).

cnf(f_884_4,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3457),U_3458)))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3458))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3457)) ),
    inference(clausify,[status(thm)],[f_884_3]) ).

fof(f_885_1,plain,
    hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),one_one(int))),
    inference(fof_nnf,[status(thm)],[fact_814_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J]) ).

fof(f_885_2,plain,
    hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),one_one(int))),
    inference(definitional_conversion,[status(esa)],[f_885_1]) ).

cnf(f_885_3,plain,
    hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),one_one(int))),
    inference(clausify,[status(thm)],[f_885_2]) ).

fof(f_886_1,plain,
    ! [P_1,Pa] :
      ( hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),Pa)) = hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),P_1))
      | ? [X_2] :
          ( ( ( ~ hBOOL(hAPP(int,bool,Pa,X_2))
              & hBOOL(hAPP(int,bool,P_1,X_2)) )
            | ( ~ hBOOL(hAPP(int,bool,P_1,X_2))
              & hBOOL(hAPP(int,bool,Pa,X_2)) ) )
          & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_815_transfer__nat__int__set__cong]) ).

fof(f_886_2,plain,
    ! [U_3461,U_3460] :
      ( hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),U_3460)) = hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),U_3461))
      | ? [U_3459] :
          ( ( ( ~ hBOOL(hAPP(int,bool,U_3460,U_3459))
              & hBOOL(hAPP(int,bool,U_3461,U_3459)) )
            | ( ~ hBOOL(hAPP(int,bool,U_3461,U_3459))
              & hBOOL(hAPP(int,bool,U_3460,U_3459)) ) )
          & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3459)) ) ),
    inference(variable_rename,[status(thm)],[f_886_1]) ).

fof(f_886_3,plain,
    ! [U_3461,U_3460] :
      ( hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),U_3460)) = hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),U_3461))
      | ( ( ( ~ hBOOL(hAPP(int,bool,U_3460,sK107(U_3461,U_3460)))
            & hBOOL(hAPP(int,bool,U_3461,sK107(U_3461,U_3460))) )
          | ( ~ hBOOL(hAPP(int,bool,U_3461,sK107(U_3461,U_3460)))
            & hBOOL(hAPP(int,bool,U_3460,sK107(U_3461,U_3460))) ) )
        & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),sK107(U_3461,U_3460))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK107]),skolemize(U_3459,sK107(U_3461,U_3460))],[f_886_2]) ).

fof(f_886_4,plain,
    ( ! [U_3460,U_3461] :
        ( ~ hBOOL(hAPP(int,bool,U_3460,sK107(U_3461,U_3460)))
        | ~ sP250(U_3460,U_3461) )
    & ! [U_3460,U_3461] :
        ( hBOOL(hAPP(int,bool,U_3461,sK107(U_3461,U_3460)))
        | ~ sP250(U_3460,U_3461) )
    & ! [U_3460,U_3461] :
        ( ~ hBOOL(hAPP(int,bool,U_3461,sK107(U_3461,U_3460)))
        | ~ sP249(U_3460,U_3461) )
    & ! [U_3460,U_3461] :
        ( hBOOL(hAPP(int,bool,U_3460,sK107(U_3461,U_3460)))
        | ~ sP249(U_3460,U_3461) )
    & ! [U_3460,U_3461] :
        ( sP250(U_3460,U_3461)
        | sP249(U_3460,U_3461)
        | ~ sP251(U_3460,U_3461) )
    & ! [U_3460,U_3461] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),sK107(U_3461,U_3460)))
        | ~ sP251(U_3460,U_3461) )
    & ! [U_3460,U_3461] :
        ( hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),U_3460)) = hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),U_3461))
        | sP251(U_3460,U_3461) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP249,sP250,sP251])],[f_886_3]) ).

cnf(f_886_5,plain,
    ( hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),U_3460)) = hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),U_3461))
    | sP251(U_3460,U_3461) ),
    inference(clausify,[status(thm)],[f_886_4]) ).

cnf(f_886_6,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),sK107(U_3461,U_3460)))
    | ~ sP251(U_3460,U_3461) ),
    inference(clausify,[status(thm)],[f_886_4]) ).

cnf(f_886_7,plain,
    ( sP250(U_3460,U_3461)
    | sP249(U_3460,U_3461)
    | ~ sP251(U_3460,U_3461) ),
    inference(clausify,[status(thm)],[f_886_4]) ).

cnf(f_886_8,plain,
    ( hBOOL(hAPP(int,bool,U_3460,sK107(U_3461,U_3460)))
    | ~ sP249(U_3460,U_3461) ),
    inference(clausify,[status(thm)],[f_886_4]) ).

cnf(f_886_9,plain,
    ( ~ hBOOL(hAPP(int,bool,U_3461,sK107(U_3461,U_3460)))
    | ~ sP249(U_3460,U_3461) ),
    inference(clausify,[status(thm)],[f_886_4]) ).

cnf(f_886_10,plain,
    ( hBOOL(hAPP(int,bool,U_3461,sK107(U_3461,U_3460)))
    | ~ sP250(U_3460,U_3461) ),
    inference(clausify,[status(thm)],[f_886_4]) ).

cnf(f_886_11,plain,
    ( ~ hBOOL(hAPP(int,bool,U_3460,sK107(U_3461,U_3460)))
    | ~ sP250(U_3460,U_3461) ),
    inference(clausify,[status(thm)],[f_886_4]) ).

fof(f_887_1,plain,
    ! [K,Pa,D_1] :
      ( ! [X_2] :
          ( hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),D_1))))
          | ~ hBOOL(hAPP(int,bool,Pa,X_2)) )
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K))
      | ? [X_2] :
          ( ~ hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),D_1)))
          & hBOOL(hAPP(int,bool,Pa,X_2)) )
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1)) ),
    inference(fof_nnf,[status(thm)],[fact_816_decr__mult__lemma]) ).

fof(f_887_2,plain,
    ! [U_3466,U_3465,U_3464] :
      ( ! [U_3463] :
          ( hBOOL(hAPP(int,bool,U_3465,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3463),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3466),U_3464))))
          | ~ hBOOL(hAPP(int,bool,U_3465,U_3463)) )
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3466))
      | ? [U_3462] :
          ( ~ hBOOL(hAPP(int,bool,U_3465,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3462),U_3464)))
          & hBOOL(hAPP(int,bool,U_3465,U_3462)) )
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3464)) ),
    inference(variable_rename,[status(thm)],[f_887_1]) ).

fof(f_887_3,plain,
    ! [U_3466,U_3465,U_3464] :
      ( ! [U_3463] :
          ( hBOOL(hAPP(int,bool,U_3465,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3463),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3466),U_3464))))
          | ~ hBOOL(hAPP(int,bool,U_3465,U_3463)) )
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3466))
      | ( ~ hBOOL(hAPP(int,bool,U_3465,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),sK108(U_3466,U_3465,U_3464)),U_3464)))
        & hBOOL(hAPP(int,bool,U_3465,sK108(U_3466,U_3465,U_3464))) )
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3464)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK108]),skolemize(U_3462,sK108(U_3466,U_3465,U_3464))],[f_887_2]) ).

fof(f_887_4,plain,
    ( ! [U_3465,U_3466,U_3464] :
        ( ~ hBOOL(hAPP(int,bool,U_3465,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),sK108(U_3466,U_3465,U_3464)),U_3464)))
        | ~ sP252(U_3465,U_3466,U_3464) )
    & ! [U_3465,U_3466,U_3464] :
        ( hBOOL(hAPP(int,bool,U_3465,sK108(U_3466,U_3465,U_3464)))
        | ~ sP252(U_3465,U_3466,U_3464) )
    & ! [U_3465,U_3466,U_3463,U_3464] :
        ( hBOOL(hAPP(int,bool,U_3465,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3463),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3466),U_3464))))
        | ~ hBOOL(hAPP(int,bool,U_3465,U_3463))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3466))
        | sP252(U_3465,U_3466,U_3464)
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3464)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP252])],[f_887_3]) ).

cnf(f_887_5,plain,
    ( hBOOL(hAPP(int,bool,U_3465,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3463),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3466),U_3464))))
    | ~ hBOOL(hAPP(int,bool,U_3465,U_3463))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3466))
    | sP252(U_3465,U_3466,U_3464)
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3464)) ),
    inference(clausify,[status(thm)],[f_887_4]) ).

cnf(f_887_6,plain,
    ( hBOOL(hAPP(int,bool,U_3465,sK108(U_3466,U_3465,U_3464)))
    | ~ sP252(U_3465,U_3466,U_3464) ),
    inference(clausify,[status(thm)],[f_887_4]) ).

cnf(f_887_7,plain,
    ( ~ hBOOL(hAPP(int,bool,U_3465,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),sK108(U_3466,U_3465,U_3464)),U_3464)))
    | ~ sP252(U_3465,U_3466,U_3464) ),
    inference(clausify,[status(thm)],[f_887_4]) ).

fof(f_888_1,plain,
    ! [P_1,Pa,X_1] :
      ( ( ( ( hBOOL(Pa)
            & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) )
          | ~ hBOOL(P_1)
          | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) )
        & ( ( hBOOL(P_1)
            & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) )
          | ~ hBOOL(Pa)
          | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) ) )
      | ( ( ( ~ hBOOL(Pa)
            & hBOOL(P_1) )
          | ( ~ hBOOL(P_1)
            & hBOOL(Pa) ) )
        & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_817_conj__le__cong]) ).

fof(f_888_2,plain,
    ! [U_3469,U_3468,U_3467] :
      ( ( ( ( hBOOL(U_3468)
            & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3467)) )
          | ~ hBOOL(U_3469)
          | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3467)) )
        & ( ( hBOOL(U_3469)
            & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3467)) )
          | ~ hBOOL(U_3468)
          | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3467)) ) )
      | ( ( ( ~ hBOOL(U_3468)
            & hBOOL(U_3469) )
          | ( ~ hBOOL(U_3469)
            & hBOOL(U_3468) ) )
        & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3467)) ) ),
    inference(variable_rename,[status(thm)],[f_888_1]) ).

fof(f_888_3,plain,
    ( ! [U_3468,U_3467] :
        ( hBOOL(U_3468)
        | ~ sP257(U_3468,U_3467) )
    & ! [U_3468,U_3467] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3467))
        | ~ sP257(U_3468,U_3467) )
    & ! [U_3469,U_3467] :
        ( hBOOL(U_3469)
        | ~ sP256(U_3469,U_3467) )
    & ! [U_3469,U_3467] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3467))
        | ~ sP256(U_3469,U_3467) )
    & ! [U_3468,U_3469,U_3467] :
        ( sP257(U_3468,U_3467)
        | ~ hBOOL(U_3469)
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3467))
        | ~ sP258(U_3468,U_3469,U_3467) )
    & ! [U_3468,U_3469,U_3467] :
        ( sP256(U_3469,U_3467)
        | ~ hBOOL(U_3468)
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3467))
        | ~ sP258(U_3468,U_3469,U_3467) )
    & ! [U_3468,U_3469] :
        ( ~ hBOOL(U_3468)
        | ~ sP254(U_3468,U_3469) )
    & ! [U_3468,U_3469] :
        ( hBOOL(U_3469)
        | ~ sP254(U_3468,U_3469) )
    & ! [U_3468,U_3469] :
        ( ~ hBOOL(U_3469)
        | ~ sP253(U_3468,U_3469) )
    & ! [U_3468,U_3469] :
        ( hBOOL(U_3468)
        | ~ sP253(U_3468,U_3469) )
    & ! [U_3468,U_3469,U_3467] :
        ( sP254(U_3468,U_3469)
        | sP253(U_3468,U_3469)
        | ~ sP255(U_3468,U_3469,U_3467) )
    & ! [U_3468,U_3469,U_3467] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3467))
        | ~ sP255(U_3468,U_3469,U_3467) )
    & ! [U_3468,U_3469,U_3467] :
        ( sP258(U_3468,U_3469,U_3467)
        | sP255(U_3468,U_3469,U_3467) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP253,sP254,sP255,sP256,sP257,sP258])],[f_888_2]) ).

cnf(f_888_4,plain,
    ( sP258(U_3468,U_3469,U_3467)
    | sP255(U_3468,U_3469,U_3467) ),
    inference(clausify,[status(thm)],[f_888_3]) ).

cnf(f_888_5,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3467))
    | ~ sP255(U_3468,U_3469,U_3467) ),
    inference(clausify,[status(thm)],[f_888_3]) ).

cnf(f_888_6,plain,
    ( sP254(U_3468,U_3469)
    | sP253(U_3468,U_3469)
    | ~ sP255(U_3468,U_3469,U_3467) ),
    inference(clausify,[status(thm)],[f_888_3]) ).

cnf(f_888_7,plain,
    ( hBOOL(U_3468)
    | ~ sP253(U_3468,U_3469) ),
    inference(clausify,[status(thm)],[f_888_3]) ).

cnf(f_888_8,plain,
    ( ~ hBOOL(U_3469)
    | ~ sP253(U_3468,U_3469) ),
    inference(clausify,[status(thm)],[f_888_3]) ).

cnf(f_888_9,plain,
    ( hBOOL(U_3469)
    | ~ sP254(U_3468,U_3469) ),
    inference(clausify,[status(thm)],[f_888_3]) ).

cnf(f_888_10,plain,
    ( ~ hBOOL(U_3468)
    | ~ sP254(U_3468,U_3469) ),
    inference(clausify,[status(thm)],[f_888_3]) ).

cnf(f_888_11,plain,
    ( sP256(U_3469,U_3467)
    | ~ hBOOL(U_3468)
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3467))
    | ~ sP258(U_3468,U_3469,U_3467) ),
    inference(clausify,[status(thm)],[f_888_3]) ).

cnf(f_888_12,plain,
    ( sP257(U_3468,U_3467)
    | ~ hBOOL(U_3469)
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3467))
    | ~ sP258(U_3468,U_3469,U_3467) ),
    inference(clausify,[status(thm)],[f_888_3]) ).

cnf(f_888_13,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3467))
    | ~ sP256(U_3469,U_3467) ),
    inference(clausify,[status(thm)],[f_888_3]) ).

cnf(f_888_14,plain,
    ( hBOOL(U_3469)
    | ~ sP256(U_3469,U_3467) ),
    inference(clausify,[status(thm)],[f_888_3]) ).

cnf(f_888_15,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3467))
    | ~ sP257(U_3468,U_3467) ),
    inference(clausify,[status(thm)],[f_888_3]) ).

cnf(f_888_16,plain,
    ( hBOOL(U_3468)
    | ~ sP257(U_3468,U_3467) ),
    inference(clausify,[status(thm)],[f_888_3]) ).

fof(f_889_1,plain,
    ! [P_1,Pa,X_1] :
      ( ( ( hBOOL(Pa)
          | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1))
          | ( ~ hBOOL(P_1)
            & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) ) )
        & ( hBOOL(P_1)
          | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1))
          | ( ~ hBOOL(Pa)
            & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) ) ) )
      | ( ( ( ~ hBOOL(Pa)
            & hBOOL(P_1) )
          | ( ~ hBOOL(P_1)
            & hBOOL(Pa) ) )
        & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_818_imp__le__cong]) ).

fof(f_889_2,plain,
    ! [U_3472,U_3471,U_3470] :
      ( ( ( hBOOL(U_3471)
          | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3470))
          | ( ~ hBOOL(U_3472)
            & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3470)) ) )
        & ( hBOOL(U_3472)
          | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3470))
          | ( ~ hBOOL(U_3471)
            & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3470)) ) ) )
      | ( ( ( ~ hBOOL(U_3471)
            & hBOOL(U_3472) )
          | ( ~ hBOOL(U_3472)
            & hBOOL(U_3471) ) )
        & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3470)) ) ),
    inference(variable_rename,[status(thm)],[f_889_1]) ).

fof(f_889_3,plain,
    ( ! [U_3470,U_3472] :
        ( ~ hBOOL(U_3472)
        | ~ sP263(U_3470,U_3472) )
    & ! [U_3470,U_3472] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3470))
        | ~ sP263(U_3470,U_3472) )
    & ! [U_3471,U_3470] :
        ( ~ hBOOL(U_3471)
        | ~ sP262(U_3471,U_3470) )
    & ! [U_3471,U_3470] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3470))
        | ~ sP262(U_3471,U_3470) )
    & ! [U_3471,U_3470,U_3472] :
        ( hBOOL(U_3471)
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3470))
        | sP263(U_3470,U_3472)
        | ~ sP264(U_3471,U_3470,U_3472) )
    & ! [U_3471,U_3470,U_3472] :
        ( hBOOL(U_3472)
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3470))
        | sP262(U_3471,U_3470)
        | ~ sP264(U_3471,U_3470,U_3472) )
    & ! [U_3471,U_3472] :
        ( ~ hBOOL(U_3471)
        | ~ sP260(U_3471,U_3472) )
    & ! [U_3471,U_3472] :
        ( hBOOL(U_3472)
        | ~ sP260(U_3471,U_3472) )
    & ! [U_3471,U_3472] :
        ( ~ hBOOL(U_3472)
        | ~ sP259(U_3471,U_3472) )
    & ! [U_3471,U_3472] :
        ( hBOOL(U_3471)
        | ~ sP259(U_3471,U_3472) )
    & ! [U_3471,U_3470,U_3472] :
        ( sP260(U_3471,U_3472)
        | sP259(U_3471,U_3472)
        | ~ sP261(U_3471,U_3470,U_3472) )
    & ! [U_3471,U_3470,U_3472] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3470))
        | ~ sP261(U_3471,U_3470,U_3472) )
    & ! [U_3471,U_3470,U_3472] :
        ( sP264(U_3471,U_3470,U_3472)
        | sP261(U_3471,U_3470,U_3472) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP259,sP260,sP261,sP262,sP263,sP264])],[f_889_2]) ).

cnf(f_889_4,plain,
    ( sP264(U_3471,U_3470,U_3472)
    | sP261(U_3471,U_3470,U_3472) ),
    inference(clausify,[status(thm)],[f_889_3]) ).

cnf(f_889_5,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3470))
    | ~ sP261(U_3471,U_3470,U_3472) ),
    inference(clausify,[status(thm)],[f_889_3]) ).

cnf(f_889_6,plain,
    ( sP260(U_3471,U_3472)
    | sP259(U_3471,U_3472)
    | ~ sP261(U_3471,U_3470,U_3472) ),
    inference(clausify,[status(thm)],[f_889_3]) ).

cnf(f_889_7,plain,
    ( hBOOL(U_3471)
    | ~ sP259(U_3471,U_3472) ),
    inference(clausify,[status(thm)],[f_889_3]) ).

cnf(f_889_8,plain,
    ( ~ hBOOL(U_3472)
    | ~ sP259(U_3471,U_3472) ),
    inference(clausify,[status(thm)],[f_889_3]) ).

cnf(f_889_9,plain,
    ( hBOOL(U_3472)
    | ~ sP260(U_3471,U_3472) ),
    inference(clausify,[status(thm)],[f_889_3]) ).

cnf(f_889_10,plain,
    ( ~ hBOOL(U_3471)
    | ~ sP260(U_3471,U_3472) ),
    inference(clausify,[status(thm)],[f_889_3]) ).

cnf(f_889_11,plain,
    ( hBOOL(U_3472)
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3470))
    | sP262(U_3471,U_3470)
    | ~ sP264(U_3471,U_3470,U_3472) ),
    inference(clausify,[status(thm)],[f_889_3]) ).

cnf(f_889_12,plain,
    ( hBOOL(U_3471)
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3470))
    | sP263(U_3470,U_3472)
    | ~ sP264(U_3471,U_3470,U_3472) ),
    inference(clausify,[status(thm)],[f_889_3]) ).

cnf(f_889_13,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3470))
    | ~ sP262(U_3471,U_3470) ),
    inference(clausify,[status(thm)],[f_889_3]) ).

cnf(f_889_14,plain,
    ( ~ hBOOL(U_3471)
    | ~ sP262(U_3471,U_3470) ),
    inference(clausify,[status(thm)],[f_889_3]) ).

cnf(f_889_15,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3470))
    | ~ sP263(U_3470,U_3472) ),
    inference(clausify,[status(thm)],[f_889_3]) ).

cnf(f_889_16,plain,
    ( ~ hBOOL(U_3472)
    | ~ sP263(U_3470,U_3472) ),
    inference(clausify,[status(thm)],[f_889_3]) ).

fof(f_890_1,plain,
    ! [K,Pa,D_1] :
      ( ! [X_2] :
          ( hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),D_1))))
          | ~ hBOOL(hAPP(int,bool,Pa,X_2)) )
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K))
      | ? [X_2] :
          ( ~ hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),D_1)))
          & hBOOL(hAPP(int,bool,Pa,X_2)) )
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1)) ),
    inference(fof_nnf,[status(thm)],[fact_819_incr__mult__lemma]) ).

fof(f_890_2,plain,
    ! [U_3477,U_3476,U_3475] :
      ( ! [U_3474] :
          ( hBOOL(hAPP(int,bool,U_3476,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3474),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3477),U_3475))))
          | ~ hBOOL(hAPP(int,bool,U_3476,U_3474)) )
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3477))
      | ? [U_3473] :
          ( ~ hBOOL(hAPP(int,bool,U_3476,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3473),U_3475)))
          & hBOOL(hAPP(int,bool,U_3476,U_3473)) )
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3475)) ),
    inference(variable_rename,[status(thm)],[f_890_1]) ).

fof(f_890_3,plain,
    ! [U_3477,U_3476,U_3475] :
      ( ! [U_3474] :
          ( hBOOL(hAPP(int,bool,U_3476,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3474),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3477),U_3475))))
          | ~ hBOOL(hAPP(int,bool,U_3476,U_3474)) )
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3477))
      | ( ~ hBOOL(hAPP(int,bool,U_3476,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),sK109(U_3477,U_3476,U_3475)),U_3475)))
        & hBOOL(hAPP(int,bool,U_3476,sK109(U_3477,U_3476,U_3475))) )
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3475)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK109]),skolemize(U_3473,sK109(U_3477,U_3476,U_3475))],[f_890_2]) ).

fof(f_890_4,plain,
    ( ! [U_3476,U_3475,U_3477] :
        ( ~ hBOOL(hAPP(int,bool,U_3476,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),sK109(U_3477,U_3476,U_3475)),U_3475)))
        | ~ sP265(U_3476,U_3475,U_3477) )
    & ! [U_3476,U_3475,U_3477] :
        ( hBOOL(hAPP(int,bool,U_3476,sK109(U_3477,U_3476,U_3475)))
        | ~ sP265(U_3476,U_3475,U_3477) )
    & ! [U_3476,U_3475,U_3477,U_3474] :
        ( hBOOL(hAPP(int,bool,U_3476,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3474),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3477),U_3475))))
        | ~ hBOOL(hAPP(int,bool,U_3476,U_3474))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3477))
        | sP265(U_3476,U_3475,U_3477)
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3475)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP265])],[f_890_3]) ).

cnf(f_890_5,plain,
    ( hBOOL(hAPP(int,bool,U_3476,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3474),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3477),U_3475))))
    | ~ hBOOL(hAPP(int,bool,U_3476,U_3474))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3477))
    | sP265(U_3476,U_3475,U_3477)
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3475)) ),
    inference(clausify,[status(thm)],[f_890_4]) ).

cnf(f_890_6,plain,
    ( hBOOL(hAPP(int,bool,U_3476,sK109(U_3477,U_3476,U_3475)))
    | ~ sP265(U_3476,U_3475,U_3477) ),
    inference(clausify,[status(thm)],[f_890_4]) ).

cnf(f_890_7,plain,
    ( ~ hBOOL(hAPP(int,bool,U_3476,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),sK109(U_3477,U_3476,U_3475)),U_3475)))
    | ~ sP265(U_3476,U_3475,U_3477) ),
    inference(clausify,[status(thm)],[f_890_4]) ).

fof(f_891_1,plain,
    ! [X_a] :
      ( ! [T_4] :
        ? [Z_3] :
        ! [X_2] :
          ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),T_4),X_2))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Z_3)) )
      | ~ linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_820_minf_I8_J]) ).

fof(f_891_2,plain,
    ! [U_3481] :
      ( ! [U_3480] :
        ? [U_3479] :
        ! [U_3478] :
          ( ~ hBOOL(hAPP(U_3481,bool,hAPP(U_3481,fun(U_3481,bool),ord_less_eq(U_3481),U_3480),U_3478))
          | ~ hBOOL(hAPP(U_3481,bool,hAPP(U_3481,fun(U_3481,bool),ord_less(U_3481),U_3478),U_3479)) )
      | ~ linorder(U_3481) ),
    inference(variable_rename,[status(thm)],[f_891_1]) ).

fof(f_891_3,plain,
    ! [U_3481] :
      ( ! [U_3480,U_3478] :
          ( ~ hBOOL(hAPP(U_3481,bool,hAPP(U_3481,fun(U_3481,bool),ord_less_eq(U_3481),U_3480),U_3478))
          | ~ hBOOL(hAPP(U_3481,bool,hAPP(U_3481,fun(U_3481,bool),ord_less(U_3481),U_3478),sK110(U_3481,U_3480))) )
      | ~ linorder(U_3481) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK110]),skolemize(U_3479,sK110(U_3481,U_3480))],[f_891_2]) ).

fof(f_891_4,plain,
    ! [U_3481,U_3480,U_3478] :
      ( ~ hBOOL(hAPP(U_3481,bool,hAPP(U_3481,fun(U_3481,bool),ord_less_eq(U_3481),U_3480),U_3478))
      | ~ hBOOL(hAPP(U_3481,bool,hAPP(U_3481,fun(U_3481,bool),ord_less(U_3481),U_3478),sK110(U_3481,U_3480)))
      | ~ linorder(U_3481) ),
    inference(definitional_conversion,[status(esa)],[f_891_3]) ).

cnf(f_891_5,plain,
    ( ~ hBOOL(hAPP(U_3481,bool,hAPP(U_3481,fun(U_3481,bool),ord_less_eq(U_3481),U_3480),U_3478))
    | ~ hBOOL(hAPP(U_3481,bool,hAPP(U_3481,fun(U_3481,bool),ord_less(U_3481),U_3478),sK110(U_3481,U_3480)))
    | ~ linorder(U_3481) ),
    inference(clausify,[status(thm)],[f_891_4]) ).

fof(f_892_1,plain,
    ! [X_a] :
      ( ! [T_4] :
        ? [Z_3] :
        ! [X_2] :
          ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),T_4))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_3),X_2)) )
      | ~ linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_821_pinf_I6_J]) ).

fof(f_892_2,plain,
    ! [U_3485] :
      ( ! [U_3484] :
        ? [U_3483] :
        ! [U_3482] :
          ( ~ hBOOL(hAPP(U_3485,bool,hAPP(U_3485,fun(U_3485,bool),ord_less_eq(U_3485),U_3482),U_3484))
          | ~ hBOOL(hAPP(U_3485,bool,hAPP(U_3485,fun(U_3485,bool),ord_less(U_3485),U_3483),U_3482)) )
      | ~ linorder(U_3485) ),
    inference(variable_rename,[status(thm)],[f_892_1]) ).

fof(f_892_3,plain,
    ! [U_3485] :
      ( ! [U_3484,U_3482] :
          ( ~ hBOOL(hAPP(U_3485,bool,hAPP(U_3485,fun(U_3485,bool),ord_less_eq(U_3485),U_3482),U_3484))
          | ~ hBOOL(hAPP(U_3485,bool,hAPP(U_3485,fun(U_3485,bool),ord_less(U_3485),sK111(U_3485,U_3484)),U_3482)) )
      | ~ linorder(U_3485) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK111]),skolemize(U_3483,sK111(U_3485,U_3484))],[f_892_2]) ).

fof(f_892_4,plain,
    ! [U_3482,U_3485,U_3484] :
      ( ~ hBOOL(hAPP(U_3485,bool,hAPP(U_3485,fun(U_3485,bool),ord_less_eq(U_3485),U_3482),U_3484))
      | ~ hBOOL(hAPP(U_3485,bool,hAPP(U_3485,fun(U_3485,bool),ord_less(U_3485),sK111(U_3485,U_3484)),U_3482))
      | ~ linorder(U_3485) ),
    inference(definitional_conversion,[status(esa)],[f_892_3]) ).

cnf(f_892_5,plain,
    ( ~ hBOOL(hAPP(U_3485,bool,hAPP(U_3485,fun(U_3485,bool),ord_less_eq(U_3485),U_3482),U_3484))
    | ~ hBOOL(hAPP(U_3485,bool,hAPP(U_3485,fun(U_3485,bool),ord_less(U_3485),sK111(U_3485,U_3484)),U_3482))
    | ~ linorder(U_3485) ),
    inference(clausify,[status(thm)],[f_892_4]) ).

fof(f_893_1,plain,
    ! [X_a] :
      ( ! [T_4] :
        ? [Z_3] :
        ! [X_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),T_4))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Z_3)) )
      | ~ linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_822_minf_I6_J]) ).

fof(f_893_2,plain,
    ! [U_3489] :
      ( ! [U_3488] :
        ? [U_3487] :
        ! [U_3486] :
          ( hBOOL(hAPP(U_3489,bool,hAPP(U_3489,fun(U_3489,bool),ord_less_eq(U_3489),U_3486),U_3488))
          | ~ hBOOL(hAPP(U_3489,bool,hAPP(U_3489,fun(U_3489,bool),ord_less(U_3489),U_3486),U_3487)) )
      | ~ linorder(U_3489) ),
    inference(variable_rename,[status(thm)],[f_893_1]) ).

fof(f_893_3,plain,
    ! [U_3489] :
      ( ! [U_3488,U_3486] :
          ( hBOOL(hAPP(U_3489,bool,hAPP(U_3489,fun(U_3489,bool),ord_less_eq(U_3489),U_3486),U_3488))
          | ~ hBOOL(hAPP(U_3489,bool,hAPP(U_3489,fun(U_3489,bool),ord_less(U_3489),U_3486),sK112(U_3489,U_3488))) )
      | ~ linorder(U_3489) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK112]),skolemize(U_3487,sK112(U_3489,U_3488))],[f_893_2]) ).

fof(f_893_4,plain,
    ! [U_3489,U_3486,U_3488] :
      ( hBOOL(hAPP(U_3489,bool,hAPP(U_3489,fun(U_3489,bool),ord_less_eq(U_3489),U_3486),U_3488))
      | ~ hBOOL(hAPP(U_3489,bool,hAPP(U_3489,fun(U_3489,bool),ord_less(U_3489),U_3486),sK112(U_3489,U_3488)))
      | ~ linorder(U_3489) ),
    inference(definitional_conversion,[status(esa)],[f_893_3]) ).

cnf(f_893_5,plain,
    ( hBOOL(hAPP(U_3489,bool,hAPP(U_3489,fun(U_3489,bool),ord_less_eq(U_3489),U_3486),U_3488))
    | ~ hBOOL(hAPP(U_3489,bool,hAPP(U_3489,fun(U_3489,bool),ord_less(U_3489),U_3486),sK112(U_3489,U_3488)))
    | ~ linorder(U_3489) ),
    inference(clausify,[status(thm)],[f_893_4]) ).

fof(f_894_1,plain,
    ! [X_a] :
      ( ! [T_4] :
        ? [Z_3] :
        ! [X_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),T_4),X_2))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_3),X_2)) )
      | ~ linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_823_pinf_I8_J]) ).

fof(f_894_2,plain,
    ! [U_3493] :
      ( ! [U_3492] :
        ? [U_3491] :
        ! [U_3490] :
          ( hBOOL(hAPP(U_3493,bool,hAPP(U_3493,fun(U_3493,bool),ord_less_eq(U_3493),U_3492),U_3490))
          | ~ hBOOL(hAPP(U_3493,bool,hAPP(U_3493,fun(U_3493,bool),ord_less(U_3493),U_3491),U_3490)) )
      | ~ linorder(U_3493) ),
    inference(variable_rename,[status(thm)],[f_894_1]) ).

fof(f_894_3,plain,
    ! [U_3493] :
      ( ! [U_3492,U_3490] :
          ( hBOOL(hAPP(U_3493,bool,hAPP(U_3493,fun(U_3493,bool),ord_less_eq(U_3493),U_3492),U_3490))
          | ~ hBOOL(hAPP(U_3493,bool,hAPP(U_3493,fun(U_3493,bool),ord_less(U_3493),sK113(U_3493,U_3492)),U_3490)) )
      | ~ linorder(U_3493) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK113]),skolemize(U_3491,sK113(U_3493,U_3492))],[f_894_2]) ).

fof(f_894_4,plain,
    ! [U_3490,U_3493,U_3492] :
      ( hBOOL(hAPP(U_3493,bool,hAPP(U_3493,fun(U_3493,bool),ord_less_eq(U_3493),U_3492),U_3490))
      | ~ hBOOL(hAPP(U_3493,bool,hAPP(U_3493,fun(U_3493,bool),ord_less(U_3493),sK113(U_3493,U_3492)),U_3490))
      | ~ linorder(U_3493) ),
    inference(definitional_conversion,[status(esa)],[f_894_3]) ).

cnf(f_894_5,plain,
    ( hBOOL(hAPP(U_3493,bool,hAPP(U_3493,fun(U_3493,bool),ord_less_eq(U_3493),U_3492),U_3490))
    | ~ hBOOL(hAPP(U_3493,bool,hAPP(U_3493,fun(U_3493,bool),ord_less(U_3493),sK113(U_3493,U_3492)),U_3490))
    | ~ linorder(U_3493) ),
    inference(clausify,[status(thm)],[f_894_4]) ).

fof(f_895_1,plain,
    ! [I_1,Pa,K] :
      ( hBOOL(hAPP(int,bool,Pa,I_1))
      | ? [I] :
          ( ~ hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),I),one_one(int))))
          & hBOOL(hAPP(int,bool,Pa,I))
          & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I),K)) )
      | ? [I] :
          ( ~ hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I),one_one(int))))
          & hBOOL(hAPP(int,bool,Pa,I))
          & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),I)) )
      | ~ hBOOL(hAPP(int,bool,Pa,K)) ),
    inference(fof_nnf,[status(thm)],[fact_824_int__induct]) ).

fof(f_895_2,plain,
    ! [U_3498,U_3497,U_3496] :
      ( hBOOL(hAPP(int,bool,U_3497,U_3498))
      | ? [U_3495] :
          ( ~ hBOOL(hAPP(int,bool,U_3497,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3495),one_one(int))))
          & hBOOL(hAPP(int,bool,U_3497,U_3495))
          & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3495),U_3496)) )
      | ? [U_3494] :
          ( ~ hBOOL(hAPP(int,bool,U_3497,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3494),one_one(int))))
          & hBOOL(hAPP(int,bool,U_3497,U_3494))
          & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3496),U_3494)) )
      | ~ hBOOL(hAPP(int,bool,U_3497,U_3496)) ),
    inference(variable_rename,[status(thm)],[f_895_1]) ).

fof(f_895_3,plain,
    ! [U_3498,U_3497,U_3496] :
      ( hBOOL(hAPP(int,bool,U_3497,U_3498))
      | ? [U_3495] :
          ( ~ hBOOL(hAPP(int,bool,U_3497,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3495),one_one(int))))
          & hBOOL(hAPP(int,bool,U_3497,U_3495))
          & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3495),U_3496)) )
      | ( ~ hBOOL(hAPP(int,bool,U_3497,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),sK114(U_3498,U_3497,U_3496)),one_one(int))))
        & hBOOL(hAPP(int,bool,U_3497,sK114(U_3498,U_3497,U_3496)))
        & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3496),sK114(U_3498,U_3497,U_3496))) )
      | ~ hBOOL(hAPP(int,bool,U_3497,U_3496)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK114]),skolemize(U_3494,sK114(U_3498,U_3497,U_3496))],[f_895_2]) ).

fof(f_895_4,plain,
    ! [U_3498,U_3497,U_3496] :
      ( hBOOL(hAPP(int,bool,U_3497,U_3498))
      | ( ~ hBOOL(hAPP(int,bool,U_3497,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),sK115(U_3498,U_3497,U_3496)),one_one(int))))
        & hBOOL(hAPP(int,bool,U_3497,sK115(U_3498,U_3497,U_3496)))
        & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),sK115(U_3498,U_3497,U_3496)),U_3496)) )
      | ( ~ hBOOL(hAPP(int,bool,U_3497,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),sK114(U_3498,U_3497,U_3496)),one_one(int))))
        & hBOOL(hAPP(int,bool,U_3497,sK114(U_3498,U_3497,U_3496)))
        & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3496),sK114(U_3498,U_3497,U_3496))) )
      | ~ hBOOL(hAPP(int,bool,U_3497,U_3496)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK115]),skolemize(U_3495,sK115(U_3498,U_3497,U_3496))],[f_895_3]) ).

fof(f_895_5,plain,
    ( ! [U_3496,U_3497,U_3498] :
        ( ~ hBOOL(hAPP(int,bool,U_3497,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),sK115(U_3498,U_3497,U_3496)),one_one(int))))
        | ~ sP267(U_3496,U_3497,U_3498) )
    & ! [U_3496,U_3497,U_3498] :
        ( hBOOL(hAPP(int,bool,U_3497,sK115(U_3498,U_3497,U_3496)))
        | ~ sP267(U_3496,U_3497,U_3498) )
    & ! [U_3496,U_3497,U_3498] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),sK115(U_3498,U_3497,U_3496)),U_3496))
        | ~ sP267(U_3496,U_3497,U_3498) )
    & ! [U_3496,U_3497,U_3498] :
        ( ~ hBOOL(hAPP(int,bool,U_3497,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),sK114(U_3498,U_3497,U_3496)),one_one(int))))
        | ~ sP266(U_3496,U_3497,U_3498) )
    & ! [U_3496,U_3497,U_3498] :
        ( hBOOL(hAPP(int,bool,U_3497,sK114(U_3498,U_3497,U_3496)))
        | ~ sP266(U_3496,U_3497,U_3498) )
    & ! [U_3496,U_3497,U_3498] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3496),sK114(U_3498,U_3497,U_3496)))
        | ~ sP266(U_3496,U_3497,U_3498) )
    & ! [U_3496,U_3497,U_3498] :
        ( hBOOL(hAPP(int,bool,U_3497,U_3498))
        | sP267(U_3496,U_3497,U_3498)
        | sP266(U_3496,U_3497,U_3498)
        | ~ hBOOL(hAPP(int,bool,U_3497,U_3496)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP266,sP267])],[f_895_4]) ).

cnf(f_895_6,plain,
    ( hBOOL(hAPP(int,bool,U_3497,U_3498))
    | sP267(U_3496,U_3497,U_3498)
    | sP266(U_3496,U_3497,U_3498)
    | ~ hBOOL(hAPP(int,bool,U_3497,U_3496)) ),
    inference(clausify,[status(thm)],[f_895_5]) ).

cnf(f_895_7,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3496),sK114(U_3498,U_3497,U_3496)))
    | ~ sP266(U_3496,U_3497,U_3498) ),
    inference(clausify,[status(thm)],[f_895_5]) ).

cnf(f_895_8,plain,
    ( hBOOL(hAPP(int,bool,U_3497,sK114(U_3498,U_3497,U_3496)))
    | ~ sP266(U_3496,U_3497,U_3498) ),
    inference(clausify,[status(thm)],[f_895_5]) ).

cnf(f_895_9,plain,
    ( ~ hBOOL(hAPP(int,bool,U_3497,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),sK114(U_3498,U_3497,U_3496)),one_one(int))))
    | ~ sP266(U_3496,U_3497,U_3498) ),
    inference(clausify,[status(thm)],[f_895_5]) ).

cnf(f_895_10,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),sK115(U_3498,U_3497,U_3496)),U_3496))
    | ~ sP267(U_3496,U_3497,U_3498) ),
    inference(clausify,[status(thm)],[f_895_5]) ).

cnf(f_895_11,plain,
    ( hBOOL(hAPP(int,bool,U_3497,sK115(U_3498,U_3497,U_3496)))
    | ~ sP267(U_3496,U_3497,U_3498) ),
    inference(clausify,[status(thm)],[f_895_5]) ).

cnf(f_895_12,plain,
    ( ~ hBOOL(hAPP(int,bool,U_3497,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),sK115(U_3498,U_3497,U_3496)),one_one(int))))
    | ~ sP267(U_3496,U_3497,U_3498) ),
    inference(clausify,[status(thm)],[f_895_5]) ).

fof(f_896_1,plain,
    ! [Pa,P1,D_1] :
      ( ? [X1] : hBOOL(hAPP(int,bool,Pa,X1))
      | ! [X1] : ~ hBOOL(hAPP(int,bool,P1,X1))
      | ! [Z_3] :
        ? [X_2] :
          ( ( ( ~ hBOOL(hAPP(int,bool,Pa,X_2))
              & hBOOL(hAPP(int,bool,P1,X_2)) )
            | ( ~ hBOOL(hAPP(int,bool,P1,X_2))
              & hBOOL(hAPP(int,bool,Pa,X_2)) ) )
          & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_2),Z_3)) )
      | ? [X_2,K_2] :
          ( ( ~ hBOOL(hAPP(int,bool,P1,X_2))
            & hBOOL(hAPP(int,bool,P1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_2),D_1)))) )
          | ( ~ hBOOL(hAPP(int,bool,P1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_2),D_1))))
            & hBOOL(hAPP(int,bool,P1,X_2)) ) )
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1)) ),
    inference(fof_nnf,[status(thm)],[fact_825_minusinfinity]) ).

fof(f_896_2,plain,
    ! [U_3507,U_3506,U_3505] :
      ( ? [U_3504] : hBOOL(hAPP(int,bool,U_3507,U_3504))
      | ! [U_3503] : ~ hBOOL(hAPP(int,bool,U_3506,U_3503))
      | ! [U_3502] :
        ? [U_3501] :
          ( ( ( ~ hBOOL(hAPP(int,bool,U_3507,U_3501))
              & hBOOL(hAPP(int,bool,U_3506,U_3501)) )
            | ( ~ hBOOL(hAPP(int,bool,U_3506,U_3501))
              & hBOOL(hAPP(int,bool,U_3507,U_3501)) ) )
          & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3501),U_3502)) )
      | ? [U_3500,U_3499] :
          ( ( ~ hBOOL(hAPP(int,bool,U_3506,U_3500))
            & hBOOL(hAPP(int,bool,U_3506,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3500),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3499),U_3505)))) )
          | ( ~ hBOOL(hAPP(int,bool,U_3506,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3500),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3499),U_3505))))
            & hBOOL(hAPP(int,bool,U_3506,U_3500)) ) )
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3505)) ),
    inference(variable_rename,[status(thm)],[f_896_1]) ).

fof(f_896_3,plain,
    ! [U_3507,U_3506,U_3505] :
      ( ? [U_3504] : hBOOL(hAPP(int,bool,U_3507,U_3504))
      | ! [U_3503] : ~ hBOOL(hAPP(int,bool,U_3506,U_3503))
      | ! [U_3502] :
        ? [U_3501] :
          ( ( ( ~ hBOOL(hAPP(int,bool,U_3507,U_3501))
              & hBOOL(hAPP(int,bool,U_3506,U_3501)) )
            | ( ~ hBOOL(hAPP(int,bool,U_3506,U_3501))
              & hBOOL(hAPP(int,bool,U_3507,U_3501)) ) )
          & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3501),U_3502)) )
      | ? [U_3511] :
          ( ? [U_3509] : hBOOL(hAPP(int,bool,U_3506,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3511),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3509),U_3505))))
          & ~ hBOOL(hAPP(int,bool,U_3506,U_3511)) )
      | ? [U_3510] :
          ( ? [U_3508] : ~ hBOOL(hAPP(int,bool,U_3506,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3510),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3508),U_3505))))
          & hBOOL(hAPP(int,bool,U_3506,U_3510)) )
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3505)) ),
    inference(miniscope,[status(thm)],[f_896_2]) ).

fof(f_896_4,plain,
    ! [U_3507,U_3506,U_3505] :
      ( ? [U_3504] : hBOOL(hAPP(int,bool,U_3507,U_3504))
      | ! [U_3503] : ~ hBOOL(hAPP(int,bool,U_3506,U_3503))
      | ! [U_3502] :
        ? [U_3501] :
          ( ( ( ~ hBOOL(hAPP(int,bool,U_3507,U_3501))
              & hBOOL(hAPP(int,bool,U_3506,U_3501)) )
            | ( ~ hBOOL(hAPP(int,bool,U_3506,U_3501))
              & hBOOL(hAPP(int,bool,U_3507,U_3501)) ) )
          & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3501),U_3502)) )
      | ? [U_3511] :
          ( ? [U_3509] : hBOOL(hAPP(int,bool,U_3506,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3511),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3509),U_3505))))
          & ~ hBOOL(hAPP(int,bool,U_3506,U_3511)) )
      | ( ? [U_3508] : ~ hBOOL(hAPP(int,bool,U_3506,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),sK116(U_3507,U_3506,U_3505)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3508),U_3505))))
        & hBOOL(hAPP(int,bool,U_3506,sK116(U_3507,U_3506,U_3505))) )
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3505)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK116]),skolemize(U_3510,sK116(U_3507,U_3506,U_3505))],[f_896_3]) ).

fof(f_896_5,plain,
    ! [U_3507,U_3506,U_3505] :
      ( ? [U_3504] : hBOOL(hAPP(int,bool,U_3507,U_3504))
      | ! [U_3503] : ~ hBOOL(hAPP(int,bool,U_3506,U_3503))
      | ! [U_3502] :
        ? [U_3501] :
          ( ( ( ~ hBOOL(hAPP(int,bool,U_3507,U_3501))
              & hBOOL(hAPP(int,bool,U_3506,U_3501)) )
            | ( ~ hBOOL(hAPP(int,bool,U_3506,U_3501))
              & hBOOL(hAPP(int,bool,U_3507,U_3501)) ) )
          & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3501),U_3502)) )
      | ? [U_3511] :
          ( ? [U_3509] : hBOOL(hAPP(int,bool,U_3506,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3511),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3509),U_3505))))
          & ~ hBOOL(hAPP(int,bool,U_3506,U_3511)) )
      | ( ~ hBOOL(hAPP(int,bool,U_3506,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),sK116(U_3507,U_3506,U_3505)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),sK117(U_3507,U_3506,U_3505)),U_3505))))
        & hBOOL(hAPP(int,bool,U_3506,sK116(U_3507,U_3506,U_3505))) )
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3505)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK117]),skolemize(U_3508,sK117(U_3507,U_3506,U_3505))],[f_896_4]) ).

fof(f_896_6,plain,
    ! [U_3507,U_3506,U_3505] :
      ( ? [U_3504] : hBOOL(hAPP(int,bool,U_3507,U_3504))
      | ! [U_3503] : ~ hBOOL(hAPP(int,bool,U_3506,U_3503))
      | ! [U_3502] :
        ? [U_3501] :
          ( ( ( ~ hBOOL(hAPP(int,bool,U_3507,U_3501))
              & hBOOL(hAPP(int,bool,U_3506,U_3501)) )
            | ( ~ hBOOL(hAPP(int,bool,U_3506,U_3501))
              & hBOOL(hAPP(int,bool,U_3507,U_3501)) ) )
          & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3501),U_3502)) )
      | ( ? [U_3509] : hBOOL(hAPP(int,bool,U_3506,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),sK118(U_3507,U_3506,U_3505)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3509),U_3505))))
        & ~ hBOOL(hAPP(int,bool,U_3506,sK118(U_3507,U_3506,U_3505))) )
      | ( ~ hBOOL(hAPP(int,bool,U_3506,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),sK116(U_3507,U_3506,U_3505)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),sK117(U_3507,U_3506,U_3505)),U_3505))))
        & hBOOL(hAPP(int,bool,U_3506,sK116(U_3507,U_3506,U_3505))) )
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3505)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK118]),skolemize(U_3511,sK118(U_3507,U_3506,U_3505))],[f_896_5]) ).

fof(f_896_7,plain,
    ! [U_3507,U_3506,U_3505] :
      ( ? [U_3504] : hBOOL(hAPP(int,bool,U_3507,U_3504))
      | ! [U_3503] : ~ hBOOL(hAPP(int,bool,U_3506,U_3503))
      | ! [U_3502] :
        ? [U_3501] :
          ( ( ( ~ hBOOL(hAPP(int,bool,U_3507,U_3501))
              & hBOOL(hAPP(int,bool,U_3506,U_3501)) )
            | ( ~ hBOOL(hAPP(int,bool,U_3506,U_3501))
              & hBOOL(hAPP(int,bool,U_3507,U_3501)) ) )
          & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3501),U_3502)) )
      | ( hBOOL(hAPP(int,bool,U_3506,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),sK118(U_3507,U_3506,U_3505)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),sK119(U_3507,U_3506,U_3505)),U_3505))))
        & ~ hBOOL(hAPP(int,bool,U_3506,sK118(U_3507,U_3506,U_3505))) )
      | ( ~ hBOOL(hAPP(int,bool,U_3506,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),sK116(U_3507,U_3506,U_3505)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),sK117(U_3507,U_3506,U_3505)),U_3505))))
        & hBOOL(hAPP(int,bool,U_3506,sK116(U_3507,U_3506,U_3505))) )
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3505)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK119]),skolemize(U_3509,sK119(U_3507,U_3506,U_3505))],[f_896_6]) ).

fof(f_896_8,plain,
    ! [U_3507,U_3506,U_3505] :
      ( ? [U_3504] : hBOOL(hAPP(int,bool,U_3507,U_3504))
      | ! [U_3503] : ~ hBOOL(hAPP(int,bool,U_3506,U_3503))
      | ! [U_3502] :
          ( ( ( ~ hBOOL(hAPP(int,bool,U_3507,sK120(U_3507,U_3506,U_3505,U_3502)))
              & hBOOL(hAPP(int,bool,U_3506,sK120(U_3507,U_3506,U_3505,U_3502))) )
            | ( ~ hBOOL(hAPP(int,bool,U_3506,sK120(U_3507,U_3506,U_3505,U_3502)))
              & hBOOL(hAPP(int,bool,U_3507,sK120(U_3507,U_3506,U_3505,U_3502))) ) )
          & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),sK120(U_3507,U_3506,U_3505,U_3502)),U_3502)) )
      | ( hBOOL(hAPP(int,bool,U_3506,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),sK118(U_3507,U_3506,U_3505)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),sK119(U_3507,U_3506,U_3505)),U_3505))))
        & ~ hBOOL(hAPP(int,bool,U_3506,sK118(U_3507,U_3506,U_3505))) )
      | ( ~ hBOOL(hAPP(int,bool,U_3506,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),sK116(U_3507,U_3506,U_3505)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),sK117(U_3507,U_3506,U_3505)),U_3505))))
        & hBOOL(hAPP(int,bool,U_3506,sK116(U_3507,U_3506,U_3505))) )
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3505)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK120]),skolemize(U_3501,sK120(U_3507,U_3506,U_3505,U_3502))],[f_896_7]) ).

fof(f_896_9,plain,
    ! [U_3507,U_3506,U_3505] :
      ( hBOOL(hAPP(int,bool,U_3507,sK121(U_3507,U_3506,U_3505)))
      | ! [U_3503] : ~ hBOOL(hAPP(int,bool,U_3506,U_3503))
      | ! [U_3502] :
          ( ( ( ~ hBOOL(hAPP(int,bool,U_3507,sK120(U_3507,U_3506,U_3505,U_3502)))
              & hBOOL(hAPP(int,bool,U_3506,sK120(U_3507,U_3506,U_3505,U_3502))) )
            | ( ~ hBOOL(hAPP(int,bool,U_3506,sK120(U_3507,U_3506,U_3505,U_3502)))
              & hBOOL(hAPP(int,bool,U_3507,sK120(U_3507,U_3506,U_3505,U_3502))) ) )
          & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),sK120(U_3507,U_3506,U_3505,U_3502)),U_3502)) )
      | ( hBOOL(hAPP(int,bool,U_3506,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),sK118(U_3507,U_3506,U_3505)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),sK119(U_3507,U_3506,U_3505)),U_3505))))
        & ~ hBOOL(hAPP(int,bool,U_3506,sK118(U_3507,U_3506,U_3505))) )
      | ( ~ hBOOL(hAPP(int,bool,U_3506,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),sK116(U_3507,U_3506,U_3505)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),sK117(U_3507,U_3506,U_3505)),U_3505))))
        & hBOOL(hAPP(int,bool,U_3506,sK116(U_3507,U_3506,U_3505))) )
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3505)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK121]),skolemize(U_3504,sK121(U_3507,U_3506,U_3505))],[f_896_8]) ).

fof(f_896_10,plain,
    ( ! [U_3506,U_3502,U_3505,U_3507] :
        ( ~ hBOOL(hAPP(int,bool,U_3507,sK120(U_3507,U_3506,U_3505,U_3502)))
        | ~ sP271(U_3506,U_3502,U_3505,U_3507) )
    & ! [U_3506,U_3502,U_3505,U_3507] :
        ( hBOOL(hAPP(int,bool,U_3506,sK120(U_3507,U_3506,U_3505,U_3502)))
        | ~ sP271(U_3506,U_3502,U_3505,U_3507) )
    & ! [U_3506,U_3502,U_3505,U_3507] :
        ( ~ hBOOL(hAPP(int,bool,U_3506,sK120(U_3507,U_3506,U_3505,U_3502)))
        | ~ sP270(U_3506,U_3502,U_3505,U_3507) )
    & ! [U_3506,U_3502,U_3505,U_3507] :
        ( hBOOL(hAPP(int,bool,U_3507,sK120(U_3507,U_3506,U_3505,U_3502)))
        | ~ sP270(U_3506,U_3502,U_3505,U_3507) )
    & ! [U_3506,U_3502,U_3505,U_3507] :
        ( sP271(U_3506,U_3502,U_3505,U_3507)
        | sP270(U_3506,U_3502,U_3505,U_3507)
        | ~ sP272(U_3506,U_3502,U_3505,U_3507) )
    & ! [U_3506,U_3502,U_3505,U_3507] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),sK120(U_3507,U_3506,U_3505,U_3502)),U_3502))
        | ~ sP272(U_3506,U_3502,U_3505,U_3507) )
    & ! [U_3506,U_3505,U_3507] :
        ( hBOOL(hAPP(int,bool,U_3506,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),sK118(U_3507,U_3506,U_3505)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),sK119(U_3507,U_3506,U_3505)),U_3505))))
        | ~ sP269(U_3506,U_3505,U_3507) )
    & ! [U_3506,U_3505,U_3507] :
        ( ~ hBOOL(hAPP(int,bool,U_3506,sK118(U_3507,U_3506,U_3505)))
        | ~ sP269(U_3506,U_3505,U_3507) )
    & ! [U_3506,U_3505,U_3507] :
        ( ~ hBOOL(hAPP(int,bool,U_3506,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),sK116(U_3507,U_3506,U_3505)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),sK117(U_3507,U_3506,U_3505)),U_3505))))
        | ~ sP268(U_3506,U_3505,U_3507) )
    & ! [U_3506,U_3505,U_3507] :
        ( hBOOL(hAPP(int,bool,U_3506,sK116(U_3507,U_3506,U_3505)))
        | ~ sP268(U_3506,U_3505,U_3507) )
    & ! [U_3503,U_3506,U_3502,U_3505,U_3507] :
        ( hBOOL(hAPP(int,bool,U_3507,sK121(U_3507,U_3506,U_3505)))
        | ~ hBOOL(hAPP(int,bool,U_3506,U_3503))
        | sP272(U_3506,U_3502,U_3505,U_3507)
        | sP269(U_3506,U_3505,U_3507)
        | sP268(U_3506,U_3505,U_3507)
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3505)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP268,sP269,sP270,sP271,sP272])],[f_896_9]) ).

cnf(f_896_11,plain,
    ( hBOOL(hAPP(int,bool,U_3507,sK121(U_3507,U_3506,U_3505)))
    | ~ hBOOL(hAPP(int,bool,U_3506,U_3503))
    | sP272(U_3506,U_3502,U_3505,U_3507)
    | sP269(U_3506,U_3505,U_3507)
    | sP268(U_3506,U_3505,U_3507)
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3505)) ),
    inference(clausify,[status(thm)],[f_896_10]) ).

cnf(f_896_12,plain,
    ( hBOOL(hAPP(int,bool,U_3506,sK116(U_3507,U_3506,U_3505)))
    | ~ sP268(U_3506,U_3505,U_3507) ),
    inference(clausify,[status(thm)],[f_896_10]) ).

cnf(f_896_13,plain,
    ( ~ hBOOL(hAPP(int,bool,U_3506,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),sK116(U_3507,U_3506,U_3505)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),sK117(U_3507,U_3506,U_3505)),U_3505))))
    | ~ sP268(U_3506,U_3505,U_3507) ),
    inference(clausify,[status(thm)],[f_896_10]) ).

cnf(f_896_14,plain,
    ( ~ hBOOL(hAPP(int,bool,U_3506,sK118(U_3507,U_3506,U_3505)))
    | ~ sP269(U_3506,U_3505,U_3507) ),
    inference(clausify,[status(thm)],[f_896_10]) ).

cnf(f_896_15,plain,
    ( hBOOL(hAPP(int,bool,U_3506,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),sK118(U_3507,U_3506,U_3505)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),sK119(U_3507,U_3506,U_3505)),U_3505))))
    | ~ sP269(U_3506,U_3505,U_3507) ),
    inference(clausify,[status(thm)],[f_896_10]) ).

cnf(f_896_16,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),sK120(U_3507,U_3506,U_3505,U_3502)),U_3502))
    | ~ sP272(U_3506,U_3502,U_3505,U_3507) ),
    inference(clausify,[status(thm)],[f_896_10]) ).

cnf(f_896_17,plain,
    ( sP271(U_3506,U_3502,U_3505,U_3507)
    | sP270(U_3506,U_3502,U_3505,U_3507)
    | ~ sP272(U_3506,U_3502,U_3505,U_3507) ),
    inference(clausify,[status(thm)],[f_896_10]) ).

cnf(f_896_18,plain,
    ( hBOOL(hAPP(int,bool,U_3507,sK120(U_3507,U_3506,U_3505,U_3502)))
    | ~ sP270(U_3506,U_3502,U_3505,U_3507) ),
    inference(clausify,[status(thm)],[f_896_10]) ).

cnf(f_896_19,plain,
    ( ~ hBOOL(hAPP(int,bool,U_3506,sK120(U_3507,U_3506,U_3505,U_3502)))
    | ~ sP270(U_3506,U_3502,U_3505,U_3507) ),
    inference(clausify,[status(thm)],[f_896_10]) ).

cnf(f_896_20,plain,
    ( hBOOL(hAPP(int,bool,U_3506,sK120(U_3507,U_3506,U_3505,U_3502)))
    | ~ sP271(U_3506,U_3502,U_3505,U_3507) ),
    inference(clausify,[status(thm)],[f_896_10]) ).

cnf(f_896_21,plain,
    ( ~ hBOOL(hAPP(int,bool,U_3507,sK120(U_3507,U_3506,U_3505,U_3502)))
    | ~ sP271(U_3506,U_3502,U_3505,U_3507) ),
    inference(clausify,[status(thm)],[f_896_10]) ).

fof(f_897_1,plain,
    ! [Pa,P_1,D_1] :
      ( ? [X1] : hBOOL(hAPP(int,bool,Pa,X1))
      | ! [X1] : ~ hBOOL(hAPP(int,bool,P_1,X1))
      | ! [Z_3] :
        ? [X_2] :
          ( ( ( ~ hBOOL(hAPP(int,bool,Pa,X_2))
              & hBOOL(hAPP(int,bool,P_1,X_2)) )
            | ( ~ hBOOL(hAPP(int,bool,P_1,X_2))
              & hBOOL(hAPP(int,bool,Pa,X_2)) ) )
          & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_3),X_2)) )
      | ? [X_2,K_2] :
          ( ( ~ hBOOL(hAPP(int,bool,P_1,X_2))
            & hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_2),D_1)))) )
          | ( ~ hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_2),D_1))))
            & hBOOL(hAPP(int,bool,P_1,X_2)) ) )
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1)) ),
    inference(fof_nnf,[status(thm)],[fact_826_plusinfinity]) ).

fof(f_897_2,plain,
    ! [U_3520,U_3519,U_3518] :
      ( ? [U_3517] : hBOOL(hAPP(int,bool,U_3520,U_3517))
      | ! [U_3516] : ~ hBOOL(hAPP(int,bool,U_3519,U_3516))
      | ! [U_3515] :
        ? [U_3514] :
          ( ( ( ~ hBOOL(hAPP(int,bool,U_3520,U_3514))
              & hBOOL(hAPP(int,bool,U_3519,U_3514)) )
            | ( ~ hBOOL(hAPP(int,bool,U_3519,U_3514))
              & hBOOL(hAPP(int,bool,U_3520,U_3514)) ) )
          & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3515),U_3514)) )
      | ? [U_3513,U_3512] :
          ( ( ~ hBOOL(hAPP(int,bool,U_3519,U_3513))
            & hBOOL(hAPP(int,bool,U_3519,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3513),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3512),U_3518)))) )
          | ( ~ hBOOL(hAPP(int,bool,U_3519,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3513),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3512),U_3518))))
            & hBOOL(hAPP(int,bool,U_3519,U_3513)) ) )
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3518)) ),
    inference(variable_rename,[status(thm)],[f_897_1]) ).

fof(f_897_3,plain,
    ! [U_3520,U_3519,U_3518] :
      ( ? [U_3517] : hBOOL(hAPP(int,bool,U_3520,U_3517))
      | ! [U_3516] : ~ hBOOL(hAPP(int,bool,U_3519,U_3516))
      | ! [U_3515] :
        ? [U_3514] :
          ( ( ( ~ hBOOL(hAPP(int,bool,U_3520,U_3514))
              & hBOOL(hAPP(int,bool,U_3519,U_3514)) )
            | ( ~ hBOOL(hAPP(int,bool,U_3519,U_3514))
              & hBOOL(hAPP(int,bool,U_3520,U_3514)) ) )
          & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3515),U_3514)) )
      | ? [U_3524] :
          ( ? [U_3522] : hBOOL(hAPP(int,bool,U_3519,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3524),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3522),U_3518))))
          & ~ hBOOL(hAPP(int,bool,U_3519,U_3524)) )
      | ? [U_3523] :
          ( ? [U_3521] : ~ hBOOL(hAPP(int,bool,U_3519,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3523),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3521),U_3518))))
          & hBOOL(hAPP(int,bool,U_3519,U_3523)) )
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3518)) ),
    inference(miniscope,[status(thm)],[f_897_2]) ).

fof(f_897_4,plain,
    ! [U_3520,U_3519,U_3518] :
      ( ? [U_3517] : hBOOL(hAPP(int,bool,U_3520,U_3517))
      | ! [U_3516] : ~ hBOOL(hAPP(int,bool,U_3519,U_3516))
      | ! [U_3515] :
        ? [U_3514] :
          ( ( ( ~ hBOOL(hAPP(int,bool,U_3520,U_3514))
              & hBOOL(hAPP(int,bool,U_3519,U_3514)) )
            | ( ~ hBOOL(hAPP(int,bool,U_3519,U_3514))
              & hBOOL(hAPP(int,bool,U_3520,U_3514)) ) )
          & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3515),U_3514)) )
      | ? [U_3524] :
          ( ? [U_3522] : hBOOL(hAPP(int,bool,U_3519,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3524),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3522),U_3518))))
          & ~ hBOOL(hAPP(int,bool,U_3519,U_3524)) )
      | ( ? [U_3521] : ~ hBOOL(hAPP(int,bool,U_3519,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),sK122(U_3520,U_3519,U_3518)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3521),U_3518))))
        & hBOOL(hAPP(int,bool,U_3519,sK122(U_3520,U_3519,U_3518))) )
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3518)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK122]),skolemize(U_3523,sK122(U_3520,U_3519,U_3518))],[f_897_3]) ).

fof(f_897_5,plain,
    ! [U_3520,U_3519,U_3518] :
      ( ? [U_3517] : hBOOL(hAPP(int,bool,U_3520,U_3517))
      | ! [U_3516] : ~ hBOOL(hAPP(int,bool,U_3519,U_3516))
      | ! [U_3515] :
        ? [U_3514] :
          ( ( ( ~ hBOOL(hAPP(int,bool,U_3520,U_3514))
              & hBOOL(hAPP(int,bool,U_3519,U_3514)) )
            | ( ~ hBOOL(hAPP(int,bool,U_3519,U_3514))
              & hBOOL(hAPP(int,bool,U_3520,U_3514)) ) )
          & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3515),U_3514)) )
      | ? [U_3524] :
          ( ? [U_3522] : hBOOL(hAPP(int,bool,U_3519,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3524),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3522),U_3518))))
          & ~ hBOOL(hAPP(int,bool,U_3519,U_3524)) )
      | ( ~ hBOOL(hAPP(int,bool,U_3519,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),sK122(U_3520,U_3519,U_3518)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),sK123(U_3520,U_3519,U_3518)),U_3518))))
        & hBOOL(hAPP(int,bool,U_3519,sK122(U_3520,U_3519,U_3518))) )
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3518)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK123]),skolemize(U_3521,sK123(U_3520,U_3519,U_3518))],[f_897_4]) ).

fof(f_897_6,plain,
    ! [U_3520,U_3519,U_3518] :
      ( ? [U_3517] : hBOOL(hAPP(int,bool,U_3520,U_3517))
      | ! [U_3516] : ~ hBOOL(hAPP(int,bool,U_3519,U_3516))
      | ! [U_3515] :
        ? [U_3514] :
          ( ( ( ~ hBOOL(hAPP(int,bool,U_3520,U_3514))
              & hBOOL(hAPP(int,bool,U_3519,U_3514)) )
            | ( ~ hBOOL(hAPP(int,bool,U_3519,U_3514))
              & hBOOL(hAPP(int,bool,U_3520,U_3514)) ) )
          & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3515),U_3514)) )
      | ( ? [U_3522] : hBOOL(hAPP(int,bool,U_3519,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),sK124(U_3520,U_3519,U_3518)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3522),U_3518))))
        & ~ hBOOL(hAPP(int,bool,U_3519,sK124(U_3520,U_3519,U_3518))) )
      | ( ~ hBOOL(hAPP(int,bool,U_3519,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),sK122(U_3520,U_3519,U_3518)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),sK123(U_3520,U_3519,U_3518)),U_3518))))
        & hBOOL(hAPP(int,bool,U_3519,sK122(U_3520,U_3519,U_3518))) )
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3518)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK124]),skolemize(U_3524,sK124(U_3520,U_3519,U_3518))],[f_897_5]) ).

fof(f_897_7,plain,
    ! [U_3520,U_3519,U_3518] :
      ( ? [U_3517] : hBOOL(hAPP(int,bool,U_3520,U_3517))
      | ! [U_3516] : ~ hBOOL(hAPP(int,bool,U_3519,U_3516))
      | ! [U_3515] :
        ? [U_3514] :
          ( ( ( ~ hBOOL(hAPP(int,bool,U_3520,U_3514))
              & hBOOL(hAPP(int,bool,U_3519,U_3514)) )
            | ( ~ hBOOL(hAPP(int,bool,U_3519,U_3514))
              & hBOOL(hAPP(int,bool,U_3520,U_3514)) ) )
          & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3515),U_3514)) )
      | ( hBOOL(hAPP(int,bool,U_3519,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),sK124(U_3520,U_3519,U_3518)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),sK125(U_3520,U_3519,U_3518)),U_3518))))
        & ~ hBOOL(hAPP(int,bool,U_3519,sK124(U_3520,U_3519,U_3518))) )
      | ( ~ hBOOL(hAPP(int,bool,U_3519,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),sK122(U_3520,U_3519,U_3518)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),sK123(U_3520,U_3519,U_3518)),U_3518))))
        & hBOOL(hAPP(int,bool,U_3519,sK122(U_3520,U_3519,U_3518))) )
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3518)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK125]),skolemize(U_3522,sK125(U_3520,U_3519,U_3518))],[f_897_6]) ).

fof(f_897_8,plain,
    ! [U_3520,U_3519,U_3518] :
      ( ? [U_3517] : hBOOL(hAPP(int,bool,U_3520,U_3517))
      | ! [U_3516] : ~ hBOOL(hAPP(int,bool,U_3519,U_3516))
      | ! [U_3515] :
          ( ( ( ~ hBOOL(hAPP(int,bool,U_3520,sK126(U_3520,U_3519,U_3518,U_3515)))
              & hBOOL(hAPP(int,bool,U_3519,sK126(U_3520,U_3519,U_3518,U_3515))) )
            | ( ~ hBOOL(hAPP(int,bool,U_3519,sK126(U_3520,U_3519,U_3518,U_3515)))
              & hBOOL(hAPP(int,bool,U_3520,sK126(U_3520,U_3519,U_3518,U_3515))) ) )
          & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3515),sK126(U_3520,U_3519,U_3518,U_3515))) )
      | ( hBOOL(hAPP(int,bool,U_3519,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),sK124(U_3520,U_3519,U_3518)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),sK125(U_3520,U_3519,U_3518)),U_3518))))
        & ~ hBOOL(hAPP(int,bool,U_3519,sK124(U_3520,U_3519,U_3518))) )
      | ( ~ hBOOL(hAPP(int,bool,U_3519,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),sK122(U_3520,U_3519,U_3518)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),sK123(U_3520,U_3519,U_3518)),U_3518))))
        & hBOOL(hAPP(int,bool,U_3519,sK122(U_3520,U_3519,U_3518))) )
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3518)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK126]),skolemize(U_3514,sK126(U_3520,U_3519,U_3518,U_3515))],[f_897_7]) ).

fof(f_897_9,plain,
    ! [U_3520,U_3519,U_3518] :
      ( hBOOL(hAPP(int,bool,U_3520,sK127(U_3520,U_3519,U_3518)))
      | ! [U_3516] : ~ hBOOL(hAPP(int,bool,U_3519,U_3516))
      | ! [U_3515] :
          ( ( ( ~ hBOOL(hAPP(int,bool,U_3520,sK126(U_3520,U_3519,U_3518,U_3515)))
              & hBOOL(hAPP(int,bool,U_3519,sK126(U_3520,U_3519,U_3518,U_3515))) )
            | ( ~ hBOOL(hAPP(int,bool,U_3519,sK126(U_3520,U_3519,U_3518,U_3515)))
              & hBOOL(hAPP(int,bool,U_3520,sK126(U_3520,U_3519,U_3518,U_3515))) ) )
          & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3515),sK126(U_3520,U_3519,U_3518,U_3515))) )
      | ( hBOOL(hAPP(int,bool,U_3519,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),sK124(U_3520,U_3519,U_3518)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),sK125(U_3520,U_3519,U_3518)),U_3518))))
        & ~ hBOOL(hAPP(int,bool,U_3519,sK124(U_3520,U_3519,U_3518))) )
      | ( ~ hBOOL(hAPP(int,bool,U_3519,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),sK122(U_3520,U_3519,U_3518)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),sK123(U_3520,U_3519,U_3518)),U_3518))))
        & hBOOL(hAPP(int,bool,U_3519,sK122(U_3520,U_3519,U_3518))) )
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3518)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK127]),skolemize(U_3517,sK127(U_3520,U_3519,U_3518))],[f_897_8]) ).

fof(f_897_10,plain,
    ( ! [U_3515,U_3518,U_3519,U_3520] :
        ( ~ hBOOL(hAPP(int,bool,U_3520,sK126(U_3520,U_3519,U_3518,U_3515)))
        | ~ sP276(U_3515,U_3518,U_3519,U_3520) )
    & ! [U_3515,U_3518,U_3519,U_3520] :
        ( hBOOL(hAPP(int,bool,U_3519,sK126(U_3520,U_3519,U_3518,U_3515)))
        | ~ sP276(U_3515,U_3518,U_3519,U_3520) )
    & ! [U_3515,U_3518,U_3519,U_3520] :
        ( ~ hBOOL(hAPP(int,bool,U_3519,sK126(U_3520,U_3519,U_3518,U_3515)))
        | ~ sP275(U_3515,U_3518,U_3519,U_3520) )
    & ! [U_3515,U_3518,U_3519,U_3520] :
        ( hBOOL(hAPP(int,bool,U_3520,sK126(U_3520,U_3519,U_3518,U_3515)))
        | ~ sP275(U_3515,U_3518,U_3519,U_3520) )
    & ! [U_3515,U_3518,U_3519,U_3520] :
        ( sP276(U_3515,U_3518,U_3519,U_3520)
        | sP275(U_3515,U_3518,U_3519,U_3520)
        | ~ sP277(U_3515,U_3518,U_3519,U_3520) )
    & ! [U_3515,U_3518,U_3519,U_3520] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3515),sK126(U_3520,U_3519,U_3518,U_3515)))
        | ~ sP277(U_3515,U_3518,U_3519,U_3520) )
    & ! [U_3518,U_3519,U_3520] :
        ( hBOOL(hAPP(int,bool,U_3519,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),sK124(U_3520,U_3519,U_3518)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),sK125(U_3520,U_3519,U_3518)),U_3518))))
        | ~ sP274(U_3518,U_3519,U_3520) )
    & ! [U_3518,U_3519,U_3520] :
        ( ~ hBOOL(hAPP(int,bool,U_3519,sK124(U_3520,U_3519,U_3518)))
        | ~ sP274(U_3518,U_3519,U_3520) )
    & ! [U_3518,U_3519,U_3520] :
        ( ~ hBOOL(hAPP(int,bool,U_3519,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),sK122(U_3520,U_3519,U_3518)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),sK123(U_3520,U_3519,U_3518)),U_3518))))
        | ~ sP273(U_3518,U_3519,U_3520) )
    & ! [U_3518,U_3519,U_3520] :
        ( hBOOL(hAPP(int,bool,U_3519,sK122(U_3520,U_3519,U_3518)))
        | ~ sP273(U_3518,U_3519,U_3520) )
    & ! [U_3515,U_3518,U_3519,U_3520,U_3516] :
        ( hBOOL(hAPP(int,bool,U_3520,sK127(U_3520,U_3519,U_3518)))
        | ~ hBOOL(hAPP(int,bool,U_3519,U_3516))
        | sP277(U_3515,U_3518,U_3519,U_3520)
        | sP274(U_3518,U_3519,U_3520)
        | sP273(U_3518,U_3519,U_3520)
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3518)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP273,sP274,sP275,sP276,sP277])],[f_897_9]) ).

cnf(f_897_11,plain,
    ( hBOOL(hAPP(int,bool,U_3520,sK127(U_3520,U_3519,U_3518)))
    | ~ hBOOL(hAPP(int,bool,U_3519,U_3516))
    | sP277(U_3515,U_3518,U_3519,U_3520)
    | sP274(U_3518,U_3519,U_3520)
    | sP273(U_3518,U_3519,U_3520)
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3518)) ),
    inference(clausify,[status(thm)],[f_897_10]) ).

cnf(f_897_12,plain,
    ( hBOOL(hAPP(int,bool,U_3519,sK122(U_3520,U_3519,U_3518)))
    | ~ sP273(U_3518,U_3519,U_3520) ),
    inference(clausify,[status(thm)],[f_897_10]) ).

cnf(f_897_13,plain,
    ( ~ hBOOL(hAPP(int,bool,U_3519,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),sK122(U_3520,U_3519,U_3518)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),sK123(U_3520,U_3519,U_3518)),U_3518))))
    | ~ sP273(U_3518,U_3519,U_3520) ),
    inference(clausify,[status(thm)],[f_897_10]) ).

cnf(f_897_14,plain,
    ( ~ hBOOL(hAPP(int,bool,U_3519,sK124(U_3520,U_3519,U_3518)))
    | ~ sP274(U_3518,U_3519,U_3520) ),
    inference(clausify,[status(thm)],[f_897_10]) ).

cnf(f_897_15,plain,
    ( hBOOL(hAPP(int,bool,U_3519,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),sK124(U_3520,U_3519,U_3518)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),sK125(U_3520,U_3519,U_3518)),U_3518))))
    | ~ sP274(U_3518,U_3519,U_3520) ),
    inference(clausify,[status(thm)],[f_897_10]) ).

cnf(f_897_16,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3515),sK126(U_3520,U_3519,U_3518,U_3515)))
    | ~ sP277(U_3515,U_3518,U_3519,U_3520) ),
    inference(clausify,[status(thm)],[f_897_10]) ).

cnf(f_897_17,plain,
    ( sP276(U_3515,U_3518,U_3519,U_3520)
    | sP275(U_3515,U_3518,U_3519,U_3520)
    | ~ sP277(U_3515,U_3518,U_3519,U_3520) ),
    inference(clausify,[status(thm)],[f_897_10]) ).

cnf(f_897_18,plain,
    ( hBOOL(hAPP(int,bool,U_3520,sK126(U_3520,U_3519,U_3518,U_3515)))
    | ~ sP275(U_3515,U_3518,U_3519,U_3520) ),
    inference(clausify,[status(thm)],[f_897_10]) ).

cnf(f_897_19,plain,
    ( ~ hBOOL(hAPP(int,bool,U_3519,sK126(U_3520,U_3519,U_3518,U_3515)))
    | ~ sP275(U_3515,U_3518,U_3519,U_3520) ),
    inference(clausify,[status(thm)],[f_897_10]) ).

cnf(f_897_20,plain,
    ( hBOOL(hAPP(int,bool,U_3519,sK126(U_3520,U_3519,U_3518,U_3515)))
    | ~ sP276(U_3515,U_3518,U_3519,U_3520) ),
    inference(clausify,[status(thm)],[f_897_10]) ).

cnf(f_897_21,plain,
    ( ~ hBOOL(hAPP(int,bool,U_3520,sK126(U_3520,U_3519,U_3518,U_3515)))
    | ~ sP276(U_3515,U_3518,U_3519,U_3520) ),
    inference(clausify,[status(thm)],[f_897_10]) ).

fof(f_898_1,plain,
    ! [Y,X] :
      ( ( hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,X),Y) = zero_zero(int)
        | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Y),X)) )
      & ( hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,X),Y) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X),Y)
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Y),X)) ) ),
    inference(fof_nnf,[status(thm)],[fact_827_tsub__def]) ).

fof(f_898_2,plain,
    ! [U_3526,U_3525] :
      ( ( hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,U_3525),U_3526) = zero_zero(int)
        | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3526),U_3525)) )
      & ( hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,U_3525),U_3526) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3525),U_3526)
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3526),U_3525)) ) ),
    inference(variable_rename,[status(thm)],[f_898_1]) ).

fof(f_898_3,plain,
    ( ! [U_3530,U_3528] :
        ( hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,U_3528),U_3530) = zero_zero(int)
        | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3530),U_3528)) )
    & ! [U_3529,U_3527] :
        ( hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,U_3527),U_3529) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3527),U_3529)
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3529),U_3527)) ) ),
    inference(miniscope,[status(thm)],[f_898_2]) ).

fof(f_898_4,plain,
    ( ! [U_3528,U_3530] :
        ( hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,U_3528),U_3530) = zero_zero(int)
        | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3530),U_3528)) )
    & ! [U_3529,U_3527] :
        ( hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,U_3527),U_3529) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3527),U_3529)
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3529),U_3527)) ) ),
    inference(definitional_conversion,[status(esa)],[f_898_3]) ).

cnf(f_898_5,plain,
    ( hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,U_3527),U_3529) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3527),U_3529)
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3529),U_3527)) ),
    inference(clausify,[status(thm)],[f_898_4]) ).

cnf(f_898_6,plain,
    ( hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,U_3528),U_3530) = zero_zero(int)
    | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3530),U_3528)) ),
    inference(clausify,[status(thm)],[f_898_4]) ).

fof(f_899_1,plain,
    ! [X_a] :
      ( ! [V] :
          ( ( hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,number_number_of(nat),V)) = zero_zero(X_a)
            | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),V))) )
          & ( hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,number_number_of(nat),V)) = hAPP(int,X_a,number_number_of(X_a),V)
            | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),V))) ) )
      | ~ number_ring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_828_of__nat__number__of__lemma]) ).

fof(f_899_2,plain,
    ! [U_3532] :
      ( ! [U_3531] :
          ( ( hAPP(nat,U_3532,semiring_1_of_nat(U_3532),hAPP(int,nat,number_number_of(nat),U_3531)) = zero_zero(U_3532)
            | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),U_3531))) )
          & ( hAPP(nat,U_3532,semiring_1_of_nat(U_3532),hAPP(int,nat,number_number_of(nat),U_3531)) = hAPP(int,U_3532,number_number_of(U_3532),U_3531)
            | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),U_3531))) ) )
      | ~ number_ring(U_3532) ),
    inference(variable_rename,[status(thm)],[f_899_1]) ).

fof(f_899_3,plain,
    ! [U_3532] :
      ( ( ! [U_3534] :
            ( hAPP(nat,U_3532,semiring_1_of_nat(U_3532),hAPP(int,nat,number_number_of(nat),U_3534)) = zero_zero(U_3532)
            | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),U_3534))) )
        & ! [U_3533] :
            ( hAPP(nat,U_3532,semiring_1_of_nat(U_3532),hAPP(int,nat,number_number_of(nat),U_3533)) = hAPP(int,U_3532,number_number_of(U_3532),U_3533)
            | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),U_3533))) ) )
      | ~ number_ring(U_3532) ),
    inference(miniscope,[status(thm)],[f_899_2]) ).

fof(f_899_4,plain,
    ( ! [U_3532,U_3534,U_3533] :
        ( hAPP(nat,U_3532,semiring_1_of_nat(U_3532),hAPP(int,nat,number_number_of(nat),U_3534)) = zero_zero(U_3532)
        | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),U_3534)))
        | ~ sP278(U_3532,U_3534,U_3533) )
    & ! [U_3532,U_3534,U_3533] :
        ( hAPP(nat,U_3532,semiring_1_of_nat(U_3532),hAPP(int,nat,number_number_of(nat),U_3533)) = hAPP(int,U_3532,number_number_of(U_3532),U_3533)
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),U_3533)))
        | ~ sP278(U_3532,U_3534,U_3533) )
    & ! [U_3532,U_3534,U_3533] :
        ( sP278(U_3532,U_3534,U_3533)
        | ~ number_ring(U_3532) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP278])],[f_899_3]) ).

cnf(f_899_5,plain,
    ( sP278(U_3532,U_3534,U_3533)
    | ~ number_ring(U_3532) ),
    inference(clausify,[status(thm)],[f_899_4]) ).

cnf(f_899_6,plain,
    ( hAPP(nat,U_3532,semiring_1_of_nat(U_3532),hAPP(int,nat,number_number_of(nat),U_3533)) = hAPP(int,U_3532,number_number_of(U_3532),U_3533)
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),U_3533)))
    | ~ sP278(U_3532,U_3534,U_3533) ),
    inference(clausify,[status(thm)],[f_899_4]) ).

cnf(f_899_7,plain,
    ( hAPP(nat,U_3532,semiring_1_of_nat(U_3532),hAPP(int,nat,number_number_of(nat),U_3534)) = zero_zero(U_3532)
    | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),U_3534)))
    | ~ sP278(U_3532,U_3534,U_3533) ),
    inference(clausify,[status(thm)],[f_899_4]) ).

fof(f_900_1,plain,
    ! [X_a] :
      ( ! [N] : hAPP(int,X_a,number_number_of(X_a),hAPP(nat,int,semiring_1_of_nat(int),N)) = hAPP(nat,X_a,semiring_1_of_nat(X_a),N)
      | ~ number_semiring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_829_number__of__int]) ).

fof(f_900_2,plain,
    ! [U_3536] :
      ( ! [U_3535] : hAPP(int,U_3536,number_number_of(U_3536),hAPP(nat,int,semiring_1_of_nat(int),U_3535)) = hAPP(nat,U_3536,semiring_1_of_nat(U_3536),U_3535)
      | ~ number_semiring(U_3536) ),
    inference(variable_rename,[status(thm)],[f_900_1]) ).

fof(f_900_3,plain,
    ! [U_3535,U_3536] :
      ( hAPP(int,U_3536,number_number_of(U_3536),hAPP(nat,int,semiring_1_of_nat(int),U_3535)) = hAPP(nat,U_3536,semiring_1_of_nat(U_3536),U_3535)
      | ~ number_semiring(U_3536) ),
    inference(definitional_conversion,[status(esa)],[f_900_2]) ).

cnf(f_900_4,plain,
    ( hAPP(int,U_3536,number_number_of(U_3536),hAPP(nat,int,semiring_1_of_nat(int),U_3535)) = hAPP(nat,U_3536,semiring_1_of_nat(U_3536),U_3535)
    | ~ number_semiring(U_3536) ),
    inference(clausify,[status(thm)],[f_900_3]) ).

fof(f_901_1,plain,
    ! [N] : hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),N))),
    inference(fof_nnf,[status(thm)],[fact_830_zero__zle__int]) ).

fof(f_901_2,plain,
    ! [U_3537] : hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),U_3537))),
    inference(variable_rename,[status(thm)],[f_901_1]) ).

fof(f_901_3,plain,
    ! [U_3537] : hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),U_3537))),
    inference(definitional_conversion,[status(esa)],[f_901_2]) ).

cnf(f_901_4,plain,
    hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),U_3537))),
    inference(clausify,[status(thm)],[f_901_3]) ).

fof(f_902_1,plain,
    ! [K_1] : ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),K_1)),zero_zero(int))),
    inference(fof_nnf,[status(thm)],[fact_831_int__less__0__conv]) ).

fof(f_902_2,plain,
    ! [U_3538] : ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),U_3538)),zero_zero(int))),
    inference(variable_rename,[status(thm)],[f_902_1]) ).

fof(f_902_3,plain,
    ! [U_3538] : ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),U_3538)),zero_zero(int))),
    inference(definitional_conversion,[status(esa)],[f_902_2]) ).

cnf(f_902_4,plain,
    ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),U_3538)),zero_zero(int))),
    inference(clausify,[status(thm)],[f_902_3]) ).

fof(f_903_1,plain,
    ! [X_a] :
      ( ! [N] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N)))
      | ~ linordered_semidom(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_832_of__nat__0__le__iff]) ).

fof(f_903_2,plain,
    ! [U_3540] :
      ( ! [U_3539] : hBOOL(hAPP(U_3540,bool,hAPP(U_3540,fun(U_3540,bool),ord_less_eq(U_3540),zero_zero(U_3540)),hAPP(nat,U_3540,semiring_1_of_nat(U_3540),U_3539)))
      | ~ linordered_semidom(U_3540) ),
    inference(variable_rename,[status(thm)],[f_903_1]) ).

fof(f_903_3,plain,
    ! [U_3540,U_3539] :
      ( hBOOL(hAPP(U_3540,bool,hAPP(U_3540,fun(U_3540,bool),ord_less_eq(U_3540),zero_zero(U_3540)),hAPP(nat,U_3540,semiring_1_of_nat(U_3540),U_3539)))
      | ~ linordered_semidom(U_3540) ),
    inference(definitional_conversion,[status(esa)],[f_903_2]) ).

cnf(f_903_4,plain,
    ( hBOOL(hAPP(U_3540,bool,hAPP(U_3540,fun(U_3540,bool),ord_less_eq(U_3540),zero_zero(U_3540)),hAPP(nat,U_3540,semiring_1_of_nat(U_3540),U_3539)))
    | ~ linordered_semidom(U_3540) ),
    inference(clausify,[status(thm)],[f_903_3]) ).

fof(f_904_1,plain,
    ! [X_a] :
      ( ! [M_1] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(nat,X_a,semiring_1_of_nat(X_a),M_1)))
      | ~ linordered_semidom(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_833_zero__le__imp__of__nat]) ).

fof(f_904_2,plain,
    ! [U_3542] :
      ( ! [U_3541] : hBOOL(hAPP(U_3542,bool,hAPP(U_3542,fun(U_3542,bool),ord_less_eq(U_3542),zero_zero(U_3542)),hAPP(nat,U_3542,semiring_1_of_nat(U_3542),U_3541)))
      | ~ linordered_semidom(U_3542) ),
    inference(variable_rename,[status(thm)],[f_904_1]) ).

fof(f_904_3,plain,
    ! [U_3542,U_3541] :
      ( hBOOL(hAPP(U_3542,bool,hAPP(U_3542,fun(U_3542,bool),ord_less_eq(U_3542),zero_zero(U_3542)),hAPP(nat,U_3542,semiring_1_of_nat(U_3542),U_3541)))
      | ~ linordered_semidom(U_3542) ),
    inference(definitional_conversion,[status(esa)],[f_904_2]) ).

cnf(f_904_4,plain,
    ( hBOOL(hAPP(U_3542,bool,hAPP(U_3542,fun(U_3542,bool),ord_less_eq(U_3542),zero_zero(U_3542)),hAPP(nat,U_3542,semiring_1_of_nat(U_3542),U_3541)))
    | ~ linordered_semidom(U_3542) ),
    inference(clausify,[status(thm)],[f_904_3]) ).

fof(f_905_1,plain,
    ! [X_a] :
      ( ! [M_1] : ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M_1)),zero_zero(X_a)))
      | ~ linordered_semidom(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_834_of__nat__less__0__iff]) ).

fof(f_905_2,plain,
    ! [U_3544] :
      ( ! [U_3543] : ~ hBOOL(hAPP(U_3544,bool,hAPP(U_3544,fun(U_3544,bool),ord_less(U_3544),hAPP(nat,U_3544,semiring_1_of_nat(U_3544),U_3543)),zero_zero(U_3544)))
      | ~ linordered_semidom(U_3544) ),
    inference(variable_rename,[status(thm)],[f_905_1]) ).

fof(f_905_3,plain,
    ! [U_3543,U_3544] :
      ( ~ hBOOL(hAPP(U_3544,bool,hAPP(U_3544,fun(U_3544,bool),ord_less(U_3544),hAPP(nat,U_3544,semiring_1_of_nat(U_3544),U_3543)),zero_zero(U_3544)))
      | ~ linordered_semidom(U_3544) ),
    inference(definitional_conversion,[status(esa)],[f_905_2]) ).

cnf(f_905_4,plain,
    ( ~ hBOOL(hAPP(U_3544,bool,hAPP(U_3544,fun(U_3544,bool),ord_less(U_3544),hAPP(nat,U_3544,semiring_1_of_nat(U_3544),U_3543)),zero_zero(U_3544)))
    | ~ linordered_semidom(U_3544) ),
    inference(clausify,[status(thm)],[f_905_3]) ).

fof(f_906_1,plain,
    ! [X_a] :
      ( hAPP(nat,X_a,semiring_1_of_nat(X_a),zero_zero(nat)) = zero_zero(X_a)
      | ~ semiring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_835_of__nat__0]) ).

fof(f_906_2,plain,
    ! [U_3545] :
      ( hAPP(nat,U_3545,semiring_1_of_nat(U_3545),zero_zero(nat)) = zero_zero(U_3545)
      | ~ semiring_1(U_3545) ),
    inference(variable_rename,[status(thm)],[f_906_1]) ).

fof(f_906_3,plain,
    ! [U_3545] :
      ( hAPP(nat,U_3545,semiring_1_of_nat(U_3545),zero_zero(nat)) = zero_zero(U_3545)
      | ~ semiring_1(U_3545) ),
    inference(definitional_conversion,[status(esa)],[f_906_2]) ).

cnf(f_906_4,plain,
    ( hAPP(nat,U_3545,semiring_1_of_nat(U_3545),zero_zero(nat)) = zero_zero(U_3545)
    | ~ semiring_1(U_3545) ),
    inference(clausify,[status(thm)],[f_906_3]) ).

fof(f_907_1,plain,
    ! [X_a] :
      ( hAPP(nat,X_a,semiring_1_of_nat(X_a),one_one(nat)) = one_one(X_a)
      | ~ semiring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_836_of__nat__1]) ).

fof(f_907_2,plain,
    ! [U_3546] :
      ( hAPP(nat,U_3546,semiring_1_of_nat(U_3546),one_one(nat)) = one_one(U_3546)
      | ~ semiring_1(U_3546) ),
    inference(variable_rename,[status(thm)],[f_907_1]) ).

fof(f_907_3,plain,
    ! [U_3546] :
      ( hAPP(nat,U_3546,semiring_1_of_nat(U_3546),one_one(nat)) = one_one(U_3546)
      | ~ semiring_1(U_3546) ),
    inference(definitional_conversion,[status(esa)],[f_907_2]) ).

cnf(f_907_4,plain,
    ( hAPP(nat,U_3546,semiring_1_of_nat(U_3546),one_one(nat)) = one_one(U_3546)
    | ~ semiring_1(U_3546) ),
    inference(clausify,[status(thm)],[f_907_3]) ).

fof(f_908_1,plain,
    hAPP(nat,int,semiring_1_of_nat(int),one_one(nat)) = one_one(int),
    inference(fof_nnf,[status(thm)],[fact_837_int__1]) ).

fof(f_908_2,plain,
    hAPP(nat,int,semiring_1_of_nat(int),one_one(nat)) = one_one(int),
    inference(definitional_conversion,[status(esa)],[f_908_1]) ).

cnf(f_908_3,plain,
    hAPP(nat,int,semiring_1_of_nat(int),one_one(nat)) = one_one(int),
    inference(clausify,[status(thm)],[f_908_2]) ).

fof(f_909_1,plain,
    hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat)) = zero_zero(int),
    inference(fof_nnf,[status(thm)],[fact_838_int__0]) ).

fof(f_909_2,plain,
    hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat)) = zero_zero(int),
    inference(definitional_conversion,[status(esa)],[f_909_1]) ).

cnf(f_909_3,plain,
    hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat)) = zero_zero(int),
    inference(clausify,[status(thm)],[f_909_2]) ).

fof(f_910_1,plain,
    ! [Na] :
      ( ( hAPP(nat,int,semiring_1_of_nat(int),Na) = zero_zero(int)
        | Na != zero_zero(nat) )
      & ( Na = zero_zero(nat)
        | hAPP(nat,int,semiring_1_of_nat(int),Na) != zero_zero(int) ) ),
    inference(fof_nnf,[status(thm)],[fact_839_int__eq__0__conv]) ).

fof(f_910_2,plain,
    ! [U_3547] :
      ( ( hAPP(nat,int,semiring_1_of_nat(int),U_3547) = zero_zero(int)
        | U_3547 != zero_zero(nat) )
      & ( U_3547 = zero_zero(nat)
        | hAPP(nat,int,semiring_1_of_nat(int),U_3547) != zero_zero(int) ) ),
    inference(variable_rename,[status(thm)],[f_910_1]) ).

fof(f_910_3,plain,
    ( ! [U_3549] :
        ( hAPP(nat,int,semiring_1_of_nat(int),U_3549) = zero_zero(int)
        | U_3549 != zero_zero(nat) )
    & ! [U_3548] :
        ( U_3548 = zero_zero(nat)
        | hAPP(nat,int,semiring_1_of_nat(int),U_3548) != zero_zero(int) ) ),
    inference(miniscope,[status(thm)],[f_910_2]) ).

fof(f_910_4,plain,
    ( ! [U_3549] :
        ( hAPP(nat,int,semiring_1_of_nat(int),U_3549) = zero_zero(int)
        | U_3549 != zero_zero(nat) )
    & ! [U_3548] :
        ( U_3548 = zero_zero(nat)
        | hAPP(nat,int,semiring_1_of_nat(int),U_3548) != zero_zero(int) ) ),
    inference(definitional_conversion,[status(esa)],[f_910_3]) ).

cnf(f_910_5,plain,
    ( U_3548 = zero_zero(nat)
    | hAPP(nat,int,semiring_1_of_nat(int),U_3548) != zero_zero(int) ),
    inference(clausify,[status(thm)],[f_910_4]) ).

cnf(f_910_6,plain,
    ( hAPP(nat,int,semiring_1_of_nat(int),U_3549) = zero_zero(int)
    | U_3549 != zero_zero(nat) ),
    inference(clausify,[status(thm)],[f_910_4]) ).

fof(f_911_1,plain,
    ! [X_b] :
      ( ! [Na] : hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(nat,X_b,semiring_1_of_nat(X_b),Na)),ring_1_Ints(X_b)))
      | ~ ring_1(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_840_Ints__of__nat]) ).

fof(f_911_2,plain,
    ! [U_3551] :
      ( ! [U_3550] : hBOOL(hAPP(fun(U_3551,bool),bool,hAPP(U_3551,fun(fun(U_3551,bool),bool),member(U_3551),hAPP(nat,U_3551,semiring_1_of_nat(U_3551),U_3550)),ring_1_Ints(U_3551)))
      | ~ ring_1(U_3551) ),
    inference(variable_rename,[status(thm)],[f_911_1]) ).

fof(f_911_3,plain,
    ! [U_3550,U_3551] :
      ( hBOOL(hAPP(fun(U_3551,bool),bool,hAPP(U_3551,fun(fun(U_3551,bool),bool),member(U_3551),hAPP(nat,U_3551,semiring_1_of_nat(U_3551),U_3550)),ring_1_Ints(U_3551)))
      | ~ ring_1(U_3551) ),
    inference(definitional_conversion,[status(esa)],[f_911_2]) ).

cnf(f_911_4,plain,
    ( hBOOL(hAPP(fun(U_3551,bool),bool,hAPP(U_3551,fun(fun(U_3551,bool),bool),member(U_3551),hAPP(nat,U_3551,semiring_1_of_nat(U_3551),U_3550)),ring_1_Ints(U_3551)))
    | ~ ring_1(U_3551) ),
    inference(clausify,[status(thm)],[f_911_3]) ).

fof(f_912_1,plain,
    ! [X_b] :
      ( ! [M,Na] :
          ( ( hAPP(nat,X_b,semiring_1_of_nat(X_b),M) = hAPP(nat,X_b,semiring_1_of_nat(X_b),Na)
            | M != Na )
          & ( M = Na
            | hAPP(nat,X_b,semiring_1_of_nat(X_b),M) != hAPP(nat,X_b,semiring_1_of_nat(X_b),Na) ) )
      | ~ semiring_char_0(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_841_of__nat__eq__iff]) ).

fof(f_912_2,plain,
    ! [U_3554] :
      ( ! [U_3553,U_3552] :
          ( ( hAPP(nat,U_3554,semiring_1_of_nat(U_3554),U_3553) = hAPP(nat,U_3554,semiring_1_of_nat(U_3554),U_3552)
            | U_3553 != U_3552 )
          & ( U_3553 = U_3552
            | hAPP(nat,U_3554,semiring_1_of_nat(U_3554),U_3553) != hAPP(nat,U_3554,semiring_1_of_nat(U_3554),U_3552) ) )
      | ~ semiring_char_0(U_3554) ),
    inference(variable_rename,[status(thm)],[f_912_1]) ).

fof(f_912_3,plain,
    ! [U_3554] :
      ( ( ! [U_3558,U_3556] :
            ( hAPP(nat,U_3554,semiring_1_of_nat(U_3554),U_3558) = hAPP(nat,U_3554,semiring_1_of_nat(U_3554),U_3556)
            | U_3558 != U_3556 )
        & ! [U_3557,U_3555] :
            ( U_3557 = U_3555
            | hAPP(nat,U_3554,semiring_1_of_nat(U_3554),U_3557) != hAPP(nat,U_3554,semiring_1_of_nat(U_3554),U_3555) ) )
      | ~ semiring_char_0(U_3554) ),
    inference(miniscope,[status(thm)],[f_912_2]) ).

fof(f_912_4,plain,
    ( ! [U_3554,U_3558,U_3556,U_3555,U_3557] :
        ( hAPP(nat,U_3554,semiring_1_of_nat(U_3554),U_3558) = hAPP(nat,U_3554,semiring_1_of_nat(U_3554),U_3556)
        | U_3558 != U_3556
        | ~ sP279(U_3554,U_3558,U_3556,U_3555,U_3557) )
    & ! [U_3554,U_3558,U_3556,U_3555,U_3557] :
        ( U_3557 = U_3555
        | hAPP(nat,U_3554,semiring_1_of_nat(U_3554),U_3557) != hAPP(nat,U_3554,semiring_1_of_nat(U_3554),U_3555)
        | ~ sP279(U_3554,U_3558,U_3556,U_3555,U_3557) )
    & ! [U_3554,U_3558,U_3556,U_3555,U_3557] :
        ( sP279(U_3554,U_3558,U_3556,U_3555,U_3557)
        | ~ semiring_char_0(U_3554) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP279])],[f_912_3]) ).

cnf(f_912_5,plain,
    ( sP279(U_3554,U_3558,U_3556,U_3555,U_3557)
    | ~ semiring_char_0(U_3554) ),
    inference(clausify,[status(thm)],[f_912_4]) ).

cnf(f_912_6,plain,
    ( U_3557 = U_3555
    | hAPP(nat,U_3554,semiring_1_of_nat(U_3554),U_3557) != hAPP(nat,U_3554,semiring_1_of_nat(U_3554),U_3555)
    | ~ sP279(U_3554,U_3558,U_3556,U_3555,U_3557) ),
    inference(clausify,[status(thm)],[f_912_4]) ).

cnf(f_912_7,plain,
    ( hAPP(nat,U_3554,semiring_1_of_nat(U_3554),U_3558) = hAPP(nat,U_3554,semiring_1_of_nat(U_3554),U_3556)
    | U_3558 != U_3556
    | ~ sP279(U_3554,U_3558,U_3556,U_3555,U_3557) ),
    inference(clausify,[status(thm)],[f_912_4]) ).

fof(f_913_1,plain,
    ! [X_a] :
      ( ! [M_1,N] : hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M_1)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N))
      | ~ semiring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_842_of__nat__add]) ).

fof(f_913_2,plain,
    ! [U_3561] :
      ( ! [U_3560,U_3559] : hAPP(nat,U_3561,semiring_1_of_nat(U_3561),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_3560),U_3559)) = hAPP(U_3561,U_3561,hAPP(U_3561,fun(U_3561,U_3561),plus_plus(U_3561),hAPP(nat,U_3561,semiring_1_of_nat(U_3561),U_3560)),hAPP(nat,U_3561,semiring_1_of_nat(U_3561),U_3559))
      | ~ semiring_1(U_3561) ),
    inference(variable_rename,[status(thm)],[f_913_1]) ).

fof(f_913_3,plain,
    ! [U_3560,U_3561,U_3559] :
      ( hAPP(nat,U_3561,semiring_1_of_nat(U_3561),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_3560),U_3559)) = hAPP(U_3561,U_3561,hAPP(U_3561,fun(U_3561,U_3561),plus_plus(U_3561),hAPP(nat,U_3561,semiring_1_of_nat(U_3561),U_3560)),hAPP(nat,U_3561,semiring_1_of_nat(U_3561),U_3559))
      | ~ semiring_1(U_3561) ),
    inference(definitional_conversion,[status(esa)],[f_913_2]) ).

cnf(f_913_4,plain,
    ( hAPP(nat,U_3561,semiring_1_of_nat(U_3561),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_3560),U_3559)) = hAPP(U_3561,U_3561,hAPP(U_3561,fun(U_3561,U_3561),plus_plus(U_3561),hAPP(nat,U_3561,semiring_1_of_nat(U_3561),U_3560)),hAPP(nat,U_3561,semiring_1_of_nat(U_3561),U_3559))
    | ~ semiring_1(U_3561) ),
    inference(clausify,[status(thm)],[f_913_3]) ).

fof(f_914_1,plain,
    ! [X_b] :
      ( ! [M,Na] :
          ( ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(nat,X_b,semiring_1_of_nat(X_b),M)),hAPP(nat,X_b,semiring_1_of_nat(X_b),Na)))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)) )
          & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na))
            | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(nat,X_b,semiring_1_of_nat(X_b),M)),hAPP(nat,X_b,semiring_1_of_nat(X_b),Na))) ) )
      | ~ linordered_semidom(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_843_of__nat__le__iff]) ).

fof(f_914_2,plain,
    ! [U_3564] :
      ( ! [U_3563,U_3562] :
          ( ( hBOOL(hAPP(U_3564,bool,hAPP(U_3564,fun(U_3564,bool),ord_less_eq(U_3564),hAPP(nat,U_3564,semiring_1_of_nat(U_3564),U_3563)),hAPP(nat,U_3564,semiring_1_of_nat(U_3564),U_3562)))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3563),U_3562)) )
          & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3563),U_3562))
            | ~ hBOOL(hAPP(U_3564,bool,hAPP(U_3564,fun(U_3564,bool),ord_less_eq(U_3564),hAPP(nat,U_3564,semiring_1_of_nat(U_3564),U_3563)),hAPP(nat,U_3564,semiring_1_of_nat(U_3564),U_3562))) ) )
      | ~ linordered_semidom(U_3564) ),
    inference(variable_rename,[status(thm)],[f_914_1]) ).

fof(f_914_3,plain,
    ! [U_3564] :
      ( ( ! [U_3568,U_3566] :
            ( hBOOL(hAPP(U_3564,bool,hAPP(U_3564,fun(U_3564,bool),ord_less_eq(U_3564),hAPP(nat,U_3564,semiring_1_of_nat(U_3564),U_3568)),hAPP(nat,U_3564,semiring_1_of_nat(U_3564),U_3566)))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3568),U_3566)) )
        & ! [U_3567,U_3565] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3567),U_3565))
            | ~ hBOOL(hAPP(U_3564,bool,hAPP(U_3564,fun(U_3564,bool),ord_less_eq(U_3564),hAPP(nat,U_3564,semiring_1_of_nat(U_3564),U_3567)),hAPP(nat,U_3564,semiring_1_of_nat(U_3564),U_3565))) ) )
      | ~ linordered_semidom(U_3564) ),
    inference(miniscope,[status(thm)],[f_914_2]) ).

fof(f_914_4,plain,
    ( ! [U_3567,U_3564,U_3565,U_3566,U_3568] :
        ( hBOOL(hAPP(U_3564,bool,hAPP(U_3564,fun(U_3564,bool),ord_less_eq(U_3564),hAPP(nat,U_3564,semiring_1_of_nat(U_3564),U_3568)),hAPP(nat,U_3564,semiring_1_of_nat(U_3564),U_3566)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3568),U_3566))
        | ~ sP280(U_3567,U_3564,U_3565,U_3566,U_3568) )
    & ! [U_3567,U_3564,U_3565,U_3566,U_3568] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3567),U_3565))
        | ~ hBOOL(hAPP(U_3564,bool,hAPP(U_3564,fun(U_3564,bool),ord_less_eq(U_3564),hAPP(nat,U_3564,semiring_1_of_nat(U_3564),U_3567)),hAPP(nat,U_3564,semiring_1_of_nat(U_3564),U_3565)))
        | ~ sP280(U_3567,U_3564,U_3565,U_3566,U_3568) )
    & ! [U_3567,U_3564,U_3565,U_3566,U_3568] :
        ( sP280(U_3567,U_3564,U_3565,U_3566,U_3568)
        | ~ linordered_semidom(U_3564) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP280])],[f_914_3]) ).

cnf(f_914_5,plain,
    ( sP280(U_3567,U_3564,U_3565,U_3566,U_3568)
    | ~ linordered_semidom(U_3564) ),
    inference(clausify,[status(thm)],[f_914_4]) ).

cnf(f_914_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3567),U_3565))
    | ~ hBOOL(hAPP(U_3564,bool,hAPP(U_3564,fun(U_3564,bool),ord_less_eq(U_3564),hAPP(nat,U_3564,semiring_1_of_nat(U_3564),U_3567)),hAPP(nat,U_3564,semiring_1_of_nat(U_3564),U_3565)))
    | ~ sP280(U_3567,U_3564,U_3565,U_3566,U_3568) ),
    inference(clausify,[status(thm)],[f_914_4]) ).

cnf(f_914_7,plain,
    ( hBOOL(hAPP(U_3564,bool,hAPP(U_3564,fun(U_3564,bool),ord_less_eq(U_3564),hAPP(nat,U_3564,semiring_1_of_nat(U_3564),U_3568)),hAPP(nat,U_3564,semiring_1_of_nat(U_3564),U_3566)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3568),U_3566))
    | ~ sP280(U_3567,U_3564,U_3565,U_3566,U_3568) ),
    inference(clausify,[status(thm)],[f_914_4]) ).

fof(f_915_1,plain,
    ! [X_b] :
      ( ! [M,Na] :
          ( ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(nat,X_b,semiring_1_of_nat(X_b),M)),hAPP(nat,X_b,semiring_1_of_nat(X_b),Na)))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)) )
          & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))
            | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(nat,X_b,semiring_1_of_nat(X_b),M)),hAPP(nat,X_b,semiring_1_of_nat(X_b),Na))) ) )
      | ~ linordered_semidom(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_844_of__nat__less__iff]) ).

fof(f_915_2,plain,
    ! [U_3571] :
      ( ! [U_3570,U_3569] :
          ( ( hBOOL(hAPP(U_3571,bool,hAPP(U_3571,fun(U_3571,bool),ord_less(U_3571),hAPP(nat,U_3571,semiring_1_of_nat(U_3571),U_3570)),hAPP(nat,U_3571,semiring_1_of_nat(U_3571),U_3569)))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3570),U_3569)) )
          & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3570),U_3569))
            | ~ hBOOL(hAPP(U_3571,bool,hAPP(U_3571,fun(U_3571,bool),ord_less(U_3571),hAPP(nat,U_3571,semiring_1_of_nat(U_3571),U_3570)),hAPP(nat,U_3571,semiring_1_of_nat(U_3571),U_3569))) ) )
      | ~ linordered_semidom(U_3571) ),
    inference(variable_rename,[status(thm)],[f_915_1]) ).

fof(f_915_3,plain,
    ! [U_3571] :
      ( ( ! [U_3575,U_3573] :
            ( hBOOL(hAPP(U_3571,bool,hAPP(U_3571,fun(U_3571,bool),ord_less(U_3571),hAPP(nat,U_3571,semiring_1_of_nat(U_3571),U_3575)),hAPP(nat,U_3571,semiring_1_of_nat(U_3571),U_3573)))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3575),U_3573)) )
        & ! [U_3574,U_3572] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3574),U_3572))
            | ~ hBOOL(hAPP(U_3571,bool,hAPP(U_3571,fun(U_3571,bool),ord_less(U_3571),hAPP(nat,U_3571,semiring_1_of_nat(U_3571),U_3574)),hAPP(nat,U_3571,semiring_1_of_nat(U_3571),U_3572))) ) )
      | ~ linordered_semidom(U_3571) ),
    inference(miniscope,[status(thm)],[f_915_2]) ).

fof(f_915_4,plain,
    ( ! [U_3572,U_3575,U_3573,U_3571,U_3574] :
        ( hBOOL(hAPP(U_3571,bool,hAPP(U_3571,fun(U_3571,bool),ord_less(U_3571),hAPP(nat,U_3571,semiring_1_of_nat(U_3571),U_3575)),hAPP(nat,U_3571,semiring_1_of_nat(U_3571),U_3573)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3575),U_3573))
        | ~ sP281(U_3572,U_3575,U_3573,U_3571,U_3574) )
    & ! [U_3572,U_3575,U_3573,U_3571,U_3574] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3574),U_3572))
        | ~ hBOOL(hAPP(U_3571,bool,hAPP(U_3571,fun(U_3571,bool),ord_less(U_3571),hAPP(nat,U_3571,semiring_1_of_nat(U_3571),U_3574)),hAPP(nat,U_3571,semiring_1_of_nat(U_3571),U_3572)))
        | ~ sP281(U_3572,U_3575,U_3573,U_3571,U_3574) )
    & ! [U_3572,U_3575,U_3573,U_3571,U_3574] :
        ( sP281(U_3572,U_3575,U_3573,U_3571,U_3574)
        | ~ linordered_semidom(U_3571) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP281])],[f_915_3]) ).

cnf(f_915_5,plain,
    ( sP281(U_3572,U_3575,U_3573,U_3571,U_3574)
    | ~ linordered_semidom(U_3571) ),
    inference(clausify,[status(thm)],[f_915_4]) ).

cnf(f_915_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3574),U_3572))
    | ~ hBOOL(hAPP(U_3571,bool,hAPP(U_3571,fun(U_3571,bool),ord_less(U_3571),hAPP(nat,U_3571,semiring_1_of_nat(U_3571),U_3574)),hAPP(nat,U_3571,semiring_1_of_nat(U_3571),U_3572)))
    | ~ sP281(U_3572,U_3575,U_3573,U_3571,U_3574) ),
    inference(clausify,[status(thm)],[f_915_4]) ).

cnf(f_915_7,plain,
    ( hBOOL(hAPP(U_3571,bool,hAPP(U_3571,fun(U_3571,bool),ord_less(U_3571),hAPP(nat,U_3571,semiring_1_of_nat(U_3571),U_3575)),hAPP(nat,U_3571,semiring_1_of_nat(U_3571),U_3573)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3575),U_3573))
    | ~ sP281(U_3572,U_3575,U_3573,U_3571,U_3574) ),
    inference(clausify,[status(thm)],[f_915_4]) ).

fof(f_916_1,plain,
    ! [X_a] :
      ( ! [M_1,N] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M_1)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N)))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)) )
      | ~ linordered_semidom(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_845_less__imp__of__nat__less]) ).

fof(f_916_2,plain,
    ! [U_3578] :
      ( ! [U_3577,U_3576] :
          ( hBOOL(hAPP(U_3578,bool,hAPP(U_3578,fun(U_3578,bool),ord_less(U_3578),hAPP(nat,U_3578,semiring_1_of_nat(U_3578),U_3577)),hAPP(nat,U_3578,semiring_1_of_nat(U_3578),U_3576)))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3577),U_3576)) )
      | ~ linordered_semidom(U_3578) ),
    inference(variable_rename,[status(thm)],[f_916_1]) ).

fof(f_916_3,plain,
    ! [U_3577,U_3578,U_3576] :
      ( hBOOL(hAPP(U_3578,bool,hAPP(U_3578,fun(U_3578,bool),ord_less(U_3578),hAPP(nat,U_3578,semiring_1_of_nat(U_3578),U_3577)),hAPP(nat,U_3578,semiring_1_of_nat(U_3578),U_3576)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3577),U_3576))
      | ~ linordered_semidom(U_3578) ),
    inference(definitional_conversion,[status(esa)],[f_916_2]) ).

cnf(f_916_4,plain,
    ( hBOOL(hAPP(U_3578,bool,hAPP(U_3578,fun(U_3578,bool),ord_less(U_3578),hAPP(nat,U_3578,semiring_1_of_nat(U_3578),U_3577)),hAPP(nat,U_3578,semiring_1_of_nat(U_3578),U_3576)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3577),U_3576))
    | ~ linordered_semidom(U_3578) ),
    inference(clausify,[status(thm)],[f_916_3]) ).

fof(f_917_1,plain,
    ! [X_a] :
      ( ! [M_1,N] :
          ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M_1)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N))) )
      | ~ linordered_semidom(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_846_of__nat__less__imp__less]) ).

fof(f_917_2,plain,
    ! [U_3581] :
      ( ! [U_3580,U_3579] :
          ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3580),U_3579))
          | ~ hBOOL(hAPP(U_3581,bool,hAPP(U_3581,fun(U_3581,bool),ord_less(U_3581),hAPP(nat,U_3581,semiring_1_of_nat(U_3581),U_3580)),hAPP(nat,U_3581,semiring_1_of_nat(U_3581),U_3579))) )
      | ~ linordered_semidom(U_3581) ),
    inference(variable_rename,[status(thm)],[f_917_1]) ).

fof(f_917_3,plain,
    ! [U_3581,U_3579,U_3580] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3580),U_3579))
      | ~ hBOOL(hAPP(U_3581,bool,hAPP(U_3581,fun(U_3581,bool),ord_less(U_3581),hAPP(nat,U_3581,semiring_1_of_nat(U_3581),U_3580)),hAPP(nat,U_3581,semiring_1_of_nat(U_3581),U_3579)))
      | ~ linordered_semidom(U_3581) ),
    inference(definitional_conversion,[status(esa)],[f_917_2]) ).

cnf(f_917_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3580),U_3579))
    | ~ hBOOL(hAPP(U_3581,bool,hAPP(U_3581,fun(U_3581,bool),ord_less(U_3581),hAPP(nat,U_3581,semiring_1_of_nat(U_3581),U_3580)),hAPP(nat,U_3581,semiring_1_of_nat(U_3581),U_3579)))
    | ~ linordered_semidom(U_3581) ),
    inference(clausify,[status(thm)],[f_917_3]) ).

fof(f_918_1,plain,
    ! [M,Na] :
      ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(nat,int,semiring_1_of_nat(int),Na)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(nat,int,semiring_1_of_nat(int),Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_847_zless__int]) ).

fof(f_918_2,plain,
    ! [U_3583,U_3582] :
      ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),U_3583)),hAPP(nat,int,semiring_1_of_nat(int),U_3582)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3583),U_3582)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3583),U_3582))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),U_3583)),hAPP(nat,int,semiring_1_of_nat(int),U_3582))) ) ),
    inference(variable_rename,[status(thm)],[f_918_1]) ).

fof(f_918_3,plain,
    ( ! [U_3587,U_3585] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),U_3587)),hAPP(nat,int,semiring_1_of_nat(int),U_3585)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3587),U_3585)) )
    & ! [U_3586,U_3584] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3586),U_3584))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),U_3586)),hAPP(nat,int,semiring_1_of_nat(int),U_3584))) ) ),
    inference(miniscope,[status(thm)],[f_918_2]) ).

fof(f_918_4,plain,
    ( ! [U_3585,U_3587] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),U_3587)),hAPP(nat,int,semiring_1_of_nat(int),U_3585)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3587),U_3585)) )
    & ! [U_3586,U_3584] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3586),U_3584))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),U_3586)),hAPP(nat,int,semiring_1_of_nat(int),U_3584))) ) ),
    inference(definitional_conversion,[status(esa)],[f_918_3]) ).

cnf(f_918_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3586),U_3584))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),U_3586)),hAPP(nat,int,semiring_1_of_nat(int),U_3584))) ),
    inference(clausify,[status(thm)],[f_918_4]) ).

cnf(f_918_6,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),U_3587)),hAPP(nat,int,semiring_1_of_nat(int),U_3585)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3587),U_3585)) ),
    inference(clausify,[status(thm)],[f_918_4]) ).

fof(f_919_1,plain,
    ! [M,Na] :
      ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(nat,int,semiring_1_of_nat(int),Na)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(nat,int,semiring_1_of_nat(int),Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_848_zle__int]) ).

fof(f_919_2,plain,
    ! [U_3589,U_3588] :
      ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),U_3589)),hAPP(nat,int,semiring_1_of_nat(int),U_3588)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3589),U_3588)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3589),U_3588))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),U_3589)),hAPP(nat,int,semiring_1_of_nat(int),U_3588))) ) ),
    inference(variable_rename,[status(thm)],[f_919_1]) ).

fof(f_919_3,plain,
    ( ! [U_3593,U_3591] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),U_3593)),hAPP(nat,int,semiring_1_of_nat(int),U_3591)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3593),U_3591)) )
    & ! [U_3592,U_3590] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3592),U_3590))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),U_3592)),hAPP(nat,int,semiring_1_of_nat(int),U_3590))) ) ),
    inference(miniscope,[status(thm)],[f_919_2]) ).

fof(f_919_4,plain,
    ( ! [U_3591,U_3593] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),U_3593)),hAPP(nat,int,semiring_1_of_nat(int),U_3591)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3593),U_3591)) )
    & ! [U_3590,U_3592] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3592),U_3590))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),U_3592)),hAPP(nat,int,semiring_1_of_nat(int),U_3590))) ) ),
    inference(definitional_conversion,[status(esa)],[f_919_3]) ).

cnf(f_919_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3592),U_3590))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),U_3592)),hAPP(nat,int,semiring_1_of_nat(int),U_3590))) ),
    inference(clausify,[status(thm)],[f_919_4]) ).

cnf(f_919_6,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),U_3593)),hAPP(nat,int,semiring_1_of_nat(int),U_3591)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3593),U_3591)) ),
    inference(clausify,[status(thm)],[f_919_4]) ).

fof(f_920_1,plain,
    ! [M_1,N] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),M_1)),hAPP(nat,int,semiring_1_of_nat(int),N)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N)),
    inference(fof_nnf,[status(thm)],[fact_849_zadd__int]) ).

fof(f_920_2,plain,
    ! [U_3595,U_3594] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),U_3595)),hAPP(nat,int,semiring_1_of_nat(int),U_3594)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_3595),U_3594)),
    inference(variable_rename,[status(thm)],[f_920_1]) ).

fof(f_920_3,plain,
    ! [U_3594,U_3595] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),U_3595)),hAPP(nat,int,semiring_1_of_nat(int),U_3594)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_3595),U_3594)),
    inference(definitional_conversion,[status(esa)],[f_920_2]) ).

cnf(f_920_4,plain,
    hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),U_3595)),hAPP(nat,int,semiring_1_of_nat(int),U_3594)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_3595),U_3594)),
    inference(clausify,[status(thm)],[f_920_3]) ).

fof(f_921_1,plain,
    ! [M_1,N,Z] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),M_1)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),N)),Z)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N))),Z),
    inference(fof_nnf,[status(thm)],[fact_850_zadd__int__left]) ).

fof(f_921_2,plain,
    ! [U_3598,U_3597,U_3596] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),U_3598)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),U_3597)),U_3596)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_3598),U_3597))),U_3596),
    inference(variable_rename,[status(thm)],[f_921_1]) ).

fof(f_921_3,plain,
    ! [U_3596,U_3597,U_3598] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),U_3598)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),U_3597)),U_3596)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_3598),U_3597))),U_3596),
    inference(definitional_conversion,[status(esa)],[f_921_2]) ).

cnf(f_921_4,plain,
    hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),U_3598)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),U_3597)),U_3596)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_3598),U_3597))),U_3596),
    inference(clausify,[status(thm)],[f_921_3]) ).

fof(f_922_1,plain,
    ! [W_1,Z_2] :
      ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W_1),Z_2))
        | ! [N_1] : Z_2 != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_1),hAPP(nat,int,semiring_1_of_nat(int),N_1)) )
      & ( ? [N_1] : Z_2 = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_1),hAPP(nat,int,semiring_1_of_nat(int),N_1))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W_1),Z_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_851_zle__iff__zadd]) ).

fof(f_922_2,plain,
    ! [U_3602,U_3601] :
      ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3602),U_3601))
        | ! [U_3600] : U_3601 != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3602),hAPP(nat,int,semiring_1_of_nat(int),U_3600)) )
      & ( ? [U_3599] : U_3601 = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3602),hAPP(nat,int,semiring_1_of_nat(int),U_3599))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3602),U_3601)) ) ),
    inference(variable_rename,[status(thm)],[f_922_1]) ).

fof(f_922_3,plain,
    ( ! [U_3606,U_3604] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3606),U_3604))
        | ! [U_3600] : U_3604 != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3606),hAPP(nat,int,semiring_1_of_nat(int),U_3600)) )
    & ! [U_3605,U_3603] :
        ( ? [U_3599] : U_3603 = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3605),hAPP(nat,int,semiring_1_of_nat(int),U_3599))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3605),U_3603)) ) ),
    inference(miniscope,[status(thm)],[f_922_2]) ).

fof(f_922_4,plain,
    ( ! [U_3606,U_3604] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3606),U_3604))
        | ! [U_3600] : U_3604 != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3606),hAPP(nat,int,semiring_1_of_nat(int),U_3600)) )
    & ! [U_3605,U_3603] :
        ( U_3603 = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3605),hAPP(nat,int,semiring_1_of_nat(int),sK128(U_3605,U_3603)))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3605),U_3603)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK128]),skolemize(U_3599,sK128(U_3605,U_3603))],[f_922_3]) ).

fof(f_922_5,plain,
    ( ! [U_3606,U_3604,U_3600] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3606),U_3604))
        | U_3604 != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3606),hAPP(nat,int,semiring_1_of_nat(int),U_3600)) )
    & ! [U_3603,U_3605] :
        ( U_3603 = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3605),hAPP(nat,int,semiring_1_of_nat(int),sK128(U_3605,U_3603)))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3605),U_3603)) ) ),
    inference(definitional_conversion,[status(esa)],[f_922_4]) ).

cnf(f_922_6,plain,
    ( U_3603 = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3605),hAPP(nat,int,semiring_1_of_nat(int),sK128(U_3605,U_3603)))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3605),U_3603)) ),
    inference(clausify,[status(thm)],[f_922_5]) ).

cnf(f_922_7,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3606),U_3604))
    | U_3604 != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3606),hAPP(nat,int,semiring_1_of_nat(int),U_3600)) ),
    inference(clausify,[status(thm)],[f_922_5]) ).

fof(f_923_1,plain,
    ! [M_1,N] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),M_1)),hAPP(nat,int,semiring_1_of_nat(int),N)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N)),
    inference(fof_nnf,[status(thm)],[fact_852_zmult__int]) ).

fof(f_923_2,plain,
    ! [U_3608,U_3607] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),U_3608)),hAPP(nat,int,semiring_1_of_nat(int),U_3607)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3608),U_3607)),
    inference(variable_rename,[status(thm)],[f_923_1]) ).

fof(f_923_3,plain,
    ! [U_3607,U_3608] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),U_3608)),hAPP(nat,int,semiring_1_of_nat(int),U_3607)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3608),U_3607)),
    inference(definitional_conversion,[status(esa)],[f_923_2]) ).

cnf(f_923_4,plain,
    hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),U_3608)),hAPP(nat,int,semiring_1_of_nat(int),U_3607)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3608),U_3607)),
    inference(clausify,[status(thm)],[f_923_3]) ).

fof(f_924_1,plain,
    ! [M_1,N] : hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),M_1)),hAPP(nat,int,semiring_1_of_nat(int),N)),
    inference(fof_nnf,[status(thm)],[fact_853_int__mult]) ).

fof(f_924_2,plain,
    ! [U_3610,U_3609] : hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3610),U_3609)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),U_3610)),hAPP(nat,int,semiring_1_of_nat(int),U_3609)),
    inference(variable_rename,[status(thm)],[f_924_1]) ).

fof(f_924_3,plain,
    ! [U_3609,U_3610] : hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3610),U_3609)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),U_3610)),hAPP(nat,int,semiring_1_of_nat(int),U_3609)),
    inference(definitional_conversion,[status(esa)],[f_924_2]) ).

cnf(f_924_4,plain,
    hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3610),U_3609)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),U_3610)),hAPP(nat,int,semiring_1_of_nat(int),U_3609)),
    inference(clausify,[status(thm)],[f_924_3]) ).

fof(f_925_1,plain,
    ! [X_a] :
      ( ! [M_1,N] : hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M_1)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N))
      | ~ semiring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_854_of__nat__mult]) ).

fof(f_925_2,plain,
    ! [U_3613] :
      ( ! [U_3612,U_3611] : hAPP(nat,U_3613,semiring_1_of_nat(U_3613),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3612),U_3611)) = hAPP(U_3613,U_3613,hAPP(U_3613,fun(U_3613,U_3613),times_times(U_3613),hAPP(nat,U_3613,semiring_1_of_nat(U_3613),U_3612)),hAPP(nat,U_3613,semiring_1_of_nat(U_3613),U_3611))
      | ~ semiring_1(U_3613) ),
    inference(variable_rename,[status(thm)],[f_925_1]) ).

fof(f_925_3,plain,
    ! [U_3613,U_3611,U_3612] :
      ( hAPP(nat,U_3613,semiring_1_of_nat(U_3613),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3612),U_3611)) = hAPP(U_3613,U_3613,hAPP(U_3613,fun(U_3613,U_3613),times_times(U_3613),hAPP(nat,U_3613,semiring_1_of_nat(U_3613),U_3612)),hAPP(nat,U_3613,semiring_1_of_nat(U_3613),U_3611))
      | ~ semiring_1(U_3613) ),
    inference(definitional_conversion,[status(esa)],[f_925_2]) ).

cnf(f_925_4,plain,
    ( hAPP(nat,U_3613,semiring_1_of_nat(U_3613),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3612),U_3611)) = hAPP(U_3613,U_3613,hAPP(U_3613,fun(U_3613,U_3613),times_times(U_3613),hAPP(nat,U_3613,semiring_1_of_nat(U_3613),U_3612)),hAPP(nat,U_3613,semiring_1_of_nat(U_3613),U_3611))
    | ~ semiring_1(U_3613) ),
    inference(clausify,[status(thm)],[f_925_3]) ).

fof(f_926_1,plain,
    ! [X,Y] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),X)),hAPP(nat,int,semiring_1_of_nat(int),Y)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X),Y)),
    inference(fof_nnf,[status(thm)],[fact_855_Nat__Transfer_Otransfer__int__nat__functions_I2_J]) ).

fof(f_926_2,plain,
    ! [U_3615,U_3614] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),U_3615)),hAPP(nat,int,semiring_1_of_nat(int),U_3614)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3615),U_3614)),
    inference(variable_rename,[status(thm)],[f_926_1]) ).

fof(f_926_3,plain,
    ! [U_3614,U_3615] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),U_3615)),hAPP(nat,int,semiring_1_of_nat(int),U_3614)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3615),U_3614)),
    inference(definitional_conversion,[status(esa)],[f_926_2]) ).

cnf(f_926_4,plain,
    hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),U_3615)),hAPP(nat,int,semiring_1_of_nat(int),U_3614)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3615),U_3614)),
    inference(clausify,[status(thm)],[f_926_3]) ).

fof(f_927_1,plain,
    ! [X_1,Y_2] :
      ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(nat,int,semiring_1_of_nat(int),Y_2)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y_2)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y_2))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(nat,int,semiring_1_of_nat(int),Y_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_856_transfer__int__nat__relations_I2_J]) ).

fof(f_927_2,plain,
    ! [U_3617,U_3616] :
      ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),U_3617)),hAPP(nat,int,semiring_1_of_nat(int),U_3616)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3617),U_3616)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3617),U_3616))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),U_3617)),hAPP(nat,int,semiring_1_of_nat(int),U_3616))) ) ),
    inference(variable_rename,[status(thm)],[f_927_1]) ).

fof(f_927_3,plain,
    ( ! [U_3621,U_3619] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),U_3621)),hAPP(nat,int,semiring_1_of_nat(int),U_3619)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3621),U_3619)) )
    & ! [U_3620,U_3618] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3620),U_3618))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),U_3620)),hAPP(nat,int,semiring_1_of_nat(int),U_3618))) ) ),
    inference(miniscope,[status(thm)],[f_927_2]) ).

fof(f_927_4,plain,
    ( ! [U_3619,U_3621] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),U_3621)),hAPP(nat,int,semiring_1_of_nat(int),U_3619)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3621),U_3619)) )
    & ! [U_3620,U_3618] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3620),U_3618))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),U_3620)),hAPP(nat,int,semiring_1_of_nat(int),U_3618))) ) ),
    inference(definitional_conversion,[status(esa)],[f_927_3]) ).

cnf(f_927_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3620),U_3618))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),U_3620)),hAPP(nat,int,semiring_1_of_nat(int),U_3618))) ),
    inference(clausify,[status(thm)],[f_927_4]) ).

cnf(f_927_6,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),U_3621)),hAPP(nat,int,semiring_1_of_nat(int),U_3619)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3621),U_3619)) ),
    inference(clausify,[status(thm)],[f_927_4]) ).

fof(f_928_1,plain,
    ! [X_1,Y_2] :
      ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(nat,int,semiring_1_of_nat(int),Y_2)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X_1),Y_2)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X_1),Y_2))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(nat,int,semiring_1_of_nat(int),Y_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_857_transfer__int__nat__relations_I3_J]) ).

fof(f_928_2,plain,
    ! [U_3623,U_3622] :
      ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),U_3623)),hAPP(nat,int,semiring_1_of_nat(int),U_3622)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3623),U_3622)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3623),U_3622))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),U_3623)),hAPP(nat,int,semiring_1_of_nat(int),U_3622))) ) ),
    inference(variable_rename,[status(thm)],[f_928_1]) ).

fof(f_928_3,plain,
    ( ! [U_3627,U_3625] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),U_3627)),hAPP(nat,int,semiring_1_of_nat(int),U_3625)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3627),U_3625)) )
    & ! [U_3626,U_3624] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3626),U_3624))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),U_3626)),hAPP(nat,int,semiring_1_of_nat(int),U_3624))) ) ),
    inference(miniscope,[status(thm)],[f_928_2]) ).

fof(f_928_4,plain,
    ( ! [U_3625,U_3627] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),U_3627)),hAPP(nat,int,semiring_1_of_nat(int),U_3625)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3627),U_3625)) )
    & ! [U_3624,U_3626] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3626),U_3624))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),U_3626)),hAPP(nat,int,semiring_1_of_nat(int),U_3624))) ) ),
    inference(definitional_conversion,[status(esa)],[f_928_3]) ).

cnf(f_928_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3626),U_3624))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),U_3626)),hAPP(nat,int,semiring_1_of_nat(int),U_3624))) ),
    inference(clausify,[status(thm)],[f_928_4]) ).

cnf(f_928_6,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),U_3627)),hAPP(nat,int,semiring_1_of_nat(int),U_3625)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3627),U_3625)) ),
    inference(clausify,[status(thm)],[f_928_4]) ).

fof(f_929_1,plain,
    ! [X,Y] : hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,hAPP(nat,int,semiring_1_of_nat(int),X)),hAPP(nat,int,semiring_1_of_nat(int),Y)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X),Y)),
    inference(fof_nnf,[status(thm)],[fact_858_Nat__Transfer_Otransfer__int__nat__functions_I3_J]) ).

fof(f_929_2,plain,
    ! [U_3629,U_3628] : hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,hAPP(nat,int,semiring_1_of_nat(int),U_3629)),hAPP(nat,int,semiring_1_of_nat(int),U_3628)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3629),U_3628)),
    inference(variable_rename,[status(thm)],[f_929_1]) ).

fof(f_929_3,plain,
    ! [U_3628,U_3629] : hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,hAPP(nat,int,semiring_1_of_nat(int),U_3629)),hAPP(nat,int,semiring_1_of_nat(int),U_3628)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3629),U_3628)),
    inference(definitional_conversion,[status(esa)],[f_929_2]) ).

cnf(f_929_4,plain,
    hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,hAPP(nat,int,semiring_1_of_nat(int),U_3629)),hAPP(nat,int,semiring_1_of_nat(int),U_3628)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3629),U_3628)),
    inference(clausify,[status(thm)],[f_929_3]) ).

fof(f_930_1,plain,
    ! [X,Y] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),X)),hAPP(nat,int,semiring_1_of_nat(int),Y)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X),Y)),
    inference(fof_nnf,[status(thm)],[fact_859_Nat__Transfer_Otransfer__int__nat__functions_I1_J]) ).

fof(f_930_2,plain,
    ! [U_3631,U_3630] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),U_3631)),hAPP(nat,int,semiring_1_of_nat(int),U_3630)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_3631),U_3630)),
    inference(variable_rename,[status(thm)],[f_930_1]) ).

fof(f_930_3,plain,
    ! [U_3630,U_3631] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),U_3631)),hAPP(nat,int,semiring_1_of_nat(int),U_3630)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_3631),U_3630)),
    inference(definitional_conversion,[status(esa)],[f_930_2]) ).

cnf(f_930_4,plain,
    hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),U_3631)),hAPP(nat,int,semiring_1_of_nat(int),U_3630)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_3631),U_3630)),
    inference(clausify,[status(thm)],[f_930_3]) ).

fof(f_931_1,plain,
    ! [A_3] : hAPP(fun(nat,bool),nat,finite_card(nat),A_3) = hAPP(fun(int,bool),nat,finite_card(int),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3)),
    inference(fof_nnf,[status(thm)],[fact_860_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J]) ).

fof(f_931_2,plain,
    ! [U_3632] : hAPP(fun(nat,bool),nat,finite_card(nat),U_3632) = hAPP(fun(int,bool),nat,finite_card(int),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3632)),
    inference(variable_rename,[status(thm)],[f_931_1]) ).

fof(f_931_3,plain,
    ! [U_3632] : hAPP(fun(nat,bool),nat,finite_card(nat),U_3632) = hAPP(fun(int,bool),nat,finite_card(int),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3632)),
    inference(definitional_conversion,[status(esa)],[f_931_2]) ).

cnf(f_931_4,plain,
    hAPP(fun(nat,bool),nat,finite_card(nat),U_3632) = hAPP(fun(int,bool),nat,finite_card(int),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3632)),
    inference(clausify,[status(thm)],[f_931_3]) ).

fof(f_932_1,plain,
    ! [A_3] :
      ( ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),A_3))
        | ~ hBOOL(hAPP(fun(int,bool),bool,finite_finite(int),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3))) )
      & ( hBOOL(hAPP(fun(int,bool),bool,finite_finite(int),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3)))
        | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),A_3)) ) ),
    inference(fof_nnf,[status(thm)],[fact_861_transfer__nat__int__set__relations_I1_J]) ).

fof(f_932_2,plain,
    ! [U_3633] :
      ( ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_3633))
        | ~ hBOOL(hAPP(fun(int,bool),bool,finite_finite(int),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3633))) )
      & ( hBOOL(hAPP(fun(int,bool),bool,finite_finite(int),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3633)))
        | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_3633)) ) ),
    inference(variable_rename,[status(thm)],[f_932_1]) ).

fof(f_932_3,plain,
    ( ! [U_3635] :
        ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_3635))
        | ~ hBOOL(hAPP(fun(int,bool),bool,finite_finite(int),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3635))) )
    & ! [U_3634] :
        ( hBOOL(hAPP(fun(int,bool),bool,finite_finite(int),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3634)))
        | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_3634)) ) ),
    inference(miniscope,[status(thm)],[f_932_2]) ).

fof(f_932_4,plain,
    ( ! [U_3635] :
        ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_3635))
        | ~ hBOOL(hAPP(fun(int,bool),bool,finite_finite(int),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3635))) )
    & ! [U_3634] :
        ( hBOOL(hAPP(fun(int,bool),bool,finite_finite(int),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3634)))
        | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_3634)) ) ),
    inference(definitional_conversion,[status(esa)],[f_932_3]) ).

cnf(f_932_5,plain,
    ( hBOOL(hAPP(fun(int,bool),bool,finite_finite(int),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3634)))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_3634)) ),
    inference(clausify,[status(thm)],[f_932_4]) ).

cnf(f_932_6,plain,
    ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_3635))
    | ~ hBOOL(hAPP(fun(int,bool),bool,finite_finite(int),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3635))) ),
    inference(clausify,[status(thm)],[f_932_4]) ).

fof(f_933_1,plain,
    one_one(int) = hAPP(nat,int,semiring_1_of_nat(int),one_one(nat)),
    inference(fof_nnf,[status(thm)],[fact_862_transfer__int__nat__numerals_I2_J]) ).

fof(f_933_2,plain,
    one_one(int) = hAPP(nat,int,semiring_1_of_nat(int),one_one(nat)),
    inference(definitional_conversion,[status(esa)],[f_933_1]) ).

cnf(f_933_3,plain,
    one_one(int) = hAPP(nat,int,semiring_1_of_nat(int),one_one(nat)),
    inference(clausify,[status(thm)],[f_933_2]) ).

fof(f_934_1,plain,
    zero_zero(int) = hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat)),
    inference(fof_nnf,[status(thm)],[fact_863_transfer__int__nat__numerals_I1_J]) ).

fof(f_934_2,plain,
    zero_zero(int) = hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat)),
    inference(definitional_conversion,[status(esa)],[f_934_1]) ).

cnf(f_934_3,plain,
    zero_zero(int) = hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat)),
    inference(clausify,[status(thm)],[f_934_2]) ).

fof(f_935_1,plain,
    ! [Pa] : hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),Pa)) = hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,int),fun(nat,bool),hAPP(fun(int,bool),fun(fun(nat,int),fun(nat,bool)),combb(int,bool,nat),Pa),semiring_1_of_nat(int)))),
    inference(fof_nnf,[status(thm)],[fact_864_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J]) ).

fof(f_935_2,plain,
    ! [U_3636] : hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),U_3636)) = hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,int),fun(nat,bool),hAPP(fun(int,bool),fun(fun(nat,int),fun(nat,bool)),combb(int,bool,nat),U_3636),semiring_1_of_nat(int)))),
    inference(variable_rename,[status(thm)],[f_935_1]) ).

fof(f_935_3,plain,
    ! [U_3636] : hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),U_3636)) = hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,int),fun(nat,bool),hAPP(fun(int,bool),fun(fun(nat,int),fun(nat,bool)),combb(int,bool,nat),U_3636),semiring_1_of_nat(int)))),
    inference(definitional_conversion,[status(esa)],[f_935_2]) ).

cnf(f_935_4,plain,
    hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),U_3636)) = hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,int),fun(nat,bool),hAPP(fun(int,bool),fun(fun(nat,int),fun(nat,bool)),combb(int,bool,nat),U_3636),semiring_1_of_nat(int)))),
    inference(clausify,[status(thm)],[f_935_3]) ).

fof(f_936_1,plain,
    ! [Z] : hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),Z))),
    inference(fof_nnf,[status(thm)],[fact_865_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J]) ).

fof(f_936_2,plain,
    ! [U_3637] : hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),U_3637))),
    inference(variable_rename,[status(thm)],[f_936_1]) ).

fof(f_936_3,plain,
    ! [U_3637] : hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),U_3637))),
    inference(definitional_conversion,[status(esa)],[f_936_2]) ).

cnf(f_936_4,plain,
    hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),U_3637))),
    inference(clausify,[status(thm)],[f_936_3]) ).

fof(f_937_1,plain,
    ! [Pa] :
      ( ( ? [X_2] :
            ( hBOOL(hAPP(int,bool,Pa,X_2))
            & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)) )
        | ! [X_2] : ~ hBOOL(hAPP(int,bool,Pa,hAPP(nat,int,semiring_1_of_nat(int),X_2))) )
      & ( ? [X_2] : hBOOL(hAPP(int,bool,Pa,hAPP(nat,int,semiring_1_of_nat(int),X_2)))
        | ! [X_2] :
            ( ~ hBOOL(hAPP(int,bool,Pa,X_2))
            | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_866_transfer__int__nat__quantifiers_I2_J]) ).

fof(f_937_2,plain,
    ! [U_3642] :
      ( ( ? [U_3641] :
            ( hBOOL(hAPP(int,bool,U_3642,U_3641))
            & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3641)) )
        | ! [U_3640] : ~ hBOOL(hAPP(int,bool,U_3642,hAPP(nat,int,semiring_1_of_nat(int),U_3640))) )
      & ( ? [U_3639] : hBOOL(hAPP(int,bool,U_3642,hAPP(nat,int,semiring_1_of_nat(int),U_3639)))
        | ! [U_3638] :
            ( ~ hBOOL(hAPP(int,bool,U_3642,U_3638))
            | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3638)) ) ) ),
    inference(variable_rename,[status(thm)],[f_937_1]) ).

fof(f_937_3,plain,
    ( ! [U_3644] :
        ( ? [U_3641] :
            ( hBOOL(hAPP(int,bool,U_3644,U_3641))
            & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3641)) )
        | ! [U_3640] : ~ hBOOL(hAPP(int,bool,U_3644,hAPP(nat,int,semiring_1_of_nat(int),U_3640))) )
    & ! [U_3643] :
        ( ? [U_3639] : hBOOL(hAPP(int,bool,U_3643,hAPP(nat,int,semiring_1_of_nat(int),U_3639)))
        | ! [U_3638] :
            ( ~ hBOOL(hAPP(int,bool,U_3643,U_3638))
            | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3638)) ) ) ),
    inference(miniscope,[status(thm)],[f_937_2]) ).

fof(f_937_4,plain,
    ( ! [U_3644] :
        ( ? [U_3641] :
            ( hBOOL(hAPP(int,bool,U_3644,U_3641))
            & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3641)) )
        | ! [U_3640] : ~ hBOOL(hAPP(int,bool,U_3644,hAPP(nat,int,semiring_1_of_nat(int),U_3640))) )
    & ! [U_3643] :
        ( hBOOL(hAPP(int,bool,U_3643,hAPP(nat,int,semiring_1_of_nat(int),sK129(U_3643))))
        | ! [U_3638] :
            ( ~ hBOOL(hAPP(int,bool,U_3643,U_3638))
            | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3638)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK129]),skolemize(U_3639,sK129(U_3643))],[f_937_3]) ).

fof(f_937_5,plain,
    ( ! [U_3644] :
        ( ( hBOOL(hAPP(int,bool,U_3644,sK130(U_3644)))
          & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),sK130(U_3644))) )
        | ! [U_3640] : ~ hBOOL(hAPP(int,bool,U_3644,hAPP(nat,int,semiring_1_of_nat(int),U_3640))) )
    & ! [U_3643] :
        ( hBOOL(hAPP(int,bool,U_3643,hAPP(nat,int,semiring_1_of_nat(int),sK129(U_3643))))
        | ! [U_3638] :
            ( ~ hBOOL(hAPP(int,bool,U_3643,U_3638))
            | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3638)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK130]),skolemize(U_3641,sK130(U_3644))],[f_937_4]) ).

fof(f_937_6,plain,
    ( ! [U_3644] :
        ( hBOOL(hAPP(int,bool,U_3644,sK130(U_3644)))
        | ~ sP282(U_3644) )
    & ! [U_3644] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),sK130(U_3644)))
        | ~ sP282(U_3644) )
    & ! [U_3640,U_3644] :
        ( sP282(U_3644)
        | ~ hBOOL(hAPP(int,bool,U_3644,hAPP(nat,int,semiring_1_of_nat(int),U_3640))) )
    & ! [U_3638,U_3643] :
        ( hBOOL(hAPP(int,bool,U_3643,hAPP(nat,int,semiring_1_of_nat(int),sK129(U_3643))))
        | ~ hBOOL(hAPP(int,bool,U_3643,U_3638))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3638)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP282])],[f_937_5]) ).

cnf(f_937_7,plain,
    ( hBOOL(hAPP(int,bool,U_3643,hAPP(nat,int,semiring_1_of_nat(int),sK129(U_3643))))
    | ~ hBOOL(hAPP(int,bool,U_3643,U_3638))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3638)) ),
    inference(clausify,[status(thm)],[f_937_6]) ).

cnf(f_937_8,plain,
    ( sP282(U_3644)
    | ~ hBOOL(hAPP(int,bool,U_3644,hAPP(nat,int,semiring_1_of_nat(int),U_3640))) ),
    inference(clausify,[status(thm)],[f_937_6]) ).

cnf(f_937_9,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),sK130(U_3644)))
    | ~ sP282(U_3644) ),
    inference(clausify,[status(thm)],[f_937_6]) ).

cnf(f_937_10,plain,
    ( hBOOL(hAPP(int,bool,U_3644,sK130(U_3644)))
    | ~ sP282(U_3644) ),
    inference(clausify,[status(thm)],[f_937_6]) ).

fof(f_938_1,plain,
    ! [Pa] :
      ( ( ! [X_2] :
            ( hBOOL(hAPP(int,bool,Pa,X_2))
            | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)) )
        | ? [X_2] : ~ hBOOL(hAPP(int,bool,Pa,hAPP(nat,int,semiring_1_of_nat(int),X_2))) )
      & ( ! [X_2] : hBOOL(hAPP(int,bool,Pa,hAPP(nat,int,semiring_1_of_nat(int),X_2)))
        | ? [X_2] :
            ( ~ hBOOL(hAPP(int,bool,Pa,X_2))
            & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_867_transfer__int__nat__quantifiers_I1_J]) ).

fof(f_938_2,plain,
    ! [U_3649] :
      ( ( ! [U_3648] :
            ( hBOOL(hAPP(int,bool,U_3649,U_3648))
            | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3648)) )
        | ? [U_3647] : ~ hBOOL(hAPP(int,bool,U_3649,hAPP(nat,int,semiring_1_of_nat(int),U_3647))) )
      & ( ! [U_3646] : hBOOL(hAPP(int,bool,U_3649,hAPP(nat,int,semiring_1_of_nat(int),U_3646)))
        | ? [U_3645] :
            ( ~ hBOOL(hAPP(int,bool,U_3649,U_3645))
            & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3645)) ) ) ),
    inference(variable_rename,[status(thm)],[f_938_1]) ).

fof(f_938_3,plain,
    ( ! [U_3651] :
        ( ! [U_3648] :
            ( hBOOL(hAPP(int,bool,U_3651,U_3648))
            | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3648)) )
        | ? [U_3647] : ~ hBOOL(hAPP(int,bool,U_3651,hAPP(nat,int,semiring_1_of_nat(int),U_3647))) )
    & ! [U_3650] :
        ( ! [U_3646] : hBOOL(hAPP(int,bool,U_3650,hAPP(nat,int,semiring_1_of_nat(int),U_3646)))
        | ? [U_3645] :
            ( ~ hBOOL(hAPP(int,bool,U_3650,U_3645))
            & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3645)) ) ) ),
    inference(miniscope,[status(thm)],[f_938_2]) ).

fof(f_938_4,plain,
    ( ! [U_3651] :
        ( ! [U_3648] :
            ( hBOOL(hAPP(int,bool,U_3651,U_3648))
            | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3648)) )
        | ? [U_3647] : ~ hBOOL(hAPP(int,bool,U_3651,hAPP(nat,int,semiring_1_of_nat(int),U_3647))) )
    & ! [U_3650] :
        ( ! [U_3646] : hBOOL(hAPP(int,bool,U_3650,hAPP(nat,int,semiring_1_of_nat(int),U_3646)))
        | ( ~ hBOOL(hAPP(int,bool,U_3650,sK131(U_3650)))
          & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),sK131(U_3650))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK131]),skolemize(U_3645,sK131(U_3650))],[f_938_3]) ).

fof(f_938_5,plain,
    ( ! [U_3651] :
        ( ! [U_3648] :
            ( hBOOL(hAPP(int,bool,U_3651,U_3648))
            | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3648)) )
        | ~ hBOOL(hAPP(int,bool,U_3651,hAPP(nat,int,semiring_1_of_nat(int),sK132(U_3651)))) )
    & ! [U_3650] :
        ( ! [U_3646] : hBOOL(hAPP(int,bool,U_3650,hAPP(nat,int,semiring_1_of_nat(int),U_3646)))
        | ( ~ hBOOL(hAPP(int,bool,U_3650,sK131(U_3650)))
          & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),sK131(U_3650))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK132]),skolemize(U_3647,sK132(U_3651))],[f_938_4]) ).

fof(f_938_6,plain,
    ( ! [U_3650] :
        ( ~ hBOOL(hAPP(int,bool,U_3650,sK131(U_3650)))
        | ~ sP283(U_3650) )
    & ! [U_3650] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),sK131(U_3650)))
        | ~ sP283(U_3650) )
    & ! [U_3648,U_3651] :
        ( hBOOL(hAPP(int,bool,U_3651,U_3648))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3648))
        | ~ hBOOL(hAPP(int,bool,U_3651,hAPP(nat,int,semiring_1_of_nat(int),sK132(U_3651)))) )
    & ! [U_3646,U_3650] :
        ( hBOOL(hAPP(int,bool,U_3650,hAPP(nat,int,semiring_1_of_nat(int),U_3646)))
        | sP283(U_3650) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP283])],[f_938_5]) ).

cnf(f_938_7,plain,
    ( hBOOL(hAPP(int,bool,U_3650,hAPP(nat,int,semiring_1_of_nat(int),U_3646)))
    | sP283(U_3650) ),
    inference(clausify,[status(thm)],[f_938_6]) ).

cnf(f_938_8,plain,
    ( hBOOL(hAPP(int,bool,U_3651,U_3648))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3648))
    | ~ hBOOL(hAPP(int,bool,U_3651,hAPP(nat,int,semiring_1_of_nat(int),sK132(U_3651)))) ),
    inference(clausify,[status(thm)],[f_938_6]) ).

cnf(f_938_9,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),sK131(U_3650)))
    | ~ sP283(U_3650) ),
    inference(clausify,[status(thm)],[f_938_6]) ).

cnf(f_938_10,plain,
    ( ~ hBOOL(hAPP(int,bool,U_3650,sK131(U_3650)))
    | ~ sP283(U_3650) ),
    inference(clausify,[status(thm)],[f_938_6]) ).

fof(f_939_1,plain,
    ! [Na] :
      ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),Na)),zero_zero(int)))
        | Na != zero_zero(nat) )
      & ( Na = zero_zero(nat)
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),Na)),zero_zero(int))) ) ),
    inference(fof_nnf,[status(thm)],[fact_868_int__le__0__conv]) ).

fof(f_939_2,plain,
    ! [U_3652] :
      ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),U_3652)),zero_zero(int)))
        | U_3652 != zero_zero(nat) )
      & ( U_3652 = zero_zero(nat)
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),U_3652)),zero_zero(int))) ) ),
    inference(variable_rename,[status(thm)],[f_939_1]) ).

fof(f_939_3,plain,
    ( ! [U_3654] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),U_3654)),zero_zero(int)))
        | U_3654 != zero_zero(nat) )
    & ! [U_3653] :
        ( U_3653 = zero_zero(nat)
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),U_3653)),zero_zero(int))) ) ),
    inference(miniscope,[status(thm)],[f_939_2]) ).

fof(f_939_4,plain,
    ( ! [U_3654] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),U_3654)),zero_zero(int)))
        | U_3654 != zero_zero(nat) )
    & ! [U_3653] :
        ( U_3653 = zero_zero(nat)
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),U_3653)),zero_zero(int))) ) ),
    inference(definitional_conversion,[status(esa)],[f_939_3]) ).

cnf(f_939_5,plain,
    ( U_3653 = zero_zero(nat)
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),U_3653)),zero_zero(int))) ),
    inference(clausify,[status(thm)],[f_939_4]) ).

cnf(f_939_6,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),U_3654)),zero_zero(int)))
    | U_3654 != zero_zero(nat) ),
    inference(clausify,[status(thm)],[f_939_4]) ).

fof(f_940_1,plain,
    hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,zero_zero(nat))) = one_one(int),
    inference(fof_nnf,[status(thm)],[fact_869_int__Suc0__eq__1]) ).

fof(f_940_2,plain,
    hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,zero_zero(nat))) = one_one(int),
    inference(definitional_conversion,[status(esa)],[f_940_1]) ).

cnf(f_940_3,plain,
    hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,zero_zero(nat))) = one_one(int),
    inference(clausify,[status(thm)],[f_940_2]) ).

fof(f_941_1,plain,
    ! [W_1,Z_2] :
      ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_2))
        | ! [N_1] : Z_2 != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_1),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,N_1))) )
      & ( ? [N_1] : Z_2 = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_1),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,N_1)))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_870_zless__iff__Suc__zadd]) ).

fof(f_941_2,plain,
    ! [U_3658,U_3657] :
      ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3658),U_3657))
        | ! [U_3656] : U_3657 != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3658),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,U_3656))) )
      & ( ? [U_3655] : U_3657 = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3658),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,U_3655)))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3658),U_3657)) ) ),
    inference(variable_rename,[status(thm)],[f_941_1]) ).

fof(f_941_3,plain,
    ( ! [U_3662,U_3660] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3662),U_3660))
        | ! [U_3656] : U_3660 != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3662),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,U_3656))) )
    & ! [U_3661,U_3659] :
        ( ? [U_3655] : U_3659 = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3661),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,U_3655)))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3661),U_3659)) ) ),
    inference(miniscope,[status(thm)],[f_941_2]) ).

fof(f_941_4,plain,
    ( ! [U_3662,U_3660] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3662),U_3660))
        | ! [U_3656] : U_3660 != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3662),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,U_3656))) )
    & ! [U_3661,U_3659] :
        ( U_3659 = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3661),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,sK133(U_3661,U_3659))))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3661),U_3659)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK133]),skolemize(U_3655,sK133(U_3661,U_3659))],[f_941_3]) ).

fof(f_941_5,plain,
    ( ! [U_3660,U_3662,U_3656] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3662),U_3660))
        | U_3660 != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3662),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,U_3656))) )
    & ! [U_3659,U_3661] :
        ( U_3659 = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3661),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,sK133(U_3661,U_3659))))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3661),U_3659)) ) ),
    inference(definitional_conversion,[status(esa)],[f_941_4]) ).

cnf(f_941_6,plain,
    ( U_3659 = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3661),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,sK133(U_3661,U_3659))))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3661),U_3659)) ),
    inference(clausify,[status(thm)],[f_941_5]) ).

cnf(f_941_7,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3662),U_3660))
    | U_3660 != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3662),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,U_3656))) ),
    inference(clausify,[status(thm)],[f_941_5]) ).

fof(f_942_1,plain,
    ! [M_1] : hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,M_1)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),M_1)),
    inference(fof_nnf,[status(thm)],[fact_871_int__Suc]) ).

fof(f_942_2,plain,
    ! [U_3663] : hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,U_3663)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),U_3663)),
    inference(variable_rename,[status(thm)],[f_942_1]) ).

fof(f_942_3,plain,
    ! [U_3663] : hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,U_3663)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),U_3663)),
    inference(definitional_conversion,[status(esa)],[f_942_2]) ).

cnf(f_942_4,plain,
    hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,U_3663)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),U_3663)),
    inference(clausify,[status(thm)],[f_942_3]) ).

fof(f_943_1,plain,
    ! [N,M_1] :
      ( hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),M_1)),hAPP(nat,int,semiring_1_of_nat(int),N)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M_1)) ),
    inference(fof_nnf,[status(thm)],[fact_872_zdiff__int]) ).

fof(f_943_2,plain,
    ! [U_3665,U_3664] :
      ( hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),U_3664)),hAPP(nat,int,semiring_1_of_nat(int),U_3665)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3664),U_3665))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3665),U_3664)) ),
    inference(variable_rename,[status(thm)],[f_943_1]) ).

fof(f_943_3,plain,
    ! [U_3664,U_3665] :
      ( hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),U_3664)),hAPP(nat,int,semiring_1_of_nat(int),U_3665)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3664),U_3665))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3665),U_3664)) ),
    inference(definitional_conversion,[status(esa)],[f_943_2]) ).

cnf(f_943_4,plain,
    ( hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),U_3664)),hAPP(nat,int,semiring_1_of_nat(int),U_3665)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3664),U_3665))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3665),U_3664)) ),
    inference(clausify,[status(thm)],[f_943_3]) ).

fof(f_944_1,plain,
    ! [X_a] :
      ( ! [M_1] : hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,suc,M_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),hAPP(nat,X_a,semiring_1_of_nat(X_a),M_1))
      | ~ semiring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_873_of__nat__Suc]) ).

fof(f_944_2,plain,
    ! [U_3667] :
      ( ! [U_3666] : hAPP(nat,U_3667,semiring_1_of_nat(U_3667),hAPP(nat,nat,suc,U_3666)) = hAPP(U_3667,U_3667,hAPP(U_3667,fun(U_3667,U_3667),plus_plus(U_3667),one_one(U_3667)),hAPP(nat,U_3667,semiring_1_of_nat(U_3667),U_3666))
      | ~ semiring_1(U_3667) ),
    inference(variable_rename,[status(thm)],[f_944_1]) ).

fof(f_944_3,plain,
    ! [U_3667,U_3666] :
      ( hAPP(nat,U_3667,semiring_1_of_nat(U_3667),hAPP(nat,nat,suc,U_3666)) = hAPP(U_3667,U_3667,hAPP(U_3667,fun(U_3667,U_3667),plus_plus(U_3667),one_one(U_3667)),hAPP(nat,U_3667,semiring_1_of_nat(U_3667),U_3666))
      | ~ semiring_1(U_3667) ),
    inference(definitional_conversion,[status(esa)],[f_944_2]) ).

cnf(f_944_4,plain,
    ( hAPP(nat,U_3667,semiring_1_of_nat(U_3667),hAPP(nat,nat,suc,U_3666)) = hAPP(U_3667,U_3667,hAPP(U_3667,fun(U_3667,U_3667),plus_plus(U_3667),one_one(U_3667)),hAPP(nat,U_3667,semiring_1_of_nat(U_3667),U_3666))
    | ~ semiring_1(U_3667) ),
    inference(clausify,[status(thm)],[f_944_3]) ).

fof(f_945_1,plain,
    ! [X_a] :
      ( ! [N,M_1] :
          ( hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M_1)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M_1)) )
      | ~ ring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_874_of__nat__diff]) ).

fof(f_945_2,plain,
    ! [U_3670] :
      ( ! [U_3669,U_3668] :
          ( hAPP(nat,U_3670,semiring_1_of_nat(U_3670),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3668),U_3669)) = hAPP(U_3670,U_3670,hAPP(U_3670,fun(U_3670,U_3670),minus_minus(U_3670),hAPP(nat,U_3670,semiring_1_of_nat(U_3670),U_3668)),hAPP(nat,U_3670,semiring_1_of_nat(U_3670),U_3669))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3669),U_3668)) )
      | ~ ring_1(U_3670) ),
    inference(variable_rename,[status(thm)],[f_945_1]) ).

fof(f_945_3,plain,
    ! [U_3668,U_3669,U_3670] :
      ( hAPP(nat,U_3670,semiring_1_of_nat(U_3670),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3668),U_3669)) = hAPP(U_3670,U_3670,hAPP(U_3670,fun(U_3670,U_3670),minus_minus(U_3670),hAPP(nat,U_3670,semiring_1_of_nat(U_3670),U_3668)),hAPP(nat,U_3670,semiring_1_of_nat(U_3670),U_3669))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3669),U_3668))
      | ~ ring_1(U_3670) ),
    inference(definitional_conversion,[status(esa)],[f_945_2]) ).

cnf(f_945_4,plain,
    ( hAPP(nat,U_3670,semiring_1_of_nat(U_3670),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3668),U_3669)) = hAPP(U_3670,U_3670,hAPP(U_3670,fun(U_3670,U_3670),minus_minus(U_3670),hAPP(nat,U_3670,semiring_1_of_nat(U_3670),U_3668)),hAPP(nat,U_3670,semiring_1_of_nat(U_3670),U_3669))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3669),U_3668))
    | ~ ring_1(U_3670) ),
    inference(clausify,[status(thm)],[f_945_3]) ).

fof(f_946_1,plain,
    ! [Na] :
      ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),Na)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_875_zero__less__int__conv]) ).

fof(f_946_2,plain,
    ! [U_3671] :
      ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),U_3671)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_3671)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_3671))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),U_3671))) ) ),
    inference(variable_rename,[status(thm)],[f_946_1]) ).

fof(f_946_3,plain,
    ( ! [U_3673] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),U_3673)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_3673)) )
    & ! [U_3672] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_3672))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),U_3672))) ) ),
    inference(miniscope,[status(thm)],[f_946_2]) ).

fof(f_946_4,plain,
    ( ! [U_3673] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),U_3673)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_3673)) )
    & ! [U_3672] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_3672))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),U_3672))) ) ),
    inference(definitional_conversion,[status(esa)],[f_946_3]) ).

cnf(f_946_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_3672))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),U_3672))) ),
    inference(clausify,[status(thm)],[f_946_4]) ).

cnf(f_946_6,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),U_3673)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_3673)) ),
    inference(clausify,[status(thm)],[f_946_4]) ).

fof(f_947_1,plain,
    ! [K_1,I_2,J] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),K_1)),I_2)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),K_1)),J)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_2),J)) ),
    inference(fof_nnf,[status(thm)],[fact_876_zmult__zless__mono2__lemma]) ).

fof(f_947_2,plain,
    ! [U_3676,U_3675,U_3674] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),U_3676)),U_3675)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),U_3676)),U_3674)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_3676))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3675),U_3674)) ),
    inference(variable_rename,[status(thm)],[f_947_1]) ).

fof(f_947_3,plain,
    ! [U_3674,U_3675,U_3676] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),U_3676)),U_3675)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),U_3676)),U_3674)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_3676))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3675),U_3674)) ),
    inference(definitional_conversion,[status(esa)],[f_947_2]) ).

cnf(f_947_4,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),U_3676)),U_3675)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),U_3676)),U_3674)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_3676))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3675),U_3674)) ),
    inference(clausify,[status(thm)],[f_947_3]) ).

fof(f_948_1,plain,
    ! [X_b] :
      ( ! [Na] :
          ( ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),hAPP(nat,X_b,semiring_1_of_nat(X_b),Na)))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)) )
          & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na))
            | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),hAPP(nat,X_b,semiring_1_of_nat(X_b),Na))) ) )
      | ~ linordered_semidom(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_877_of__nat__0__less__iff]) ).

fof(f_948_2,plain,
    ! [U_3678] :
      ( ! [U_3677] :
          ( ( hBOOL(hAPP(U_3678,bool,hAPP(U_3678,fun(U_3678,bool),ord_less(U_3678),zero_zero(U_3678)),hAPP(nat,U_3678,semiring_1_of_nat(U_3678),U_3677)))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_3677)) )
          & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_3677))
            | ~ hBOOL(hAPP(U_3678,bool,hAPP(U_3678,fun(U_3678,bool),ord_less(U_3678),zero_zero(U_3678)),hAPP(nat,U_3678,semiring_1_of_nat(U_3678),U_3677))) ) )
      | ~ linordered_semidom(U_3678) ),
    inference(variable_rename,[status(thm)],[f_948_1]) ).

fof(f_948_3,plain,
    ! [U_3678] :
      ( ( ! [U_3680] :
            ( hBOOL(hAPP(U_3678,bool,hAPP(U_3678,fun(U_3678,bool),ord_less(U_3678),zero_zero(U_3678)),hAPP(nat,U_3678,semiring_1_of_nat(U_3678),U_3680)))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_3680)) )
        & ! [U_3679] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_3679))
            | ~ hBOOL(hAPP(U_3678,bool,hAPP(U_3678,fun(U_3678,bool),ord_less(U_3678),zero_zero(U_3678)),hAPP(nat,U_3678,semiring_1_of_nat(U_3678),U_3679))) ) )
      | ~ linordered_semidom(U_3678) ),
    inference(miniscope,[status(thm)],[f_948_2]) ).

fof(f_948_4,plain,
    ( ! [U_3678,U_3680,U_3679] :
        ( hBOOL(hAPP(U_3678,bool,hAPP(U_3678,fun(U_3678,bool),ord_less(U_3678),zero_zero(U_3678)),hAPP(nat,U_3678,semiring_1_of_nat(U_3678),U_3680)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_3680))
        | ~ sP284(U_3678,U_3680,U_3679) )
    & ! [U_3678,U_3680,U_3679] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_3679))
        | ~ hBOOL(hAPP(U_3678,bool,hAPP(U_3678,fun(U_3678,bool),ord_less(U_3678),zero_zero(U_3678)),hAPP(nat,U_3678,semiring_1_of_nat(U_3678),U_3679)))
        | ~ sP284(U_3678,U_3680,U_3679) )
    & ! [U_3678,U_3680,U_3679] :
        ( sP284(U_3678,U_3680,U_3679)
        | ~ linordered_semidom(U_3678) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP284])],[f_948_3]) ).

cnf(f_948_5,plain,
    ( sP284(U_3678,U_3680,U_3679)
    | ~ linordered_semidom(U_3678) ),
    inference(clausify,[status(thm)],[f_948_4]) ).

cnf(f_948_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_3679))
    | ~ hBOOL(hAPP(U_3678,bool,hAPP(U_3678,fun(U_3678,bool),ord_less(U_3678),zero_zero(U_3678)),hAPP(nat,U_3678,semiring_1_of_nat(U_3678),U_3679)))
    | ~ sP284(U_3678,U_3680,U_3679) ),
    inference(clausify,[status(thm)],[f_948_4]) ).

cnf(f_948_7,plain,
    ( hBOOL(hAPP(U_3678,bool,hAPP(U_3678,fun(U_3678,bool),ord_less(U_3678),zero_zero(U_3678)),hAPP(nat,U_3678,semiring_1_of_nat(U_3678),U_3680)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_3680))
    | ~ sP284(U_3678,U_3680,U_3679) ),
    inference(clausify,[status(thm)],[f_948_4]) ).

fof(f_949_1,plain,
    ! [Y,X] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,X),Y)))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) ),
    inference(fof_nnf,[status(thm)],[fact_878_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J]) ).

fof(f_949_2,plain,
    ! [U_3682,U_3681] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,U_3681),U_3682)))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3682))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3681)) ),
    inference(variable_rename,[status(thm)],[f_949_1]) ).

fof(f_949_3,plain,
    ! [U_3682,U_3681] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,U_3681),U_3682)))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3682))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3681)) ),
    inference(definitional_conversion,[status(esa)],[f_949_2]) ).

cnf(f_949_4,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,U_3681),U_3682)))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3682))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3681)) ),
    inference(clausify,[status(thm)],[f_949_3]) ).

fof(f_950_1,plain,
    ! [Pa,X_1,Y_2] :
      ( ( hBOOL(hAPP(int,bool,Pa,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X_1),Y_2))))
        | ( ~ hBOOL(hAPP(int,bool,Pa,zero_zero(int)))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y_2)) )
        | ( ~ hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(nat,int,semiring_1_of_nat(int),Y_2))))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Y_2),X_1)) ) )
      & ( ( ( hBOOL(hAPP(int,bool,Pa,zero_zero(int)))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y_2)) )
          & ( hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(nat,int,semiring_1_of_nat(int),Y_2))))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Y_2),X_1)) ) )
        | ~ hBOOL(hAPP(int,bool,Pa,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X_1),Y_2)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_879_zdiff__int__split]) ).

fof(f_950_2,plain,
    ! [U_3685,U_3684,U_3683] :
      ( ( hBOOL(hAPP(int,bool,U_3685,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3684),U_3683))))
        | ( ~ hBOOL(hAPP(int,bool,U_3685,zero_zero(int)))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3684),U_3683)) )
        | ( ~ hBOOL(hAPP(int,bool,U_3685,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),U_3684)),hAPP(nat,int,semiring_1_of_nat(int),U_3683))))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3683),U_3684)) ) )
      & ( ( ( hBOOL(hAPP(int,bool,U_3685,zero_zero(int)))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3684),U_3683)) )
          & ( hBOOL(hAPP(int,bool,U_3685,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),U_3684)),hAPP(nat,int,semiring_1_of_nat(int),U_3683))))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3683),U_3684)) ) )
        | ~ hBOOL(hAPP(int,bool,U_3685,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3684),U_3683)))) ) ),
    inference(variable_rename,[status(thm)],[f_950_1]) ).

fof(f_950_3,plain,
    ( ! [U_3691,U_3689,U_3687] :
        ( hBOOL(hAPP(int,bool,U_3691,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3689),U_3687))))
        | ( ~ hBOOL(hAPP(int,bool,U_3691,zero_zero(int)))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3689),U_3687)) )
        | ( ~ hBOOL(hAPP(int,bool,U_3691,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),U_3689)),hAPP(nat,int,semiring_1_of_nat(int),U_3687))))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3687),U_3689)) ) )
    & ! [U_3690,U_3688,U_3686] :
        ( ( ( hBOOL(hAPP(int,bool,U_3690,zero_zero(int)))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3688),U_3686)) )
          & ( hBOOL(hAPP(int,bool,U_3690,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),U_3688)),hAPP(nat,int,semiring_1_of_nat(int),U_3686))))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3686),U_3688)) ) )
        | ~ hBOOL(hAPP(int,bool,U_3690,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3688),U_3686)))) ) ),
    inference(miniscope,[status(thm)],[f_950_2]) ).

fof(f_950_4,plain,
    ( ! [U_3689,U_3687,U_3691] :
        ( ~ hBOOL(hAPP(int,bool,U_3691,zero_zero(int)))
        | ~ sP287(U_3689,U_3687,U_3691) )
    & ! [U_3689,U_3687,U_3691] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3689),U_3687))
        | ~ sP287(U_3689,U_3687,U_3691) )
    & ! [U_3689,U_3687,U_3691] :
        ( ~ hBOOL(hAPP(int,bool,U_3691,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),U_3689)),hAPP(nat,int,semiring_1_of_nat(int),U_3687))))
        | ~ sP286(U_3689,U_3687,U_3691) )
    & ! [U_3689,U_3687,U_3691] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3687),U_3689))
        | ~ sP286(U_3689,U_3687,U_3691) )
    & ! [U_3690,U_3686,U_3688] :
        ( hBOOL(hAPP(int,bool,U_3690,zero_zero(int)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3688),U_3686))
        | ~ sP285(U_3690,U_3686,U_3688) )
    & ! [U_3690,U_3686,U_3688] :
        ( hBOOL(hAPP(int,bool,U_3690,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),U_3688)),hAPP(nat,int,semiring_1_of_nat(int),U_3686))))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3686),U_3688))
        | ~ sP285(U_3690,U_3686,U_3688) )
    & ! [U_3689,U_3687,U_3691] :
        ( hBOOL(hAPP(int,bool,U_3691,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3689),U_3687))))
        | sP287(U_3689,U_3687,U_3691)
        | sP286(U_3689,U_3687,U_3691) )
    & ! [U_3690,U_3686,U_3688] :
        ( sP285(U_3690,U_3686,U_3688)
        | ~ hBOOL(hAPP(int,bool,U_3690,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3688),U_3686)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP285,sP286,sP287])],[f_950_3]) ).

cnf(f_950_5,plain,
    ( sP285(U_3690,U_3686,U_3688)
    | ~ hBOOL(hAPP(int,bool,U_3690,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3688),U_3686)))) ),
    inference(clausify,[status(thm)],[f_950_4]) ).

cnf(f_950_6,plain,
    ( hBOOL(hAPP(int,bool,U_3691,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_3689),U_3687))))
    | sP287(U_3689,U_3687,U_3691)
    | sP286(U_3689,U_3687,U_3691) ),
    inference(clausify,[status(thm)],[f_950_4]) ).

cnf(f_950_7,plain,
    ( hBOOL(hAPP(int,bool,U_3690,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),U_3688)),hAPP(nat,int,semiring_1_of_nat(int),U_3686))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3686),U_3688))
    | ~ sP285(U_3690,U_3686,U_3688) ),
    inference(clausify,[status(thm)],[f_950_4]) ).

cnf(f_950_8,plain,
    ( hBOOL(hAPP(int,bool,U_3690,zero_zero(int)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3688),U_3686))
    | ~ sP285(U_3690,U_3686,U_3688) ),
    inference(clausify,[status(thm)],[f_950_4]) ).

cnf(f_950_9,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3687),U_3689))
    | ~ sP286(U_3689,U_3687,U_3691) ),
    inference(clausify,[status(thm)],[f_950_4]) ).

cnf(f_950_10,plain,
    ( ~ hBOOL(hAPP(int,bool,U_3691,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),U_3689)),hAPP(nat,int,semiring_1_of_nat(int),U_3687))))
    | ~ sP286(U_3689,U_3687,U_3691) ),
    inference(clausify,[status(thm)],[f_950_4]) ).

cnf(f_950_11,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3689),U_3687))
    | ~ sP287(U_3689,U_3687,U_3691) ),
    inference(clausify,[status(thm)],[f_950_4]) ).

cnf(f_950_12,plain,
    ( ~ hBOOL(hAPP(int,bool,U_3691,zero_zero(int)))
    | ~ sP287(U_3689,U_3687,U_3691) ),
    inference(clausify,[status(thm)],[f_950_4]) ).

fof(f_951_1,plain,
    ! [Y,X] :
      ( hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,X),Y) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X),Y)
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Y),X)) ),
    inference(fof_nnf,[status(thm)],[fact_880_tsub__eq]) ).

fof(f_951_2,plain,
    ! [U_3693,U_3692] :
      ( hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,U_3692),U_3693) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3692),U_3693)
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3693),U_3692)) ),
    inference(variable_rename,[status(thm)],[f_951_1]) ).

fof(f_951_3,plain,
    ! [U_3693,U_3692] :
      ( hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,U_3692),U_3693) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3692),U_3693)
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3693),U_3692)) ),
    inference(definitional_conversion,[status(esa)],[f_951_2]) ).

cnf(f_951_4,plain,
    ( hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,U_3692),U_3693) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3692),U_3693)
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3693),U_3692)) ),
    inference(clausify,[status(thm)],[f_951_3]) ).

fof(f_952_1,plain,
    ! [K_1] :
      ( ? [N_1] :
          ( K_1 = hAPP(nat,int,semiring_1_of_nat(int),N_1)
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) )
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K_1)) ),
    inference(fof_nnf,[status(thm)],[fact_881_zero__less__imp__eq__int]) ).

fof(f_952_2,plain,
    ! [U_3695] :
      ( ? [U_3694] :
          ( U_3695 = hAPP(nat,int,semiring_1_of_nat(int),U_3694)
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_3694)) )
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3695)) ),
    inference(variable_rename,[status(thm)],[f_952_1]) ).

fof(f_952_3,plain,
    ! [U_3695] :
      ( ( U_3695 = hAPP(nat,int,semiring_1_of_nat(int),sK134(U_3695))
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),sK134(U_3695))) )
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3695)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK134]),skolemize(U_3694,sK134(U_3695))],[f_952_2]) ).

fof(f_952_4,plain,
    ( ! [U_3695] :
        ( U_3695 = hAPP(nat,int,semiring_1_of_nat(int),sK134(U_3695))
        | ~ sP288(U_3695) )
    & ! [U_3695] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),sK134(U_3695)))
        | ~ sP288(U_3695) )
    & ! [U_3695] :
        ( sP288(U_3695)
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3695)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP288])],[f_952_3]) ).

cnf(f_952_5,plain,
    ( sP288(U_3695)
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3695)) ),
    inference(clausify,[status(thm)],[f_952_4]) ).

cnf(f_952_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),sK134(U_3695)))
    | ~ sP288(U_3695) ),
    inference(clausify,[status(thm)],[f_952_4]) ).

cnf(f_952_7,plain,
    ( U_3695 = hAPP(nat,int,semiring_1_of_nat(int),sK134(U_3695))
    | ~ sP288(U_3695) ),
    inference(clausify,[status(thm)],[f_952_4]) ).

fof(f_953_1,plain,
    ! [X_b] :
      ( ! [Na] : hAPP(nat,X_b,semiring_1_of_nat(X_b),Na) = hAPP(X_b,X_b,hAPP(nat,fun(X_b,X_b),hAPP(fun(X_b,X_b),fun(nat,fun(X_b,X_b)),semiri532925092at_aux(X_b),hAPP(X_b,fun(X_b,X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(X_b,X_b)),combc(X_b,X_b,X_b),plus_plus(X_b)),one_one(X_b))),Na),zero_zero(X_b))
      | ~ semiring_1(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_882_semiring__1__class_Oof__nat__code]) ).

fof(f_953_2,plain,
    ! [U_3697] :
      ( ! [U_3696] : hAPP(nat,U_3697,semiring_1_of_nat(U_3697),U_3696) = hAPP(U_3697,U_3697,hAPP(nat,fun(U_3697,U_3697),hAPP(fun(U_3697,U_3697),fun(nat,fun(U_3697,U_3697)),semiri532925092at_aux(U_3697),hAPP(U_3697,fun(U_3697,U_3697),hAPP(fun(U_3697,fun(U_3697,U_3697)),fun(U_3697,fun(U_3697,U_3697)),combc(U_3697,U_3697,U_3697),plus_plus(U_3697)),one_one(U_3697))),U_3696),zero_zero(U_3697))
      | ~ semiring_1(U_3697) ),
    inference(variable_rename,[status(thm)],[f_953_1]) ).

fof(f_953_3,plain,
    ! [U_3696,U_3697] :
      ( hAPP(nat,U_3697,semiring_1_of_nat(U_3697),U_3696) = hAPP(U_3697,U_3697,hAPP(nat,fun(U_3697,U_3697),hAPP(fun(U_3697,U_3697),fun(nat,fun(U_3697,U_3697)),semiri532925092at_aux(U_3697),hAPP(U_3697,fun(U_3697,U_3697),hAPP(fun(U_3697,fun(U_3697,U_3697)),fun(U_3697,fun(U_3697,U_3697)),combc(U_3697,U_3697,U_3697),plus_plus(U_3697)),one_one(U_3697))),U_3696),zero_zero(U_3697))
      | ~ semiring_1(U_3697) ),
    inference(definitional_conversion,[status(esa)],[f_953_2]) ).

cnf(f_953_4,plain,
    ( hAPP(nat,U_3697,semiring_1_of_nat(U_3697),U_3696) = hAPP(U_3697,U_3697,hAPP(nat,fun(U_3697,U_3697),hAPP(fun(U_3697,U_3697),fun(nat,fun(U_3697,U_3697)),semiri532925092at_aux(U_3697),hAPP(U_3697,fun(U_3697,U_3697),hAPP(fun(U_3697,fun(U_3697,U_3697)),fun(U_3697,fun(U_3697,U_3697)),combc(U_3697,U_3697,U_3697),plus_plus(U_3697)),one_one(U_3697))),U_3696),zero_zero(U_3697))
    | ~ semiring_1(U_3697) ),
    inference(clausify,[status(thm)],[f_953_3]) ).

fof(f_954_1,plain,
    ! [M,Na] :
      ( ( hAPP(nat,int,semiring_1_of_nat(int),M) = hAPP(nat,int,semiring_1_of_nat(int),Na)
        | M != Na )
      & ( M = Na
        | hAPP(nat,int,semiring_1_of_nat(int),M) != hAPP(nat,int,semiring_1_of_nat(int),Na) ) ),
    inference(fof_nnf,[status(thm)],[fact_883_int__int__eq]) ).

fof(f_954_2,plain,
    ! [U_3699,U_3698] :
      ( ( hAPP(nat,int,semiring_1_of_nat(int),U_3699) = hAPP(nat,int,semiring_1_of_nat(int),U_3698)
        | U_3699 != U_3698 )
      & ( U_3699 = U_3698
        | hAPP(nat,int,semiring_1_of_nat(int),U_3699) != hAPP(nat,int,semiring_1_of_nat(int),U_3698) ) ),
    inference(variable_rename,[status(thm)],[f_954_1]) ).

fof(f_954_3,plain,
    ( ! [U_3703,U_3701] :
        ( hAPP(nat,int,semiring_1_of_nat(int),U_3703) = hAPP(nat,int,semiring_1_of_nat(int),U_3701)
        | U_3703 != U_3701 )
    & ! [U_3702,U_3700] :
        ( U_3702 = U_3700
        | hAPP(nat,int,semiring_1_of_nat(int),U_3702) != hAPP(nat,int,semiring_1_of_nat(int),U_3700) ) ),
    inference(miniscope,[status(thm)],[f_954_2]) ).

fof(f_954_4,plain,
    ( ! [U_3703,U_3701] :
        ( hAPP(nat,int,semiring_1_of_nat(int),U_3703) = hAPP(nat,int,semiring_1_of_nat(int),U_3701)
        | U_3703 != U_3701 )
    & ! [U_3700,U_3702] :
        ( U_3702 = U_3700
        | hAPP(nat,int,semiring_1_of_nat(int),U_3702) != hAPP(nat,int,semiring_1_of_nat(int),U_3700) ) ),
    inference(definitional_conversion,[status(esa)],[f_954_3]) ).

cnf(f_954_5,plain,
    ( U_3702 = U_3700
    | hAPP(nat,int,semiring_1_of_nat(int),U_3702) != hAPP(nat,int,semiring_1_of_nat(int),U_3700) ),
    inference(clausify,[status(thm)],[f_954_4]) ).

cnf(f_954_6,plain,
    ( hAPP(nat,int,semiring_1_of_nat(int),U_3703) = hAPP(nat,int,semiring_1_of_nat(int),U_3701)
    | U_3703 != U_3701 ),
    inference(clausify,[status(thm)],[f_954_4]) ).

fof(f_955_1,plain,
    ! [A_3,B_1] :
      ( ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less(fun(nat,bool)),A_3),B_1))
        | ~ hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less(fun(int,bool)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B_1))) )
      & ( hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less(fun(int,bool)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B_1)))
        | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less(fun(nat,bool)),A_3),B_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_884_transfer__nat__int__set__relations_I4_J]) ).

fof(f_955_2,plain,
    ! [U_3705,U_3704] :
      ( ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less(fun(nat,bool)),U_3705),U_3704))
        | ~ hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less(fun(int,bool)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3705)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3704))) )
      & ( hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less(fun(int,bool)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3705)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3704)))
        | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less(fun(nat,bool)),U_3705),U_3704)) ) ),
    inference(variable_rename,[status(thm)],[f_955_1]) ).

fof(f_955_3,plain,
    ( ! [U_3709,U_3707] :
        ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less(fun(nat,bool)),U_3709),U_3707))
        | ~ hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less(fun(int,bool)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3709)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3707))) )
    & ! [U_3708,U_3706] :
        ( hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less(fun(int,bool)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3708)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3706)))
        | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less(fun(nat,bool)),U_3708),U_3706)) ) ),
    inference(miniscope,[status(thm)],[f_955_2]) ).

fof(f_955_4,plain,
    ( ! [U_3707,U_3709] :
        ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less(fun(nat,bool)),U_3709),U_3707))
        | ~ hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less(fun(int,bool)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3709)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3707))) )
    & ! [U_3708,U_3706] :
        ( hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less(fun(int,bool)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3708)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3706)))
        | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less(fun(nat,bool)),U_3708),U_3706)) ) ),
    inference(definitional_conversion,[status(esa)],[f_955_3]) ).

cnf(f_955_5,plain,
    ( hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less(fun(int,bool)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3708)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3706)))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less(fun(nat,bool)),U_3708),U_3706)) ),
    inference(clausify,[status(thm)],[f_955_4]) ).

cnf(f_955_6,plain,
    ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less(fun(nat,bool)),U_3709),U_3707))
    | ~ hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less(fun(int,bool)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3709)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3707))) ),
    inference(clausify,[status(thm)],[f_955_4]) ).

fof(f_956_1,plain,
    ! [A_3,B_1] :
      ( ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),A_3),B_1))
        | ~ hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B_1))) )
      & ( hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B_1)))
        | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),A_3),B_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_885_transfer__nat__int__set__relations_I5_J]) ).

fof(f_956_2,plain,
    ! [U_3711,U_3710] :
      ( ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),U_3711),U_3710))
        | ~ hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3711)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3710))) )
      & ( hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3711)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3710)))
        | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),U_3711),U_3710)) ) ),
    inference(variable_rename,[status(thm)],[f_956_1]) ).

fof(f_956_3,plain,
    ( ! [U_3715,U_3713] :
        ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),U_3715),U_3713))
        | ~ hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3715)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3713))) )
    & ! [U_3714,U_3712] :
        ( hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3714)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3712)))
        | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),U_3714),U_3712)) ) ),
    inference(miniscope,[status(thm)],[f_956_2]) ).

fof(f_956_4,plain,
    ( ! [U_3713,U_3715] :
        ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),U_3715),U_3713))
        | ~ hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3715)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3713))) )
    & ! [U_3712,U_3714] :
        ( hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3714)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3712)))
        | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),U_3714),U_3712)) ) ),
    inference(definitional_conversion,[status(esa)],[f_956_3]) ).

cnf(f_956_5,plain,
    ( hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3714)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3712)))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),U_3714),U_3712)) ),
    inference(clausify,[status(thm)],[f_956_4]) ).

cnf(f_956_6,plain,
    ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),U_3715),U_3713))
    | ~ hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3715)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3713))) ),
    inference(clausify,[status(thm)],[f_956_4]) ).

fof(f_957_1,plain,
    bot_bot(fun(int,bool)) = hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),bot_bot(fun(nat,bool))),
    inference(fof_nnf,[status(thm)],[fact_886_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J]) ).

fof(f_957_2,plain,
    bot_bot(fun(int,bool)) = hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),bot_bot(fun(nat,bool))),
    inference(definitional_conversion,[status(esa)],[f_957_1]) ).

cnf(f_957_3,plain,
    bot_bot(fun(int,bool)) = hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),bot_bot(fun(nat,bool))),
    inference(clausify,[status(thm)],[f_957_2]) ).

fof(f_958_1,plain,
    ! [A_3,B_1] :
      ( ( A_3 = B_1
        | hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3) != hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B_1) )
      & ( hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3) = hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B_1)
        | A_3 != B_1 ) ),
    inference(fof_nnf,[status(thm)],[fact_887_transfer__nat__int__set__relations_I3_J]) ).

fof(f_958_2,plain,
    ! [U_3717,U_3716] :
      ( ( U_3717 = U_3716
        | hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3717) != hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3716) )
      & ( hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3717) = hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3716)
        | U_3717 != U_3716 ) ),
    inference(variable_rename,[status(thm)],[f_958_1]) ).

fof(f_958_3,plain,
    ( ! [U_3721,U_3719] :
        ( U_3721 = U_3719
        | hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3721) != hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3719) )
    & ! [U_3720,U_3718] :
        ( hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3720) = hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3718)
        | U_3720 != U_3718 ) ),
    inference(miniscope,[status(thm)],[f_958_2]) ).

fof(f_958_4,plain,
    ( ! [U_3721,U_3719] :
        ( U_3721 = U_3719
        | hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3721) != hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3719) )
    & ! [U_3718,U_3720] :
        ( hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3720) = hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3718)
        | U_3720 != U_3718 ) ),
    inference(definitional_conversion,[status(esa)],[f_958_3]) ).

cnf(f_958_5,plain,
    ( hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3720) = hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3718)
    | U_3720 != U_3718 ),
    inference(clausify,[status(thm)],[f_958_4]) ).

cnf(f_958_6,plain,
    ( U_3721 = U_3719
    | hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3721) != hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3719) ),
    inference(clausify,[status(thm)],[f_958_4]) ).

fof(f_959_1,plain,
    ! [X_1,A_3] :
      ( ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_1),A_3))
        | ~ hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3))) )
      & ( hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3)))
        | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_1),A_3)) ) ),
    inference(fof_nnf,[status(thm)],[fact_888_transfer__nat__int__set__relations_I2_J]) ).

fof(f_959_2,plain,
    ! [U_3723,U_3722] :
      ( ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_3723),U_3722))
        | ~ hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(nat,int,semiring_1_of_nat(int),U_3723)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3722))) )
      & ( hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(nat,int,semiring_1_of_nat(int),U_3723)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3722)))
        | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_3723),U_3722)) ) ),
    inference(variable_rename,[status(thm)],[f_959_1]) ).

fof(f_959_3,plain,
    ( ! [U_3727,U_3725] :
        ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_3727),U_3725))
        | ~ hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(nat,int,semiring_1_of_nat(int),U_3727)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3725))) )
    & ! [U_3726,U_3724] :
        ( hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(nat,int,semiring_1_of_nat(int),U_3726)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3724)))
        | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_3726),U_3724)) ) ),
    inference(miniscope,[status(thm)],[f_959_2]) ).

fof(f_959_4,plain,
    ( ! [U_3725,U_3727] :
        ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_3727),U_3725))
        | ~ hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(nat,int,semiring_1_of_nat(int),U_3727)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3725))) )
    & ! [U_3726,U_3724] :
        ( hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(nat,int,semiring_1_of_nat(int),U_3726)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3724)))
        | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_3726),U_3724)) ) ),
    inference(definitional_conversion,[status(esa)],[f_959_3]) ).

cnf(f_959_5,plain,
    ( hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(nat,int,semiring_1_of_nat(int),U_3726)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3724)))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_3726),U_3724)) ),
    inference(clausify,[status(thm)],[f_959_4]) ).

cnf(f_959_6,plain,
    ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_3727),U_3725))
    | ~ hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(nat,int,semiring_1_of_nat(int),U_3727)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),U_3725))) ),
    inference(clausify,[status(thm)],[f_959_4]) ).

fof(f_960_1,plain,
    ! [X_1,Y_2,Pa] :
      ( ( hAPP(nat,int,semiring_1_of_nat(int),Y_2) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),Pa),X_1),Y_2))
        | hBOOL(Pa) )
      & ( hAPP(nat,int,semiring_1_of_nat(int),X_1) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),Pa),X_1),Y_2))
        | ~ hBOOL(Pa) ) ),
    inference(fof_nnf,[status(thm)],[fact_889_int__if__cong]) ).

fof(f_960_2,plain,
    ! [U_3730,U_3729,U_3728] :
      ( ( hAPP(nat,int,semiring_1_of_nat(int),U_3729) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),U_3728),U_3730),U_3729))
        | hBOOL(U_3728) )
      & ( hAPP(nat,int,semiring_1_of_nat(int),U_3730) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),U_3728),U_3730),U_3729))
        | ~ hBOOL(U_3728) ) ),
    inference(variable_rename,[status(thm)],[f_960_1]) ).

fof(f_960_3,plain,
    ( ! [U_3736,U_3734,U_3732] :
        ( hAPP(nat,int,semiring_1_of_nat(int),U_3734) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),U_3732),U_3736),U_3734))
        | hBOOL(U_3732) )
    & ! [U_3735,U_3733,U_3731] :
        ( hAPP(nat,int,semiring_1_of_nat(int),U_3735) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),U_3731),U_3735),U_3733))
        | ~ hBOOL(U_3731) ) ),
    inference(miniscope,[status(thm)],[f_960_2]) ).

fof(f_960_4,plain,
    ( ! [U_3732,U_3734,U_3736] :
        ( hAPP(nat,int,semiring_1_of_nat(int),U_3734) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),U_3732),U_3736),U_3734))
        | hBOOL(U_3732) )
    & ! [U_3731,U_3733,U_3735] :
        ( hAPP(nat,int,semiring_1_of_nat(int),U_3735) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),U_3731),U_3735),U_3733))
        | ~ hBOOL(U_3731) ) ),
    inference(definitional_conversion,[status(esa)],[f_960_3]) ).

cnf(f_960_5,plain,
    ( hAPP(nat,int,semiring_1_of_nat(int),U_3735) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),U_3731),U_3735),U_3733))
    | ~ hBOOL(U_3731) ),
    inference(clausify,[status(thm)],[f_960_4]) ).

cnf(f_960_6,plain,
    ( hAPP(nat,int,semiring_1_of_nat(int),U_3734) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),U_3732),U_3736),U_3734))
    | hBOOL(U_3732) ),
    inference(clausify,[status(thm)],[f_960_4]) ).

fof(f_961_1,plain,
    ! [X_1,Y_2] :
      ( ( hAPP(nat,int,semiring_1_of_nat(int),X_1) = hAPP(nat,int,semiring_1_of_nat(int),Y_2)
        | X_1 != Y_2 )
      & ( X_1 = Y_2
        | hAPP(nat,int,semiring_1_of_nat(int),X_1) != hAPP(nat,int,semiring_1_of_nat(int),Y_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_890_transfer__int__nat__relations_I1_J]) ).

fof(f_961_2,plain,
    ! [U_3738,U_3737] :
      ( ( hAPP(nat,int,semiring_1_of_nat(int),U_3738) = hAPP(nat,int,semiring_1_of_nat(int),U_3737)
        | U_3738 != U_3737 )
      & ( U_3738 = U_3737
        | hAPP(nat,int,semiring_1_of_nat(int),U_3738) != hAPP(nat,int,semiring_1_of_nat(int),U_3737) ) ),
    inference(variable_rename,[status(thm)],[f_961_1]) ).

fof(f_961_3,plain,
    ( ! [U_3742,U_3740] :
        ( hAPP(nat,int,semiring_1_of_nat(int),U_3742) = hAPP(nat,int,semiring_1_of_nat(int),U_3740)
        | U_3742 != U_3740 )
    & ! [U_3741,U_3739] :
        ( U_3741 = U_3739
        | hAPP(nat,int,semiring_1_of_nat(int),U_3741) != hAPP(nat,int,semiring_1_of_nat(int),U_3739) ) ),
    inference(miniscope,[status(thm)],[f_961_2]) ).

fof(f_961_4,plain,
    ( ! [U_3742,U_3740] :
        ( hAPP(nat,int,semiring_1_of_nat(int),U_3742) = hAPP(nat,int,semiring_1_of_nat(int),U_3740)
        | U_3742 != U_3740 )
    & ! [U_3739,U_3741] :
        ( U_3741 = U_3739
        | hAPP(nat,int,semiring_1_of_nat(int),U_3741) != hAPP(nat,int,semiring_1_of_nat(int),U_3739) ) ),
    inference(definitional_conversion,[status(esa)],[f_961_3]) ).

cnf(f_961_5,plain,
    ( U_3741 = U_3739
    | hAPP(nat,int,semiring_1_of_nat(int),U_3741) != hAPP(nat,int,semiring_1_of_nat(int),U_3739) ),
    inference(clausify,[status(thm)],[f_961_4]) ).

cnf(f_961_6,plain,
    ( hAPP(nat,int,semiring_1_of_nat(int),U_3742) = hAPP(nat,int,semiring_1_of_nat(int),U_3740)
    | U_3742 != U_3740 ),
    inference(clausify,[status(thm)],[f_961_4]) ).

fof(f_962_1,plain,
    ! [X_b] :
      ( ! [Inc,I_1] : hAPP(X_b,X_b,hAPP(nat,fun(X_b,X_b),hAPP(fun(X_b,X_b),fun(nat,fun(X_b,X_b)),semiri532925092at_aux(X_b),Inc),zero_zero(nat)),I_1) = ti(X_b,I_1)
      | ~ semiring_1(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_891_of__nat__aux_Osimps_I1_J]) ).

fof(f_962_2,plain,
    ! [U_3745] :
      ( ! [U_3744,U_3743] : hAPP(U_3745,U_3745,hAPP(nat,fun(U_3745,U_3745),hAPP(fun(U_3745,U_3745),fun(nat,fun(U_3745,U_3745)),semiri532925092at_aux(U_3745),U_3744),zero_zero(nat)),U_3743) = ti(U_3745,U_3743)
      | ~ semiring_1(U_3745) ),
    inference(variable_rename,[status(thm)],[f_962_1]) ).

fof(f_962_3,plain,
    ! [U_3743,U_3745,U_3744] :
      ( hAPP(U_3745,U_3745,hAPP(nat,fun(U_3745,U_3745),hAPP(fun(U_3745,U_3745),fun(nat,fun(U_3745,U_3745)),semiri532925092at_aux(U_3745),U_3744),zero_zero(nat)),U_3743) = ti(U_3745,U_3743)
      | ~ semiring_1(U_3745) ),
    inference(definitional_conversion,[status(esa)],[f_962_2]) ).

cnf(f_962_4,plain,
    ( hAPP(U_3745,U_3745,hAPP(nat,fun(U_3745,U_3745),hAPP(fun(U_3745,U_3745),fun(nat,fun(U_3745,U_3745)),semiri532925092at_aux(U_3745),U_3744),zero_zero(nat)),U_3743) = ti(U_3745,U_3743)
    | ~ semiring_1(U_3745) ),
    inference(clausify,[status(thm)],[f_962_3]) ).

fof(f_963_1,plain,
    ! [X_b] :
      ( ! [Inc,Na,I_1] : hAPP(X_b,X_b,hAPP(nat,fun(X_b,X_b),hAPP(fun(X_b,X_b),fun(nat,fun(X_b,X_b)),semiri532925092at_aux(X_b),Inc),hAPP(nat,nat,suc,Na)),I_1) = hAPP(X_b,X_b,hAPP(nat,fun(X_b,X_b),hAPP(fun(X_b,X_b),fun(nat,fun(X_b,X_b)),semiri532925092at_aux(X_b),Inc),Na),hAPP(X_b,X_b,Inc,I_1))
      | ~ semiring_1(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_892_of__nat__aux_Osimps_I2_J]) ).

fof(f_963_2,plain,
    ! [U_3749] :
      ( ! [U_3748,U_3747,U_3746] : hAPP(U_3749,U_3749,hAPP(nat,fun(U_3749,U_3749),hAPP(fun(U_3749,U_3749),fun(nat,fun(U_3749,U_3749)),semiri532925092at_aux(U_3749),U_3748),hAPP(nat,nat,suc,U_3747)),U_3746) = hAPP(U_3749,U_3749,hAPP(nat,fun(U_3749,U_3749),hAPP(fun(U_3749,U_3749),fun(nat,fun(U_3749,U_3749)),semiri532925092at_aux(U_3749),U_3748),U_3747),hAPP(U_3749,U_3749,U_3748,U_3746))
      | ~ semiring_1(U_3749) ),
    inference(variable_rename,[status(thm)],[f_963_1]) ).

fof(f_963_3,plain,
    ! [U_3746,U_3748,U_3749,U_3747] :
      ( hAPP(U_3749,U_3749,hAPP(nat,fun(U_3749,U_3749),hAPP(fun(U_3749,U_3749),fun(nat,fun(U_3749,U_3749)),semiri532925092at_aux(U_3749),U_3748),hAPP(nat,nat,suc,U_3747)),U_3746) = hAPP(U_3749,U_3749,hAPP(nat,fun(U_3749,U_3749),hAPP(fun(U_3749,U_3749),fun(nat,fun(U_3749,U_3749)),semiri532925092at_aux(U_3749),U_3748),U_3747),hAPP(U_3749,U_3749,U_3748,U_3746))
      | ~ semiring_1(U_3749) ),
    inference(definitional_conversion,[status(esa)],[f_963_2]) ).

cnf(f_963_4,plain,
    ( hAPP(U_3749,U_3749,hAPP(nat,fun(U_3749,U_3749),hAPP(fun(U_3749,U_3749),fun(nat,fun(U_3749,U_3749)),semiri532925092at_aux(U_3749),U_3748),hAPP(nat,nat,suc,U_3747)),U_3746) = hAPP(U_3749,U_3749,hAPP(nat,fun(U_3749,U_3749),hAPP(fun(U_3749,U_3749),fun(nat,fun(U_3749,U_3749)),semiri532925092at_aux(U_3749),U_3748),U_3747),hAPP(U_3749,U_3749,U_3748,U_3746))
    | ~ semiring_1(U_3749) ),
    inference(clausify,[status(thm)],[f_963_3]) ).

fof(f_964_1,plain,
    ! [K_1] :
      ( ? [N_1] : K_1 = hAPP(nat,int,semiring_1_of_nat(int),N_1)
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K_1)) ),
    inference(fof_nnf,[status(thm)],[fact_893_nonneg__int__cases]) ).

fof(f_964_2,plain,
    ! [U_3751] :
      ( ? [U_3750] : U_3751 = hAPP(nat,int,semiring_1_of_nat(int),U_3750)
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3751)) ),
    inference(variable_rename,[status(thm)],[f_964_1]) ).

fof(f_964_3,plain,
    ! [U_3751] :
      ( U_3751 = hAPP(nat,int,semiring_1_of_nat(int),sK135(U_3751))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3751)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK135]),skolemize(U_3750,sK135(U_3751))],[f_964_2]) ).

fof(f_964_4,plain,
    ! [U_3751] :
      ( U_3751 = hAPP(nat,int,semiring_1_of_nat(int),sK135(U_3751))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3751)) ),
    inference(definitional_conversion,[status(esa)],[f_964_3]) ).

cnf(f_964_5,plain,
    ( U_3751 = hAPP(nat,int,semiring_1_of_nat(int),sK135(U_3751))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3751)) ),
    inference(clausify,[status(thm)],[f_964_4]) ).

fof(f_965_1,plain,
    ! [Z] :
      ( ? [M_2] : Z = hAPP(nat,int,semiring_1_of_nat(int),M_2)
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z)) ),
    inference(fof_nnf,[status(thm)],[fact_894_nonneg__eq__int]) ).

fof(f_965_2,plain,
    ! [U_3753] :
      ( ? [U_3752] : U_3753 = hAPP(nat,int,semiring_1_of_nat(int),U_3752)
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3753)) ),
    inference(variable_rename,[status(thm)],[f_965_1]) ).

fof(f_965_3,plain,
    ! [U_3753] :
      ( U_3753 = hAPP(nat,int,semiring_1_of_nat(int),sK136(U_3753))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3753)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK136]),skolemize(U_3752,sK136(U_3753))],[f_965_2]) ).

fof(f_965_4,plain,
    ! [U_3753] :
      ( U_3753 = hAPP(nat,int,semiring_1_of_nat(int),sK136(U_3753))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3753)) ),
    inference(definitional_conversion,[status(esa)],[f_965_3]) ).

cnf(f_965_5,plain,
    ( U_3753 = hAPP(nat,int,semiring_1_of_nat(int),sK136(U_3753))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3753)) ),
    inference(clausify,[status(thm)],[f_965_4]) ).

fof(f_966_1,plain,
    ! [K_1] :
      ( ? [N_1] : K_1 = hAPP(nat,int,semiring_1_of_nat(int),N_1)
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K_1)) ),
    inference(fof_nnf,[status(thm)],[fact_895_zero__le__imp__eq__int]) ).

fof(f_966_2,plain,
    ! [U_3755] :
      ( ? [U_3754] : U_3755 = hAPP(nat,int,semiring_1_of_nat(int),U_3754)
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3755)) ),
    inference(variable_rename,[status(thm)],[f_966_1]) ).

fof(f_966_3,plain,
    ! [U_3755] :
      ( U_3755 = hAPP(nat,int,semiring_1_of_nat(int),sK137(U_3755))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3755)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK137]),skolemize(U_3754,sK137(U_3755))],[f_966_2]) ).

fof(f_966_4,plain,
    ! [U_3755] :
      ( U_3755 = hAPP(nat,int,semiring_1_of_nat(int),sK137(U_3755))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3755)) ),
    inference(definitional_conversion,[status(esa)],[f_966_3]) ).

cnf(f_966_5,plain,
    ( U_3755 = hAPP(nat,int,semiring_1_of_nat(int),sK137(U_3755))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3755)) ),
    inference(clausify,[status(thm)],[f_966_4]) ).

fof(f_967_1,plain,
    ! [Z] :
    ? [M_2,N_1] : Z = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),M_2)),hAPP(nat,int,semiring_1_of_nat(int),N_1)),
    inference(fof_nnf,[status(thm)],[fact_896_int__diff__cases]) ).

fof(f_967_2,plain,
    ! [U_3758] :
    ? [U_3757,U_3756] : U_3758 = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),U_3757)),hAPP(nat,int,semiring_1_of_nat(int),U_3756)),
    inference(variable_rename,[status(thm)],[f_967_1]) ).

fof(f_967_3,plain,
    ! [U_3758] :
    ? [U_3756] : U_3758 = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),sK138(U_3758))),hAPP(nat,int,semiring_1_of_nat(int),U_3756)),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK138]),skolemize(U_3757,sK138(U_3758))],[f_967_2]) ).

fof(f_967_4,plain,
    ! [U_3758] : U_3758 = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),sK138(U_3758))),hAPP(nat,int,semiring_1_of_nat(int),sK139(U_3758))),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK139]),skolemize(U_3756,sK139(U_3758))],[f_967_3]) ).

fof(f_967_5,plain,
    ! [U_3758] : U_3758 = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),sK138(U_3758))),hAPP(nat,int,semiring_1_of_nat(int),sK139(U_3758))),
    inference(definitional_conversion,[status(esa)],[f_967_4]) ).

cnf(f_967_6,plain,
    U_3758 = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),sK138(U_3758))),hAPP(nat,int,semiring_1_of_nat(int),sK139(U_3758))),
    inference(clausify,[status(thm)],[f_967_5]) ).

fof(f_968_1,plain,
    ! [X_c,X_b] :
      ( ! [H,G,S,R_1,E] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,hAPP(fun(X_c,bool),X_b,hAPP(X_b,fun(fun(X_c,bool),X_b),hAPP(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b))),finite_fold_image(X_b,X_c),times_times(X_b)),H),E),S)),hAPP(fun(X_c,bool),X_b,hAPP(X_b,fun(fun(X_c,bool),X_b),hAPP(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b))),finite_fold_image(X_b,X_c),times_times(X_b)),G),E),S)))
          | ? [X_2] :
              ( ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,hAPP(X_c,X_b,H,X_2)),hAPP(X_c,X_b,G,X_2)))
              & hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_2),S)) )
          | ~ hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),S))
          | ? [X1,Y1,X2,Y2] :
              ( ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X1),Y1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X2),Y2)))
              & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,Y1),Y2))
              & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,X1),X2)) )
          | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,E),E)) )
      | ~ comm_monoid_mult(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_897_fold__image__related]) ).

fof(f_968_2,plain,
    ! [U_3770,U_3769] :
      ( ! [U_3768,U_3767,U_3766,U_3765,U_3764] :
          ( hBOOL(hAPP(U_3769,bool,hAPP(U_3769,fun(U_3769,bool),U_3765,hAPP(fun(U_3770,bool),U_3769,hAPP(U_3769,fun(fun(U_3770,bool),U_3769),hAPP(fun(U_3770,U_3769),fun(U_3769,fun(fun(U_3770,bool),U_3769)),hAPP(fun(U_3769,fun(U_3769,U_3769)),fun(fun(U_3770,U_3769),fun(U_3769,fun(fun(U_3770,bool),U_3769))),finite_fold_image(U_3769,U_3770),times_times(U_3769)),U_3768),U_3764),U_3766)),hAPP(fun(U_3770,bool),U_3769,hAPP(U_3769,fun(fun(U_3770,bool),U_3769),hAPP(fun(U_3770,U_3769),fun(U_3769,fun(fun(U_3770,bool),U_3769)),hAPP(fun(U_3769,fun(U_3769,U_3769)),fun(fun(U_3770,U_3769),fun(U_3769,fun(fun(U_3770,bool),U_3769))),finite_fold_image(U_3769,U_3770),times_times(U_3769)),U_3767),U_3764),U_3766)))
          | ? [U_3763] :
              ( ~ hBOOL(hAPP(U_3769,bool,hAPP(U_3769,fun(U_3769,bool),U_3765,hAPP(U_3770,U_3769,U_3768,U_3763)),hAPP(U_3770,U_3769,U_3767,U_3763)))
              & hBOOL(hAPP(fun(U_3770,bool),bool,hAPP(U_3770,fun(fun(U_3770,bool),bool),member(U_3770),U_3763),U_3766)) )
          | ~ hBOOL(hAPP(fun(U_3770,bool),bool,finite_finite(U_3770),U_3766))
          | ? [U_3762,U_3761,U_3760,U_3759] :
              ( ~ hBOOL(hAPP(U_3769,bool,hAPP(U_3769,fun(U_3769,bool),U_3765,hAPP(U_3769,U_3769,hAPP(U_3769,fun(U_3769,U_3769),times_times(U_3769),U_3762),U_3761)),hAPP(U_3769,U_3769,hAPP(U_3769,fun(U_3769,U_3769),times_times(U_3769),U_3760),U_3759)))
              & hBOOL(hAPP(U_3769,bool,hAPP(U_3769,fun(U_3769,bool),U_3765,U_3761),U_3759))
              & hBOOL(hAPP(U_3769,bool,hAPP(U_3769,fun(U_3769,bool),U_3765,U_3762),U_3760)) )
          | ~ hBOOL(hAPP(U_3769,bool,hAPP(U_3769,fun(U_3769,bool),U_3765,U_3764),U_3764)) )
      | ~ comm_monoid_mult(U_3769) ),
    inference(variable_rename,[status(thm)],[f_968_1]) ).

fof(f_968_3,plain,
    ! [U_3770,U_3769] :
      ( ! [U_3768,U_3767,U_3766,U_3765,U_3764] :
          ( hBOOL(hAPP(U_3769,bool,hAPP(U_3769,fun(U_3769,bool),U_3765,hAPP(fun(U_3770,bool),U_3769,hAPP(U_3769,fun(fun(U_3770,bool),U_3769),hAPP(fun(U_3770,U_3769),fun(U_3769,fun(fun(U_3770,bool),U_3769)),hAPP(fun(U_3769,fun(U_3769,U_3769)),fun(fun(U_3770,U_3769),fun(U_3769,fun(fun(U_3770,bool),U_3769))),finite_fold_image(U_3769,U_3770),times_times(U_3769)),U_3768),U_3764),U_3766)),hAPP(fun(U_3770,bool),U_3769,hAPP(U_3769,fun(fun(U_3770,bool),U_3769),hAPP(fun(U_3770,U_3769),fun(U_3769,fun(fun(U_3770,bool),U_3769)),hAPP(fun(U_3769,fun(U_3769,U_3769)),fun(fun(U_3770,U_3769),fun(U_3769,fun(fun(U_3770,bool),U_3769))),finite_fold_image(U_3769,U_3770),times_times(U_3769)),U_3767),U_3764),U_3766)))
          | ? [U_3763] :
              ( ~ hBOOL(hAPP(U_3769,bool,hAPP(U_3769,fun(U_3769,bool),U_3765,hAPP(U_3770,U_3769,U_3768,U_3763)),hAPP(U_3770,U_3769,U_3767,U_3763)))
              & hBOOL(hAPP(fun(U_3770,bool),bool,hAPP(U_3770,fun(fun(U_3770,bool),bool),member(U_3770),U_3763),U_3766)) )
          | ~ hBOOL(hAPP(fun(U_3770,bool),bool,finite_finite(U_3770),U_3766))
          | ? [U_3761,U_3760,U_3759] :
              ( ~ hBOOL(hAPP(U_3769,bool,hAPP(U_3769,fun(U_3769,bool),U_3765,hAPP(U_3769,U_3769,hAPP(U_3769,fun(U_3769,U_3769),times_times(U_3769),sK140(U_3770,U_3769,U_3768,U_3767,U_3766,U_3765,U_3764)),U_3761)),hAPP(U_3769,U_3769,hAPP(U_3769,fun(U_3769,U_3769),times_times(U_3769),U_3760),U_3759)))
              & hBOOL(hAPP(U_3769,bool,hAPP(U_3769,fun(U_3769,bool),U_3765,U_3761),U_3759))
              & hBOOL(hAPP(U_3769,bool,hAPP(U_3769,fun(U_3769,bool),U_3765,sK140(U_3770,U_3769,U_3768,U_3767,U_3766,U_3765,U_3764)),U_3760)) )
          | ~ hBOOL(hAPP(U_3769,bool,hAPP(U_3769,fun(U_3769,bool),U_3765,U_3764),U_3764)) )
      | ~ comm_monoid_mult(U_3769) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK140]),skolemize(U_3762,sK140(U_3770,U_3769,U_3768,U_3767,U_3766,U_3765,U_3764))],[f_968_2]) ).

fof(f_968_4,plain,
    ! [U_3770,U_3769] :
      ( ! [U_3768,U_3767,U_3766,U_3765,U_3764] :
          ( hBOOL(hAPP(U_3769,bool,hAPP(U_3769,fun(U_3769,bool),U_3765,hAPP(fun(U_3770,bool),U_3769,hAPP(U_3769,fun(fun(U_3770,bool),U_3769),hAPP(fun(U_3770,U_3769),fun(U_3769,fun(fun(U_3770,bool),U_3769)),hAPP(fun(U_3769,fun(U_3769,U_3769)),fun(fun(U_3770,U_3769),fun(U_3769,fun(fun(U_3770,bool),U_3769))),finite_fold_image(U_3769,U_3770),times_times(U_3769)),U_3768),U_3764),U_3766)),hAPP(fun(U_3770,bool),U_3769,hAPP(U_3769,fun(fun(U_3770,bool),U_3769),hAPP(fun(U_3770,U_3769),fun(U_3769,fun(fun(U_3770,bool),U_3769)),hAPP(fun(U_3769,fun(U_3769,U_3769)),fun(fun(U_3770,U_3769),fun(U_3769,fun(fun(U_3770,bool),U_3769))),finite_fold_image(U_3769,U_3770),times_times(U_3769)),U_3767),U_3764),U_3766)))
          | ? [U_3763] :
              ( ~ hBOOL(hAPP(U_3769,bool,hAPP(U_3769,fun(U_3769,bool),U_3765,hAPP(U_3770,U_3769,U_3768,U_3763)),hAPP(U_3770,U_3769,U_3767,U_3763)))
              & hBOOL(hAPP(fun(U_3770,bool),bool,hAPP(U_3770,fun(fun(U_3770,bool),bool),member(U_3770),U_3763),U_3766)) )
          | ~ hBOOL(hAPP(fun(U_3770,bool),bool,finite_finite(U_3770),U_3766))
          | ? [U_3760,U_3759] :
              ( ~ hBOOL(hAPP(U_3769,bool,hAPP(U_3769,fun(U_3769,bool),U_3765,hAPP(U_3769,U_3769,hAPP(U_3769,fun(U_3769,U_3769),times_times(U_3769),sK140(U_3770,U_3769,U_3768,U_3767,U_3766,U_3765,U_3764)),sK141(U_3770,U_3769,U_3768,U_3767,U_3766,U_3765,U_3764))),hAPP(U_3769,U_3769,hAPP(U_3769,fun(U_3769,U_3769),times_times(U_3769),U_3760),U_3759)))
              & hBOOL(hAPP(U_3769,bool,hAPP(U_3769,fun(U_3769,bool),U_3765,sK141(U_3770,U_3769,U_3768,U_3767,U_3766,U_3765,U_3764)),U_3759))
              & hBOOL(hAPP(U_3769,bool,hAPP(U_3769,fun(U_3769,bool),U_3765,sK140(U_3770,U_3769,U_3768,U_3767,U_3766,U_3765,U_3764)),U_3760)) )
          | ~ hBOOL(hAPP(U_3769,bool,hAPP(U_3769,fun(U_3769,bool),U_3765,U_3764),U_3764)) )
      | ~ comm_monoid_mult(U_3769) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK141]),skolemize(U_3761,sK141(U_3770,U_3769,U_3768,U_3767,U_3766,U_3765,U_3764))],[f_968_3]) ).

fof(f_968_5,plain,
    ! [U_3770,U_3769] :
      ( ! [U_3768,U_3767,U_3766,U_3765,U_3764] :
          ( hBOOL(hAPP(U_3769,bool,hAPP(U_3769,fun(U_3769,bool),U_3765,hAPP(fun(U_3770,bool),U_3769,hAPP(U_3769,fun(fun(U_3770,bool),U_3769),hAPP(fun(U_3770,U_3769),fun(U_3769,fun(fun(U_3770,bool),U_3769)),hAPP(fun(U_3769,fun(U_3769,U_3769)),fun(fun(U_3770,U_3769),fun(U_3769,fun(fun(U_3770,bool),U_3769))),finite_fold_image(U_3769,U_3770),times_times(U_3769)),U_3768),U_3764),U_3766)),hAPP(fun(U_3770,bool),U_3769,hAPP(U_3769,fun(fun(U_3770,bool),U_3769),hAPP(fun(U_3770,U_3769),fun(U_3769,fun(fun(U_3770,bool),U_3769)),hAPP(fun(U_3769,fun(U_3769,U_3769)),fun(fun(U_3770,U_3769),fun(U_3769,fun(fun(U_3770,bool),U_3769))),finite_fold_image(U_3769,U_3770),times_times(U_3769)),U_3767),U_3764),U_3766)))
          | ? [U_3763] :
              ( ~ hBOOL(hAPP(U_3769,bool,hAPP(U_3769,fun(U_3769,bool),U_3765,hAPP(U_3770,U_3769,U_3768,U_3763)),hAPP(U_3770,U_3769,U_3767,U_3763)))
              & hBOOL(hAPP(fun(U_3770,bool),bool,hAPP(U_3770,fun(fun(U_3770,bool),bool),member(U_3770),U_3763),U_3766)) )
          | ~ hBOOL(hAPP(fun(U_3770,bool),bool,finite_finite(U_3770),U_3766))
          | ? [U_3759] :
              ( ~ hBOOL(hAPP(U_3769,bool,hAPP(U_3769,fun(U_3769,bool),U_3765,hAPP(U_3769,U_3769,hAPP(U_3769,fun(U_3769,U_3769),times_times(U_3769),sK140(U_3770,U_3769,U_3768,U_3767,U_3766,U_3765,U_3764)),sK141(U_3770,U_3769,U_3768,U_3767,U_3766,U_3765,U_3764))),hAPP(U_3769,U_3769,hAPP(U_3769,fun(U_3769,U_3769),times_times(U_3769),sK142(U_3770,U_3769,U_3768,U_3767,U_3766,U_3765,U_3764)),U_3759)))
              & hBOOL(hAPP(U_3769,bool,hAPP(U_3769,fun(U_3769,bool),U_3765,sK141(U_3770,U_3769,U_3768,U_3767,U_3766,U_3765,U_3764)),U_3759))
              & hBOOL(hAPP(U_3769,bool,hAPP(U_3769,fun(U_3769,bool),U_3765,sK140(U_3770,U_3769,U_3768,U_3767,U_3766,U_3765,U_3764)),sK142(U_3770,U_3769,U_3768,U_3767,U_3766,U_3765,U_3764))) )
          | ~ hBOOL(hAPP(U_3769,bool,hAPP(U_3769,fun(U_3769,bool),U_3765,U_3764),U_3764)) )
      | ~ comm_monoid_mult(U_3769) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK142]),skolemize(U_3760,sK142(U_3770,U_3769,U_3768,U_3767,U_3766,U_3765,U_3764))],[f_968_4]) ).

fof(f_968_6,plain,
    ! [U_3770,U_3769] :
      ( ! [U_3768,U_3767,U_3766,U_3765,U_3764] :
          ( hBOOL(hAPP(U_3769,bool,hAPP(U_3769,fun(U_3769,bool),U_3765,hAPP(fun(U_3770,bool),U_3769,hAPP(U_3769,fun(fun(U_3770,bool),U_3769),hAPP(fun(U_3770,U_3769),fun(U_3769,fun(fun(U_3770,bool),U_3769)),hAPP(fun(U_3769,fun(U_3769,U_3769)),fun(fun(U_3770,U_3769),fun(U_3769,fun(fun(U_3770,bool),U_3769))),finite_fold_image(U_3769,U_3770),times_times(U_3769)),U_3768),U_3764),U_3766)),hAPP(fun(U_3770,bool),U_3769,hAPP(U_3769,fun(fun(U_3770,bool),U_3769),hAPP(fun(U_3770,U_3769),fun(U_3769,fun(fun(U_3770,bool),U_3769)),hAPP(fun(U_3769,fun(U_3769,U_3769)),fun(fun(U_3770,U_3769),fun(U_3769,fun(fun(U_3770,bool),U_3769))),finite_fold_image(U_3769,U_3770),times_times(U_3769)),U_3767),U_3764),U_3766)))
          | ? [U_3763] :
              ( ~ hBOOL(hAPP(U_3769,bool,hAPP(U_3769,fun(U_3769,bool),U_3765,hAPP(U_3770,U_3769,U_3768,U_3763)),hAPP(U_3770,U_3769,U_3767,U_3763)))
              & hBOOL(hAPP(fun(U_3770,bool),bool,hAPP(U_3770,fun(fun(U_3770,bool),bool),member(U_3770),U_3763),U_3766)) )
          | ~ hBOOL(hAPP(fun(U_3770,bool),bool,finite_finite(U_3770),U_3766))
          | ( ~ hBOOL(hAPP(U_3769,bool,hAPP(U_3769,fun(U_3769,bool),U_3765,hAPP(U_3769,U_3769,hAPP(U_3769,fun(U_3769,U_3769),times_times(U_3769),sK140(U_3770,U_3769,U_3768,U_3767,U_3766,U_3765,U_3764)),sK141(U_3770,U_3769,U_3768,U_3767,U_3766,U_3765,U_3764))),hAPP(U_3769,U_3769,hAPP(U_3769,fun(U_3769,U_3769),times_times(U_3769),sK142(U_3770,U_3769,U_3768,U_3767,U_3766,U_3765,U_3764)),sK143(U_3770,U_3769,U_3768,U_3767,U_3766,U_3765,U_3764))))
            & hBOOL(hAPP(U_3769,bool,hAPP(U_3769,fun(U_3769,bool),U_3765,sK141(U_3770,U_3769,U_3768,U_3767,U_3766,U_3765,U_3764)),sK143(U_3770,U_3769,U_3768,U_3767,U_3766,U_3765,U_3764)))
            & hBOOL(hAPP(U_3769,bool,hAPP(U_3769,fun(U_3769,bool),U_3765,sK140(U_3770,U_3769,U_3768,U_3767,U_3766,U_3765,U_3764)),sK142(U_3770,U_3769,U_3768,U_3767,U_3766,U_3765,U_3764))) )
          | ~ hBOOL(hAPP(U_3769,bool,hAPP(U_3769,fun(U_3769,bool),U_3765,U_3764),U_3764)) )
      | ~ comm_monoid_mult(U_3769) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK143]),skolemize(U_3759,sK143(U_3770,U_3769,U_3768,U_3767,U_3766,U_3765,U_3764))],[f_968_5]) ).

fof(f_968_7,plain,
    ! [U_3770,U_3769] :
      ( ! [U_3768,U_3767,U_3766,U_3765,U_3764] :
          ( hBOOL(hAPP(U_3769,bool,hAPP(U_3769,fun(U_3769,bool),U_3765,hAPP(fun(U_3770,bool),U_3769,hAPP(U_3769,fun(fun(U_3770,bool),U_3769),hAPP(fun(U_3770,U_3769),fun(U_3769,fun(fun(U_3770,bool),U_3769)),hAPP(fun(U_3769,fun(U_3769,U_3769)),fun(fun(U_3770,U_3769),fun(U_3769,fun(fun(U_3770,bool),U_3769))),finite_fold_image(U_3769,U_3770),times_times(U_3769)),U_3768),U_3764),U_3766)),hAPP(fun(U_3770,bool),U_3769,hAPP(U_3769,fun(fun(U_3770,bool),U_3769),hAPP(fun(U_3770,U_3769),fun(U_3769,fun(fun(U_3770,bool),U_3769)),hAPP(fun(U_3769,fun(U_3769,U_3769)),fun(fun(U_3770,U_3769),fun(U_3769,fun(fun(U_3770,bool),U_3769))),finite_fold_image(U_3769,U_3770),times_times(U_3769)),U_3767),U_3764),U_3766)))
          | ( ~ hBOOL(hAPP(U_3769,bool,hAPP(U_3769,fun(U_3769,bool),U_3765,hAPP(U_3770,U_3769,U_3768,sK144(U_3770,U_3769,U_3768,U_3767,U_3766,U_3765,U_3764))),hAPP(U_3770,U_3769,U_3767,sK144(U_3770,U_3769,U_3768,U_3767,U_3766,U_3765,U_3764))))
            & hBOOL(hAPP(fun(U_3770,bool),bool,hAPP(U_3770,fun(fun(U_3770,bool),bool),member(U_3770),sK144(U_3770,U_3769,U_3768,U_3767,U_3766,U_3765,U_3764)),U_3766)) )
          | ~ hBOOL(hAPP(fun(U_3770,bool),bool,finite_finite(U_3770),U_3766))
          | ( ~ hBOOL(hAPP(U_3769,bool,hAPP(U_3769,fun(U_3769,bool),U_3765,hAPP(U_3769,U_3769,hAPP(U_3769,fun(U_3769,U_3769),times_times(U_3769),sK140(U_3770,U_3769,U_3768,U_3767,U_3766,U_3765,U_3764)),sK141(U_3770,U_3769,U_3768,U_3767,U_3766,U_3765,U_3764))),hAPP(U_3769,U_3769,hAPP(U_3769,fun(U_3769,U_3769),times_times(U_3769),sK142(U_3770,U_3769,U_3768,U_3767,U_3766,U_3765,U_3764)),sK143(U_3770,U_3769,U_3768,U_3767,U_3766,U_3765,U_3764))))
            & hBOOL(hAPP(U_3769,bool,hAPP(U_3769,fun(U_3769,bool),U_3765,sK141(U_3770,U_3769,U_3768,U_3767,U_3766,U_3765,U_3764)),sK143(U_3770,U_3769,U_3768,U_3767,U_3766,U_3765,U_3764)))
            & hBOOL(hAPP(U_3769,bool,hAPP(U_3769,fun(U_3769,bool),U_3765,sK140(U_3770,U_3769,U_3768,U_3767,U_3766,U_3765,U_3764)),sK142(U_3770,U_3769,U_3768,U_3767,U_3766,U_3765,U_3764))) )
          | ~ hBOOL(hAPP(U_3769,bool,hAPP(U_3769,fun(U_3769,bool),U_3765,U_3764),U_3764)) )
      | ~ comm_monoid_mult(U_3769) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK144]),skolemize(U_3763,sK144(U_3770,U_3769,U_3768,U_3767,U_3766,U_3765,U_3764))],[f_968_6]) ).

fof(f_968_8,plain,
    ( ! [U_3765,U_3764,U_3769,U_3766,U_3767,U_3768,U_3770] :
        ( ~ hBOOL(hAPP(U_3769,bool,hAPP(U_3769,fun(U_3769,bool),U_3765,hAPP(U_3770,U_3769,U_3768,sK144(U_3770,U_3769,U_3768,U_3767,U_3766,U_3765,U_3764))),hAPP(U_3770,U_3769,U_3767,sK144(U_3770,U_3769,U_3768,U_3767,U_3766,U_3765,U_3764))))
        | ~ sP290(U_3765,U_3764,U_3769,U_3766,U_3767,U_3768,U_3770) )
    & ! [U_3765,U_3764,U_3769,U_3766,U_3767,U_3768,U_3770] :
        ( hBOOL(hAPP(fun(U_3770,bool),bool,hAPP(U_3770,fun(fun(U_3770,bool),bool),member(U_3770),sK144(U_3770,U_3769,U_3768,U_3767,U_3766,U_3765,U_3764)),U_3766))
        | ~ sP290(U_3765,U_3764,U_3769,U_3766,U_3767,U_3768,U_3770) )
    & ! [U_3765,U_3764,U_3769,U_3766,U_3767,U_3768,U_3770] :
        ( ~ hBOOL(hAPP(U_3769,bool,hAPP(U_3769,fun(U_3769,bool),U_3765,hAPP(U_3769,U_3769,hAPP(U_3769,fun(U_3769,U_3769),times_times(U_3769),sK140(U_3770,U_3769,U_3768,U_3767,U_3766,U_3765,U_3764)),sK141(U_3770,U_3769,U_3768,U_3767,U_3766,U_3765,U_3764))),hAPP(U_3769,U_3769,hAPP(U_3769,fun(U_3769,U_3769),times_times(U_3769),sK142(U_3770,U_3769,U_3768,U_3767,U_3766,U_3765,U_3764)),sK143(U_3770,U_3769,U_3768,U_3767,U_3766,U_3765,U_3764))))
        | ~ sP289(U_3765,U_3764,U_3769,U_3766,U_3767,U_3768,U_3770) )
    & ! [U_3765,U_3764,U_3769,U_3766,U_3767,U_3768,U_3770] :
        ( hBOOL(hAPP(U_3769,bool,hAPP(U_3769,fun(U_3769,bool),U_3765,sK141(U_3770,U_3769,U_3768,U_3767,U_3766,U_3765,U_3764)),sK143(U_3770,U_3769,U_3768,U_3767,U_3766,U_3765,U_3764)))
        | ~ sP289(U_3765,U_3764,U_3769,U_3766,U_3767,U_3768,U_3770) )
    & ! [U_3765,U_3764,U_3769,U_3766,U_3767,U_3768,U_3770] :
        ( hBOOL(hAPP(U_3769,bool,hAPP(U_3769,fun(U_3769,bool),U_3765,sK140(U_3770,U_3769,U_3768,U_3767,U_3766,U_3765,U_3764)),sK142(U_3770,U_3769,U_3768,U_3767,U_3766,U_3765,U_3764)))
        | ~ sP289(U_3765,U_3764,U_3769,U_3766,U_3767,U_3768,U_3770) )
    & ! [U_3765,U_3764,U_3769,U_3766,U_3767,U_3768,U_3770] :
        ( hBOOL(hAPP(U_3769,bool,hAPP(U_3769,fun(U_3769,bool),U_3765,hAPP(fun(U_3770,bool),U_3769,hAPP(U_3769,fun(fun(U_3770,bool),U_3769),hAPP(fun(U_3770,U_3769),fun(U_3769,fun(fun(U_3770,bool),U_3769)),hAPP(fun(U_3769,fun(U_3769,U_3769)),fun(fun(U_3770,U_3769),fun(U_3769,fun(fun(U_3770,bool),U_3769))),finite_fold_image(U_3769,U_3770),times_times(U_3769)),U_3768),U_3764),U_3766)),hAPP(fun(U_3770,bool),U_3769,hAPP(U_3769,fun(fun(U_3770,bool),U_3769),hAPP(fun(U_3770,U_3769),fun(U_3769,fun(fun(U_3770,bool),U_3769)),hAPP(fun(U_3769,fun(U_3769,U_3769)),fun(fun(U_3770,U_3769),fun(U_3769,fun(fun(U_3770,bool),U_3769))),finite_fold_image(U_3769,U_3770),times_times(U_3769)),U_3767),U_3764),U_3766)))
        | sP290(U_3765,U_3764,U_3769,U_3766,U_3767,U_3768,U_3770)
        | ~ hBOOL(hAPP(fun(U_3770,bool),bool,finite_finite(U_3770),U_3766))
        | sP289(U_3765,U_3764,U_3769,U_3766,U_3767,U_3768,U_3770)
        | ~ hBOOL(hAPP(U_3769,bool,hAPP(U_3769,fun(U_3769,bool),U_3765,U_3764),U_3764))
        | ~ comm_monoid_mult(U_3769) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP289,sP290])],[f_968_7]) ).

cnf(f_968_9,plain,
    ( hBOOL(hAPP(U_3769,bool,hAPP(U_3769,fun(U_3769,bool),U_3765,hAPP(fun(U_3770,bool),U_3769,hAPP(U_3769,fun(fun(U_3770,bool),U_3769),hAPP(fun(U_3770,U_3769),fun(U_3769,fun(fun(U_3770,bool),U_3769)),hAPP(fun(U_3769,fun(U_3769,U_3769)),fun(fun(U_3770,U_3769),fun(U_3769,fun(fun(U_3770,bool),U_3769))),finite_fold_image(U_3769,U_3770),times_times(U_3769)),U_3768),U_3764),U_3766)),hAPP(fun(U_3770,bool),U_3769,hAPP(U_3769,fun(fun(U_3770,bool),U_3769),hAPP(fun(U_3770,U_3769),fun(U_3769,fun(fun(U_3770,bool),U_3769)),hAPP(fun(U_3769,fun(U_3769,U_3769)),fun(fun(U_3770,U_3769),fun(U_3769,fun(fun(U_3770,bool),U_3769))),finite_fold_image(U_3769,U_3770),times_times(U_3769)),U_3767),U_3764),U_3766)))
    | sP290(U_3765,U_3764,U_3769,U_3766,U_3767,U_3768,U_3770)
    | ~ hBOOL(hAPP(fun(U_3770,bool),bool,finite_finite(U_3770),U_3766))
    | sP289(U_3765,U_3764,U_3769,U_3766,U_3767,U_3768,U_3770)
    | ~ hBOOL(hAPP(U_3769,bool,hAPP(U_3769,fun(U_3769,bool),U_3765,U_3764),U_3764))
    | ~ comm_monoid_mult(U_3769) ),
    inference(clausify,[status(thm)],[f_968_8]) ).

cnf(f_968_10,plain,
    ( hBOOL(hAPP(U_3769,bool,hAPP(U_3769,fun(U_3769,bool),U_3765,sK140(U_3770,U_3769,U_3768,U_3767,U_3766,U_3765,U_3764)),sK142(U_3770,U_3769,U_3768,U_3767,U_3766,U_3765,U_3764)))
    | ~ sP289(U_3765,U_3764,U_3769,U_3766,U_3767,U_3768,U_3770) ),
    inference(clausify,[status(thm)],[f_968_8]) ).

cnf(f_968_11,plain,
    ( hBOOL(hAPP(U_3769,bool,hAPP(U_3769,fun(U_3769,bool),U_3765,sK141(U_3770,U_3769,U_3768,U_3767,U_3766,U_3765,U_3764)),sK143(U_3770,U_3769,U_3768,U_3767,U_3766,U_3765,U_3764)))
    | ~ sP289(U_3765,U_3764,U_3769,U_3766,U_3767,U_3768,U_3770) ),
    inference(clausify,[status(thm)],[f_968_8]) ).

cnf(f_968_12,plain,
    ( ~ hBOOL(hAPP(U_3769,bool,hAPP(U_3769,fun(U_3769,bool),U_3765,hAPP(U_3769,U_3769,hAPP(U_3769,fun(U_3769,U_3769),times_times(U_3769),sK140(U_3770,U_3769,U_3768,U_3767,U_3766,U_3765,U_3764)),sK141(U_3770,U_3769,U_3768,U_3767,U_3766,U_3765,U_3764))),hAPP(U_3769,U_3769,hAPP(U_3769,fun(U_3769,U_3769),times_times(U_3769),sK142(U_3770,U_3769,U_3768,U_3767,U_3766,U_3765,U_3764)),sK143(U_3770,U_3769,U_3768,U_3767,U_3766,U_3765,U_3764))))
    | ~ sP289(U_3765,U_3764,U_3769,U_3766,U_3767,U_3768,U_3770) ),
    inference(clausify,[status(thm)],[f_968_8]) ).

cnf(f_968_13,plain,
    ( hBOOL(hAPP(fun(U_3770,bool),bool,hAPP(U_3770,fun(fun(U_3770,bool),bool),member(U_3770),sK144(U_3770,U_3769,U_3768,U_3767,U_3766,U_3765,U_3764)),U_3766))
    | ~ sP290(U_3765,U_3764,U_3769,U_3766,U_3767,U_3768,U_3770) ),
    inference(clausify,[status(thm)],[f_968_8]) ).

cnf(f_968_14,plain,
    ( ~ hBOOL(hAPP(U_3769,bool,hAPP(U_3769,fun(U_3769,bool),U_3765,hAPP(U_3770,U_3769,U_3768,sK144(U_3770,U_3769,U_3768,U_3767,U_3766,U_3765,U_3764))),hAPP(U_3770,U_3769,U_3767,sK144(U_3770,U_3769,U_3768,U_3767,U_3766,U_3765,U_3764))))
    | ~ sP290(U_3765,U_3764,U_3769,U_3766,U_3767,U_3768,U_3770) ),
    inference(clausify,[status(thm)],[f_968_8]) ).

fof(f_969_1,plain,
    ! [X_c,X_b,X_d] :
      ( ! [E,G,F,H,K,T_3,S] :
          ( hAPP(fun(X_b,bool),X_d,hAPP(X_d,fun(fun(X_b,bool),X_d),hAPP(fun(X_b,X_d),fun(X_d,fun(fun(X_b,bool),X_d)),hAPP(fun(X_d,fun(X_d,X_d)),fun(fun(X_b,X_d),fun(X_d,fun(fun(X_b,bool),X_d))),finite_fold_image(X_d,X_b),times_times(X_d)),F),E),S) = hAPP(fun(X_c,bool),X_d,hAPP(X_d,fun(fun(X_c,bool),X_d),hAPP(fun(X_c,X_d),fun(X_d,fun(fun(X_c,bool),X_d)),hAPP(fun(X_d,fun(X_d,X_d)),fun(fun(X_c,X_d),fun(X_d,fun(fun(X_c,bool),X_d))),finite_fold_image(X_d,X_c),times_times(X_d)),G),E),T_3)
          | ? [X_2] :
              ( ( hAPP(X_c,X_d,G,hAPP(X_b,X_c,H,X_2)) != hAPP(X_b,X_d,F,X_2)
                | hAPP(X_c,X_b,K,hAPP(X_b,X_c,H,X_2)) != ti(X_b,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,H,X_2)),T_3)) )
              & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),S)) )
          | ? [Y_1] :
              ( ( hAPP(X_b,X_c,H,hAPP(X_c,X_b,K,Y_1)) != ti(X_c,Y_1)
                | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_c,X_b,K,Y_1)),S)) )
              & hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),Y_1),T_3)) )
          | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),S)) )
      | ~ comm_monoid_mult(X_d) ),
    inference(fof_nnf,[status(thm)],[fact_898_fold__image__eq__general__inverses]) ).

fof(f_969_2,plain,
    ! [U_3782,U_3781,U_3780] :
      ( ! [U_3779,U_3778,U_3777,U_3776,U_3775,U_3774,U_3773] :
          ( hAPP(fun(U_3781,bool),U_3780,hAPP(U_3780,fun(fun(U_3781,bool),U_3780),hAPP(fun(U_3781,U_3780),fun(U_3780,fun(fun(U_3781,bool),U_3780)),hAPP(fun(U_3780,fun(U_3780,U_3780)),fun(fun(U_3781,U_3780),fun(U_3780,fun(fun(U_3781,bool),U_3780))),finite_fold_image(U_3780,U_3781),times_times(U_3780)),U_3777),U_3779),U_3773) = hAPP(fun(U_3782,bool),U_3780,hAPP(U_3780,fun(fun(U_3782,bool),U_3780),hAPP(fun(U_3782,U_3780),fun(U_3780,fun(fun(U_3782,bool),U_3780)),hAPP(fun(U_3780,fun(U_3780,U_3780)),fun(fun(U_3782,U_3780),fun(U_3780,fun(fun(U_3782,bool),U_3780))),finite_fold_image(U_3780,U_3782),times_times(U_3780)),U_3778),U_3779),U_3774)
          | ? [U_3772] :
              ( ( hAPP(U_3782,U_3780,U_3778,hAPP(U_3781,U_3782,U_3776,U_3772)) != hAPP(U_3781,U_3780,U_3777,U_3772)
                | hAPP(U_3782,U_3781,U_3775,hAPP(U_3781,U_3782,U_3776,U_3772)) != ti(U_3781,U_3772)
                | ~ hBOOL(hAPP(fun(U_3782,bool),bool,hAPP(U_3782,fun(fun(U_3782,bool),bool),member(U_3782),hAPP(U_3781,U_3782,U_3776,U_3772)),U_3774)) )
              & hBOOL(hAPP(fun(U_3781,bool),bool,hAPP(U_3781,fun(fun(U_3781,bool),bool),member(U_3781),U_3772),U_3773)) )
          | ? [U_3771] :
              ( ( hAPP(U_3781,U_3782,U_3776,hAPP(U_3782,U_3781,U_3775,U_3771)) != ti(U_3782,U_3771)
                | ~ hBOOL(hAPP(fun(U_3781,bool),bool,hAPP(U_3781,fun(fun(U_3781,bool),bool),member(U_3781),hAPP(U_3782,U_3781,U_3775,U_3771)),U_3773)) )
              & hBOOL(hAPP(fun(U_3782,bool),bool,hAPP(U_3782,fun(fun(U_3782,bool),bool),member(U_3782),U_3771),U_3774)) )
          | ~ hBOOL(hAPP(fun(U_3781,bool),bool,finite_finite(U_3781),U_3773)) )
      | ~ comm_monoid_mult(U_3780) ),
    inference(variable_rename,[status(thm)],[f_969_1]) ).

fof(f_969_3,plain,
    ! [U_3782,U_3781,U_3780] :
      ( ! [U_3779,U_3778,U_3777,U_3776,U_3775,U_3774,U_3773] :
          ( hAPP(fun(U_3781,bool),U_3780,hAPP(U_3780,fun(fun(U_3781,bool),U_3780),hAPP(fun(U_3781,U_3780),fun(U_3780,fun(fun(U_3781,bool),U_3780)),hAPP(fun(U_3780,fun(U_3780,U_3780)),fun(fun(U_3781,U_3780),fun(U_3780,fun(fun(U_3781,bool),U_3780))),finite_fold_image(U_3780,U_3781),times_times(U_3780)),U_3777),U_3779),U_3773) = hAPP(fun(U_3782,bool),U_3780,hAPP(U_3780,fun(fun(U_3782,bool),U_3780),hAPP(fun(U_3782,U_3780),fun(U_3780,fun(fun(U_3782,bool),U_3780)),hAPP(fun(U_3780,fun(U_3780,U_3780)),fun(fun(U_3782,U_3780),fun(U_3780,fun(fun(U_3782,bool),U_3780))),finite_fold_image(U_3780,U_3782),times_times(U_3780)),U_3778),U_3779),U_3774)
          | ? [U_3772] :
              ( ( hAPP(U_3782,U_3780,U_3778,hAPP(U_3781,U_3782,U_3776,U_3772)) != hAPP(U_3781,U_3780,U_3777,U_3772)
                | hAPP(U_3782,U_3781,U_3775,hAPP(U_3781,U_3782,U_3776,U_3772)) != ti(U_3781,U_3772)
                | ~ hBOOL(hAPP(fun(U_3782,bool),bool,hAPP(U_3782,fun(fun(U_3782,bool),bool),member(U_3782),hAPP(U_3781,U_3782,U_3776,U_3772)),U_3774)) )
              & hBOOL(hAPP(fun(U_3781,bool),bool,hAPP(U_3781,fun(fun(U_3781,bool),bool),member(U_3781),U_3772),U_3773)) )
          | ( ( hAPP(U_3781,U_3782,U_3776,hAPP(U_3782,U_3781,U_3775,sK145(U_3782,U_3781,U_3780,U_3779,U_3778,U_3777,U_3776,U_3775,U_3774,U_3773))) != ti(U_3782,sK145(U_3782,U_3781,U_3780,U_3779,U_3778,U_3777,U_3776,U_3775,U_3774,U_3773))
              | ~ hBOOL(hAPP(fun(U_3781,bool),bool,hAPP(U_3781,fun(fun(U_3781,bool),bool),member(U_3781),hAPP(U_3782,U_3781,U_3775,sK145(U_3782,U_3781,U_3780,U_3779,U_3778,U_3777,U_3776,U_3775,U_3774,U_3773))),U_3773)) )
            & hBOOL(hAPP(fun(U_3782,bool),bool,hAPP(U_3782,fun(fun(U_3782,bool),bool),member(U_3782),sK145(U_3782,U_3781,U_3780,U_3779,U_3778,U_3777,U_3776,U_3775,U_3774,U_3773)),U_3774)) )
          | ~ hBOOL(hAPP(fun(U_3781,bool),bool,finite_finite(U_3781),U_3773)) )
      | ~ comm_monoid_mult(U_3780) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK145]),skolemize(U_3771,sK145(U_3782,U_3781,U_3780,U_3779,U_3778,U_3777,U_3776,U_3775,U_3774,U_3773))],[f_969_2]) ).

fof(f_969_4,plain,
    ! [U_3782,U_3781,U_3780] :
      ( ! [U_3779,U_3778,U_3777,U_3776,U_3775,U_3774,U_3773] :
          ( hAPP(fun(U_3781,bool),U_3780,hAPP(U_3780,fun(fun(U_3781,bool),U_3780),hAPP(fun(U_3781,U_3780),fun(U_3780,fun(fun(U_3781,bool),U_3780)),hAPP(fun(U_3780,fun(U_3780,U_3780)),fun(fun(U_3781,U_3780),fun(U_3780,fun(fun(U_3781,bool),U_3780))),finite_fold_image(U_3780,U_3781),times_times(U_3780)),U_3777),U_3779),U_3773) = hAPP(fun(U_3782,bool),U_3780,hAPP(U_3780,fun(fun(U_3782,bool),U_3780),hAPP(fun(U_3782,U_3780),fun(U_3780,fun(fun(U_3782,bool),U_3780)),hAPP(fun(U_3780,fun(U_3780,U_3780)),fun(fun(U_3782,U_3780),fun(U_3780,fun(fun(U_3782,bool),U_3780))),finite_fold_image(U_3780,U_3782),times_times(U_3780)),U_3778),U_3779),U_3774)
          | ( ( hAPP(U_3782,U_3780,U_3778,hAPP(U_3781,U_3782,U_3776,sK146(U_3782,U_3781,U_3780,U_3779,U_3778,U_3777,U_3776,U_3775,U_3774,U_3773))) != hAPP(U_3781,U_3780,U_3777,sK146(U_3782,U_3781,U_3780,U_3779,U_3778,U_3777,U_3776,U_3775,U_3774,U_3773))
              | hAPP(U_3782,U_3781,U_3775,hAPP(U_3781,U_3782,U_3776,sK146(U_3782,U_3781,U_3780,U_3779,U_3778,U_3777,U_3776,U_3775,U_3774,U_3773))) != ti(U_3781,sK146(U_3782,U_3781,U_3780,U_3779,U_3778,U_3777,U_3776,U_3775,U_3774,U_3773))
              | ~ hBOOL(hAPP(fun(U_3782,bool),bool,hAPP(U_3782,fun(fun(U_3782,bool),bool),member(U_3782),hAPP(U_3781,U_3782,U_3776,sK146(U_3782,U_3781,U_3780,U_3779,U_3778,U_3777,U_3776,U_3775,U_3774,U_3773))),U_3774)) )
            & hBOOL(hAPP(fun(U_3781,bool),bool,hAPP(U_3781,fun(fun(U_3781,bool),bool),member(U_3781),sK146(U_3782,U_3781,U_3780,U_3779,U_3778,U_3777,U_3776,U_3775,U_3774,U_3773)),U_3773)) )
          | ( ( hAPP(U_3781,U_3782,U_3776,hAPP(U_3782,U_3781,U_3775,sK145(U_3782,U_3781,U_3780,U_3779,U_3778,U_3777,U_3776,U_3775,U_3774,U_3773))) != ti(U_3782,sK145(U_3782,U_3781,U_3780,U_3779,U_3778,U_3777,U_3776,U_3775,U_3774,U_3773))
              | ~ hBOOL(hAPP(fun(U_3781,bool),bool,hAPP(U_3781,fun(fun(U_3781,bool),bool),member(U_3781),hAPP(U_3782,U_3781,U_3775,sK145(U_3782,U_3781,U_3780,U_3779,U_3778,U_3777,U_3776,U_3775,U_3774,U_3773))),U_3773)) )
            & hBOOL(hAPP(fun(U_3782,bool),bool,hAPP(U_3782,fun(fun(U_3782,bool),bool),member(U_3782),sK145(U_3782,U_3781,U_3780,U_3779,U_3778,U_3777,U_3776,U_3775,U_3774,U_3773)),U_3774)) )
          | ~ hBOOL(hAPP(fun(U_3781,bool),bool,finite_finite(U_3781),U_3773)) )
      | ~ comm_monoid_mult(U_3780) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK146]),skolemize(U_3772,sK146(U_3782,U_3781,U_3780,U_3779,U_3778,U_3777,U_3776,U_3775,U_3774,U_3773))],[f_969_3]) ).

fof(f_969_5,plain,
    ( ! [U_3776,U_3777,U_3773,U_3780,U_3778,U_3775,U_3774,U_3779,U_3781,U_3782] :
        ( hAPP(U_3782,U_3780,U_3778,hAPP(U_3781,U_3782,U_3776,sK146(U_3782,U_3781,U_3780,U_3779,U_3778,U_3777,U_3776,U_3775,U_3774,U_3773))) != hAPP(U_3781,U_3780,U_3777,sK146(U_3782,U_3781,U_3780,U_3779,U_3778,U_3777,U_3776,U_3775,U_3774,U_3773))
        | hAPP(U_3782,U_3781,U_3775,hAPP(U_3781,U_3782,U_3776,sK146(U_3782,U_3781,U_3780,U_3779,U_3778,U_3777,U_3776,U_3775,U_3774,U_3773))) != ti(U_3781,sK146(U_3782,U_3781,U_3780,U_3779,U_3778,U_3777,U_3776,U_3775,U_3774,U_3773))
        | ~ hBOOL(hAPP(fun(U_3782,bool),bool,hAPP(U_3782,fun(fun(U_3782,bool),bool),member(U_3782),hAPP(U_3781,U_3782,U_3776,sK146(U_3782,U_3781,U_3780,U_3779,U_3778,U_3777,U_3776,U_3775,U_3774,U_3773))),U_3774))
        | ~ sP292(U_3776,U_3777,U_3773,U_3780,U_3778,U_3775,U_3774,U_3779,U_3781,U_3782) )
    & ! [U_3776,U_3777,U_3773,U_3780,U_3778,U_3775,U_3774,U_3779,U_3781,U_3782] :
        ( hBOOL(hAPP(fun(U_3781,bool),bool,hAPP(U_3781,fun(fun(U_3781,bool),bool),member(U_3781),sK146(U_3782,U_3781,U_3780,U_3779,U_3778,U_3777,U_3776,U_3775,U_3774,U_3773)),U_3773))
        | ~ sP292(U_3776,U_3777,U_3773,U_3780,U_3778,U_3775,U_3774,U_3779,U_3781,U_3782) )
    & ! [U_3776,U_3777,U_3773,U_3780,U_3778,U_3775,U_3774,U_3779,U_3781,U_3782] :
        ( hAPP(U_3781,U_3782,U_3776,hAPP(U_3782,U_3781,U_3775,sK145(U_3782,U_3781,U_3780,U_3779,U_3778,U_3777,U_3776,U_3775,U_3774,U_3773))) != ti(U_3782,sK145(U_3782,U_3781,U_3780,U_3779,U_3778,U_3777,U_3776,U_3775,U_3774,U_3773))
        | ~ hBOOL(hAPP(fun(U_3781,bool),bool,hAPP(U_3781,fun(fun(U_3781,bool),bool),member(U_3781),hAPP(U_3782,U_3781,U_3775,sK145(U_3782,U_3781,U_3780,U_3779,U_3778,U_3777,U_3776,U_3775,U_3774,U_3773))),U_3773))
        | ~ sP291(U_3776,U_3777,U_3773,U_3780,U_3778,U_3775,U_3774,U_3779,U_3781,U_3782) )
    & ! [U_3776,U_3777,U_3773,U_3780,U_3778,U_3775,U_3774,U_3779,U_3781,U_3782] :
        ( hBOOL(hAPP(fun(U_3782,bool),bool,hAPP(U_3782,fun(fun(U_3782,bool),bool),member(U_3782),sK145(U_3782,U_3781,U_3780,U_3779,U_3778,U_3777,U_3776,U_3775,U_3774,U_3773)),U_3774))
        | ~ sP291(U_3776,U_3777,U_3773,U_3780,U_3778,U_3775,U_3774,U_3779,U_3781,U_3782) )
    & ! [U_3776,U_3777,U_3773,U_3780,U_3778,U_3775,U_3774,U_3779,U_3781,U_3782] :
        ( hAPP(fun(U_3781,bool),U_3780,hAPP(U_3780,fun(fun(U_3781,bool),U_3780),hAPP(fun(U_3781,U_3780),fun(U_3780,fun(fun(U_3781,bool),U_3780)),hAPP(fun(U_3780,fun(U_3780,U_3780)),fun(fun(U_3781,U_3780),fun(U_3780,fun(fun(U_3781,bool),U_3780))),finite_fold_image(U_3780,U_3781),times_times(U_3780)),U_3777),U_3779),U_3773) = hAPP(fun(U_3782,bool),U_3780,hAPP(U_3780,fun(fun(U_3782,bool),U_3780),hAPP(fun(U_3782,U_3780),fun(U_3780,fun(fun(U_3782,bool),U_3780)),hAPP(fun(U_3780,fun(U_3780,U_3780)),fun(fun(U_3782,U_3780),fun(U_3780,fun(fun(U_3782,bool),U_3780))),finite_fold_image(U_3780,U_3782),times_times(U_3780)),U_3778),U_3779),U_3774)
        | sP292(U_3776,U_3777,U_3773,U_3780,U_3778,U_3775,U_3774,U_3779,U_3781,U_3782)
        | sP291(U_3776,U_3777,U_3773,U_3780,U_3778,U_3775,U_3774,U_3779,U_3781,U_3782)
        | ~ hBOOL(hAPP(fun(U_3781,bool),bool,finite_finite(U_3781),U_3773))
        | ~ comm_monoid_mult(U_3780) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP291,sP292])],[f_969_4]) ).

cnf(f_969_6,plain,
    ( hAPP(fun(U_3781,bool),U_3780,hAPP(U_3780,fun(fun(U_3781,bool),U_3780),hAPP(fun(U_3781,U_3780),fun(U_3780,fun(fun(U_3781,bool),U_3780)),hAPP(fun(U_3780,fun(U_3780,U_3780)),fun(fun(U_3781,U_3780),fun(U_3780,fun(fun(U_3781,bool),U_3780))),finite_fold_image(U_3780,U_3781),times_times(U_3780)),U_3777),U_3779),U_3773) = hAPP(fun(U_3782,bool),U_3780,hAPP(U_3780,fun(fun(U_3782,bool),U_3780),hAPP(fun(U_3782,U_3780),fun(U_3780,fun(fun(U_3782,bool),U_3780)),hAPP(fun(U_3780,fun(U_3780,U_3780)),fun(fun(U_3782,U_3780),fun(U_3780,fun(fun(U_3782,bool),U_3780))),finite_fold_image(U_3780,U_3782),times_times(U_3780)),U_3778),U_3779),U_3774)
    | sP292(U_3776,U_3777,U_3773,U_3780,U_3778,U_3775,U_3774,U_3779,U_3781,U_3782)
    | sP291(U_3776,U_3777,U_3773,U_3780,U_3778,U_3775,U_3774,U_3779,U_3781,U_3782)
    | ~ hBOOL(hAPP(fun(U_3781,bool),bool,finite_finite(U_3781),U_3773))
    | ~ comm_monoid_mult(U_3780) ),
    inference(clausify,[status(thm)],[f_969_5]) ).

cnf(f_969_7,plain,
    ( hBOOL(hAPP(fun(U_3782,bool),bool,hAPP(U_3782,fun(fun(U_3782,bool),bool),member(U_3782),sK145(U_3782,U_3781,U_3780,U_3779,U_3778,U_3777,U_3776,U_3775,U_3774,U_3773)),U_3774))
    | ~ sP291(U_3776,U_3777,U_3773,U_3780,U_3778,U_3775,U_3774,U_3779,U_3781,U_3782) ),
    inference(clausify,[status(thm)],[f_969_5]) ).

cnf(f_969_8,plain,
    ( hAPP(U_3781,U_3782,U_3776,hAPP(U_3782,U_3781,U_3775,sK145(U_3782,U_3781,U_3780,U_3779,U_3778,U_3777,U_3776,U_3775,U_3774,U_3773))) != ti(U_3782,sK145(U_3782,U_3781,U_3780,U_3779,U_3778,U_3777,U_3776,U_3775,U_3774,U_3773))
    | ~ hBOOL(hAPP(fun(U_3781,bool),bool,hAPP(U_3781,fun(fun(U_3781,bool),bool),member(U_3781),hAPP(U_3782,U_3781,U_3775,sK145(U_3782,U_3781,U_3780,U_3779,U_3778,U_3777,U_3776,U_3775,U_3774,U_3773))),U_3773))
    | ~ sP291(U_3776,U_3777,U_3773,U_3780,U_3778,U_3775,U_3774,U_3779,U_3781,U_3782) ),
    inference(clausify,[status(thm)],[f_969_5]) ).

cnf(f_969_9,plain,
    ( hBOOL(hAPP(fun(U_3781,bool),bool,hAPP(U_3781,fun(fun(U_3781,bool),bool),member(U_3781),sK146(U_3782,U_3781,U_3780,U_3779,U_3778,U_3777,U_3776,U_3775,U_3774,U_3773)),U_3773))
    | ~ sP292(U_3776,U_3777,U_3773,U_3780,U_3778,U_3775,U_3774,U_3779,U_3781,U_3782) ),
    inference(clausify,[status(thm)],[f_969_5]) ).

cnf(f_969_10,plain,
    ( hAPP(U_3782,U_3780,U_3778,hAPP(U_3781,U_3782,U_3776,sK146(U_3782,U_3781,U_3780,U_3779,U_3778,U_3777,U_3776,U_3775,U_3774,U_3773))) != hAPP(U_3781,U_3780,U_3777,sK146(U_3782,U_3781,U_3780,U_3779,U_3778,U_3777,U_3776,U_3775,U_3774,U_3773))
    | hAPP(U_3782,U_3781,U_3775,hAPP(U_3781,U_3782,U_3776,sK146(U_3782,U_3781,U_3780,U_3779,U_3778,U_3777,U_3776,U_3775,U_3774,U_3773))) != ti(U_3781,sK146(U_3782,U_3781,U_3780,U_3779,U_3778,U_3777,U_3776,U_3775,U_3774,U_3773))
    | ~ hBOOL(hAPP(fun(U_3782,bool),bool,hAPP(U_3782,fun(fun(U_3782,bool),bool),member(U_3782),hAPP(U_3781,U_3782,U_3776,sK146(U_3782,U_3781,U_3780,U_3779,U_3778,U_3777,U_3776,U_3775,U_3774,U_3773))),U_3774))
    | ~ sP292(U_3776,U_3777,U_3773,U_3780,U_3778,U_3775,U_3774,U_3779,U_3781,U_3782) ),
    inference(clausify,[status(thm)],[f_969_5]) ).

fof(f_970_1,plain,
    ! [X_a] :
      ( ! [V] :
          ( ( hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,number_number_of(nat),V)) = hAPP(int,X_a,number_number_of(X_a),V)
            | hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) )
          & ( hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,number_number_of(nat),V)) = zero_zero(X_a)
            | ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) ) )
      | ~ number_ring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_899_of__nat__number__of__eq]) ).

fof(f_970_2,plain,
    ! [U_3784] :
      ( ! [U_3783] :
          ( ( hAPP(nat,U_3784,semiring_1_of_nat(U_3784),hAPP(int,nat,number_number_of(nat),U_3783)) = hAPP(int,U_3784,number_number_of(U_3784),U_3783)
            | hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3783))) )
          & ( hAPP(nat,U_3784,semiring_1_of_nat(U_3784),hAPP(int,nat,number_number_of(nat),U_3783)) = zero_zero(U_3784)
            | ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3783))) ) )
      | ~ number_ring(U_3784) ),
    inference(variable_rename,[status(thm)],[f_970_1]) ).

fof(f_970_3,plain,
    ! [U_3784] :
      ( ( ! [U_3786] :
            ( hAPP(nat,U_3784,semiring_1_of_nat(U_3784),hAPP(int,nat,number_number_of(nat),U_3786)) = hAPP(int,U_3784,number_number_of(U_3784),U_3786)
            | hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3786))) )
        & ! [U_3785] :
            ( hAPP(nat,U_3784,semiring_1_of_nat(U_3784),hAPP(int,nat,number_number_of(nat),U_3785)) = zero_zero(U_3784)
            | ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3785))) ) )
      | ~ number_ring(U_3784) ),
    inference(miniscope,[status(thm)],[f_970_2]) ).

fof(f_970_4,plain,
    ( ! [U_3786,U_3784,U_3785] :
        ( hAPP(nat,U_3784,semiring_1_of_nat(U_3784),hAPP(int,nat,number_number_of(nat),U_3786)) = hAPP(int,U_3784,number_number_of(U_3784),U_3786)
        | hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3786)))
        | ~ sP293(U_3786,U_3784,U_3785) )
    & ! [U_3786,U_3784,U_3785] :
        ( hAPP(nat,U_3784,semiring_1_of_nat(U_3784),hAPP(int,nat,number_number_of(nat),U_3785)) = zero_zero(U_3784)
        | ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3785)))
        | ~ sP293(U_3786,U_3784,U_3785) )
    & ! [U_3786,U_3784,U_3785] :
        ( sP293(U_3786,U_3784,U_3785)
        | ~ number_ring(U_3784) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP293])],[f_970_3]) ).

cnf(f_970_5,plain,
    ( sP293(U_3786,U_3784,U_3785)
    | ~ number_ring(U_3784) ),
    inference(clausify,[status(thm)],[f_970_4]) ).

cnf(f_970_6,plain,
    ( hAPP(nat,U_3784,semiring_1_of_nat(U_3784),hAPP(int,nat,number_number_of(nat),U_3785)) = zero_zero(U_3784)
    | ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3785)))
    | ~ sP293(U_3786,U_3784,U_3785) ),
    inference(clausify,[status(thm)],[f_970_4]) ).

cnf(f_970_7,plain,
    ( hAPP(nat,U_3784,semiring_1_of_nat(U_3784),hAPP(int,nat,number_number_of(nat),U_3786)) = hAPP(int,U_3784,number_number_of(U_3784),U_3786)
    | hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3786)))
    | ~ sP293(U_3786,U_3784,U_3785) ),
    inference(clausify,[status(thm)],[f_970_4]) ).

fof(f_971_1,plain,
    ! [X,Z,D] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X),Z))),one_one(int))),D))),Z))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D)) ),
    inference(fof_nnf,[status(thm)],[fact_900_decr__lemma]) ).

fof(f_971_2,plain,
    ! [U_3789,U_3788,U_3787] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3789),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3789),U_3788))),one_one(int))),U_3787))),U_3788))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3787)) ),
    inference(variable_rename,[status(thm)],[f_971_1]) ).

fof(f_971_3,plain,
    ! [U_3788,U_3789,U_3787] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3789),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3789),U_3788))),one_one(int))),U_3787))),U_3788))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3787)) ),
    inference(definitional_conversion,[status(esa)],[f_971_2]) ).

cnf(f_971_4,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3789),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3789),U_3788))),one_one(int))),U_3787))),U_3788))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3787)) ),
    inference(clausify,[status(thm)],[f_971_3]) ).

fof(f_972_1,plain,
    ! [X_a] :
      ( ! [A_1,B] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B))))
      | ~ ordere142940540dd_abs(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_901_abs__triangle__ineq4]) ).

fof(f_972_2,plain,
    ! [U_3792] :
      ( ! [U_3791,U_3790] : hBOOL(hAPP(U_3792,bool,hAPP(U_3792,fun(U_3792,bool),ord_less_eq(U_3792),hAPP(U_3792,U_3792,abs_abs(U_3792),hAPP(U_3792,U_3792,hAPP(U_3792,fun(U_3792,U_3792),minus_minus(U_3792),U_3791),U_3790))),hAPP(U_3792,U_3792,hAPP(U_3792,fun(U_3792,U_3792),plus_plus(U_3792),hAPP(U_3792,U_3792,abs_abs(U_3792),U_3791)),hAPP(U_3792,U_3792,abs_abs(U_3792),U_3790))))
      | ~ ordere142940540dd_abs(U_3792) ),
    inference(variable_rename,[status(thm)],[f_972_1]) ).

fof(f_972_3,plain,
    ! [U_3792,U_3790,U_3791] :
      ( hBOOL(hAPP(U_3792,bool,hAPP(U_3792,fun(U_3792,bool),ord_less_eq(U_3792),hAPP(U_3792,U_3792,abs_abs(U_3792),hAPP(U_3792,U_3792,hAPP(U_3792,fun(U_3792,U_3792),minus_minus(U_3792),U_3791),U_3790))),hAPP(U_3792,U_3792,hAPP(U_3792,fun(U_3792,U_3792),plus_plus(U_3792),hAPP(U_3792,U_3792,abs_abs(U_3792),U_3791)),hAPP(U_3792,U_3792,abs_abs(U_3792),U_3790))))
      | ~ ordere142940540dd_abs(U_3792) ),
    inference(definitional_conversion,[status(esa)],[f_972_2]) ).

cnf(f_972_4,plain,
    ( hBOOL(hAPP(U_3792,bool,hAPP(U_3792,fun(U_3792,bool),ord_less_eq(U_3792),hAPP(U_3792,U_3792,abs_abs(U_3792),hAPP(U_3792,U_3792,hAPP(U_3792,fun(U_3792,U_3792),minus_minus(U_3792),U_3791),U_3790))),hAPP(U_3792,U_3792,hAPP(U_3792,fun(U_3792,U_3792),plus_plus(U_3792),hAPP(U_3792,U_3792,abs_abs(U_3792),U_3791)),hAPP(U_3792,U_3792,abs_abs(U_3792),U_3790))))
    | ~ ordere142940540dd_abs(U_3792) ),
    inference(clausify,[status(thm)],[f_972_3]) ).

fof(f_973_1,plain,
    ! [X_a] :
      ( ! [A_1,B,C,D] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,abs_abs(X_a),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)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),D)))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),C))),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B),D)))))
      | ~ ordere142940540dd_abs(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_902_abs__diff__triangle__ineq]) ).

fof(f_973_2,plain,
    ! [U_3797] :
      ( ! [U_3796,U_3795,U_3794,U_3793] : hBOOL(hAPP(U_3797,bool,hAPP(U_3797,fun(U_3797,bool),ord_less_eq(U_3797),hAPP(U_3797,U_3797,abs_abs(U_3797),hAPP(U_3797,U_3797,hAPP(U_3797,fun(U_3797,U_3797),minus_minus(U_3797),hAPP(U_3797,U_3797,hAPP(U_3797,fun(U_3797,U_3797),plus_plus(U_3797),U_3796),U_3795)),hAPP(U_3797,U_3797,hAPP(U_3797,fun(U_3797,U_3797),plus_plus(U_3797),U_3794),U_3793)))),hAPP(U_3797,U_3797,hAPP(U_3797,fun(U_3797,U_3797),plus_plus(U_3797),hAPP(U_3797,U_3797,abs_abs(U_3797),hAPP(U_3797,U_3797,hAPP(U_3797,fun(U_3797,U_3797),minus_minus(U_3797),U_3796),U_3794))),hAPP(U_3797,U_3797,abs_abs(U_3797),hAPP(U_3797,U_3797,hAPP(U_3797,fun(U_3797,U_3797),minus_minus(U_3797),U_3795),U_3793)))))
      | ~ ordere142940540dd_abs(U_3797) ),
    inference(variable_rename,[status(thm)],[f_973_1]) ).

fof(f_973_3,plain,
    ! [U_3797,U_3793,U_3794,U_3795,U_3796] :
      ( hBOOL(hAPP(U_3797,bool,hAPP(U_3797,fun(U_3797,bool),ord_less_eq(U_3797),hAPP(U_3797,U_3797,abs_abs(U_3797),hAPP(U_3797,U_3797,hAPP(U_3797,fun(U_3797,U_3797),minus_minus(U_3797),hAPP(U_3797,U_3797,hAPP(U_3797,fun(U_3797,U_3797),plus_plus(U_3797),U_3796),U_3795)),hAPP(U_3797,U_3797,hAPP(U_3797,fun(U_3797,U_3797),plus_plus(U_3797),U_3794),U_3793)))),hAPP(U_3797,U_3797,hAPP(U_3797,fun(U_3797,U_3797),plus_plus(U_3797),hAPP(U_3797,U_3797,abs_abs(U_3797),hAPP(U_3797,U_3797,hAPP(U_3797,fun(U_3797,U_3797),minus_minus(U_3797),U_3796),U_3794))),hAPP(U_3797,U_3797,abs_abs(U_3797),hAPP(U_3797,U_3797,hAPP(U_3797,fun(U_3797,U_3797),minus_minus(U_3797),U_3795),U_3793)))))
      | ~ ordere142940540dd_abs(U_3797) ),
    inference(definitional_conversion,[status(esa)],[f_973_2]) ).

cnf(f_973_4,plain,
    ( hBOOL(hAPP(U_3797,bool,hAPP(U_3797,fun(U_3797,bool),ord_less_eq(U_3797),hAPP(U_3797,U_3797,abs_abs(U_3797),hAPP(U_3797,U_3797,hAPP(U_3797,fun(U_3797,U_3797),minus_minus(U_3797),hAPP(U_3797,U_3797,hAPP(U_3797,fun(U_3797,U_3797),plus_plus(U_3797),U_3796),U_3795)),hAPP(U_3797,U_3797,hAPP(U_3797,fun(U_3797,U_3797),plus_plus(U_3797),U_3794),U_3793)))),hAPP(U_3797,U_3797,hAPP(U_3797,fun(U_3797,U_3797),plus_plus(U_3797),hAPP(U_3797,U_3797,abs_abs(U_3797),hAPP(U_3797,U_3797,hAPP(U_3797,fun(U_3797,U_3797),minus_minus(U_3797),U_3796),U_3794))),hAPP(U_3797,U_3797,abs_abs(U_3797),hAPP(U_3797,U_3797,hAPP(U_3797,fun(U_3797,U_3797),minus_minus(U_3797),U_3795),U_3793)))))
    | ~ ordere142940540dd_abs(U_3797) ),
    inference(clausify,[status(thm)],[f_973_3]) ).

fof(f_974_1,plain,
    ! [Z_2] :
      ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),Z_2)),one_one(int)))
        | Z_2 != zero_zero(int) )
      & ( Z_2 = zero_zero(int)
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),Z_2)),one_one(int))) ) ),
    inference(fof_nnf,[status(thm)],[fact_903_zabs__less__one__iff]) ).

fof(f_974_2,plain,
    ! [U_3798] :
      ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),U_3798)),one_one(int)))
        | U_3798 != zero_zero(int) )
      & ( U_3798 = zero_zero(int)
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),U_3798)),one_one(int))) ) ),
    inference(variable_rename,[status(thm)],[f_974_1]) ).

fof(f_974_3,plain,
    ( ! [U_3800] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),U_3800)),one_one(int)))
        | U_3800 != zero_zero(int) )
    & ! [U_3799] :
        ( U_3799 = zero_zero(int)
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),U_3799)),one_one(int))) ) ),
    inference(miniscope,[status(thm)],[f_974_2]) ).

fof(f_974_4,plain,
    ( ! [U_3800] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),U_3800)),one_one(int)))
        | U_3800 != zero_zero(int) )
    & ! [U_3799] :
        ( U_3799 = zero_zero(int)
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),U_3799)),one_one(int))) ) ),
    inference(definitional_conversion,[status(esa)],[f_974_3]) ).

cnf(f_974_5,plain,
    ( U_3799 = zero_zero(int)
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),U_3799)),one_one(int))) ),
    inference(clausify,[status(thm)],[f_974_4]) ).

cnf(f_974_6,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),U_3800)),one_one(int)))
    | U_3800 != zero_zero(int) ),
    inference(clausify,[status(thm)],[f_974_4]) ).

fof(f_975_1,plain,
    ! [Z_1] :
      ( ( hBOOL(hAPP(int,bool,nat_neg,Z_1))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_1),zero_zero(int))) )
      & ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_1),zero_zero(int)))
        | ~ hBOOL(hAPP(int,bool,nat_neg,Z_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_904_neg__def]) ).

fof(f_975_2,plain,
    ! [U_3801] :
      ( ( hBOOL(hAPP(int,bool,nat_neg,U_3801))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3801),zero_zero(int))) )
      & ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3801),zero_zero(int)))
        | ~ hBOOL(hAPP(int,bool,nat_neg,U_3801)) ) ),
    inference(variable_rename,[status(thm)],[f_975_1]) ).

fof(f_975_3,plain,
    ( ! [U_3803] :
        ( hBOOL(hAPP(int,bool,nat_neg,U_3803))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3803),zero_zero(int))) )
    & ! [U_3802] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3802),zero_zero(int)))
        | ~ hBOOL(hAPP(int,bool,nat_neg,U_3802)) ) ),
    inference(miniscope,[status(thm)],[f_975_2]) ).

fof(f_975_4,plain,
    ( ! [U_3803] :
        ( hBOOL(hAPP(int,bool,nat_neg,U_3803))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3803),zero_zero(int))) )
    & ! [U_3802] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3802),zero_zero(int)))
        | ~ hBOOL(hAPP(int,bool,nat_neg,U_3802)) ) ),
    inference(definitional_conversion,[status(esa)],[f_975_3]) ).

cnf(f_975_5,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3802),zero_zero(int)))
    | ~ hBOOL(hAPP(int,bool,nat_neg,U_3802)) ),
    inference(clausify,[status(thm)],[f_975_4]) ).

cnf(f_975_6,plain,
    ( hBOOL(hAPP(int,bool,nat_neg,U_3803))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3803),zero_zero(int))) ),
    inference(clausify,[status(thm)],[f_975_4]) ).

fof(f_976_1,plain,
    ! [X_1] :
      ( ( ~ hBOOL(hAPP(int,bool,nat_neg,X_1))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) )
      & ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1))
        | hBOOL(hAPP(int,bool,nat_neg,X_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_905_not__neg__eq__ge__0]) ).

fof(f_976_2,plain,
    ! [U_3804] :
      ( ( ~ hBOOL(hAPP(int,bool,nat_neg,U_3804))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3804)) )
      & ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3804))
        | hBOOL(hAPP(int,bool,nat_neg,U_3804)) ) ),
    inference(variable_rename,[status(thm)],[f_976_1]) ).

fof(f_976_3,plain,
    ( ! [U_3806] :
        ( ~ hBOOL(hAPP(int,bool,nat_neg,U_3806))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3806)) )
    & ! [U_3805] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3805))
        | hBOOL(hAPP(int,bool,nat_neg,U_3805)) ) ),
    inference(miniscope,[status(thm)],[f_976_2]) ).

fof(f_976_4,plain,
    ( ! [U_3806] :
        ( ~ hBOOL(hAPP(int,bool,nat_neg,U_3806))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3806)) )
    & ! [U_3805] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3805))
        | hBOOL(hAPP(int,bool,nat_neg,U_3805)) ) ),
    inference(definitional_conversion,[status(esa)],[f_976_3]) ).

cnf(f_976_5,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3805))
    | hBOOL(hAPP(int,bool,nat_neg,U_3805)) ),
    inference(clausify,[status(thm)],[f_976_4]) ).

cnf(f_976_6,plain,
    ( ~ hBOOL(hAPP(int,bool,nat_neg,U_3806))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_3806)) ),
    inference(clausify,[status(thm)],[f_976_4]) ).

fof(f_977_1,plain,
    ! [X_a] :
      ( ! [A_1] :
          ( hAPP(X_a,X_a,abs_abs(X_a),A_1) = ti(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)),A_1)) )
      | ~ ordere142940540dd_abs(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_906_abs__of__nonneg]) ).

fof(f_977_2,plain,
    ! [U_3808] :
      ( ! [U_3807] :
          ( hAPP(U_3808,U_3808,abs_abs(U_3808),U_3807) = ti(U_3808,U_3807)
          | ~ hBOOL(hAPP(U_3808,bool,hAPP(U_3808,fun(U_3808,bool),ord_less_eq(U_3808),zero_zero(U_3808)),U_3807)) )
      | ~ ordere142940540dd_abs(U_3808) ),
    inference(variable_rename,[status(thm)],[f_977_1]) ).

fof(f_977_3,plain,
    ! [U_3807,U_3808] :
      ( hAPP(U_3808,U_3808,abs_abs(U_3808),U_3807) = ti(U_3808,U_3807)
      | ~ hBOOL(hAPP(U_3808,bool,hAPP(U_3808,fun(U_3808,bool),ord_less_eq(U_3808),zero_zero(U_3808)),U_3807))
      | ~ ordere142940540dd_abs(U_3808) ),
    inference(definitional_conversion,[status(esa)],[f_977_2]) ).

cnf(f_977_4,plain,
    ( hAPP(U_3808,U_3808,abs_abs(U_3808),U_3807) = ti(U_3808,U_3807)
    | ~ hBOOL(hAPP(U_3808,bool,hAPP(U_3808,fun(U_3808,bool),ord_less_eq(U_3808),zero_zero(U_3808)),U_3807))
    | ~ ordere142940540dd_abs(U_3808) ),
    inference(clausify,[status(thm)],[f_977_3]) ).

fof(f_978_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,abs_abs(X_b),A_2)),zero_zero(X_b)))
            | ti(X_b,A_2) != zero_zero(X_b) )
          & ( ti(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,abs_abs(X_b),A_2)),zero_zero(X_b))) ) )
      | ~ ordere142940540dd_abs(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_907_abs__le__zero__iff]) ).

fof(f_978_2,plain,
    ! [U_3810] :
      ( ! [U_3809] :
          ( ( hBOOL(hAPP(U_3810,bool,hAPP(U_3810,fun(U_3810,bool),ord_less_eq(U_3810),hAPP(U_3810,U_3810,abs_abs(U_3810),U_3809)),zero_zero(U_3810)))
            | ti(U_3810,U_3809) != zero_zero(U_3810) )
          & ( ti(U_3810,U_3809) = zero_zero(U_3810)
            | ~ hBOOL(hAPP(U_3810,bool,hAPP(U_3810,fun(U_3810,bool),ord_less_eq(U_3810),hAPP(U_3810,U_3810,abs_abs(U_3810),U_3809)),zero_zero(U_3810))) ) )
      | ~ ordere142940540dd_abs(U_3810) ),
    inference(variable_rename,[status(thm)],[f_978_1]) ).

fof(f_978_3,plain,
    ! [U_3810] :
      ( ( ! [U_3812] :
            ( hBOOL(hAPP(U_3810,bool,hAPP(U_3810,fun(U_3810,bool),ord_less_eq(U_3810),hAPP(U_3810,U_3810,abs_abs(U_3810),U_3812)),zero_zero(U_3810)))
            | ti(U_3810,U_3812) != zero_zero(U_3810) )
        & ! [U_3811] :
            ( ti(U_3810,U_3811) = zero_zero(U_3810)
            | ~ hBOOL(hAPP(U_3810,bool,hAPP(U_3810,fun(U_3810,bool),ord_less_eq(U_3810),hAPP(U_3810,U_3810,abs_abs(U_3810),U_3811)),zero_zero(U_3810))) ) )
      | ~ ordere142940540dd_abs(U_3810) ),
    inference(miniscope,[status(thm)],[f_978_2]) ).

fof(f_978_4,plain,
    ( ! [U_3810,U_3811,U_3812] :
        ( hBOOL(hAPP(U_3810,bool,hAPP(U_3810,fun(U_3810,bool),ord_less_eq(U_3810),hAPP(U_3810,U_3810,abs_abs(U_3810),U_3812)),zero_zero(U_3810)))
        | ti(U_3810,U_3812) != zero_zero(U_3810)
        | ~ sP294(U_3810,U_3811,U_3812) )
    & ! [U_3810,U_3811,U_3812] :
        ( ti(U_3810,U_3811) = zero_zero(U_3810)
        | ~ hBOOL(hAPP(U_3810,bool,hAPP(U_3810,fun(U_3810,bool),ord_less_eq(U_3810),hAPP(U_3810,U_3810,abs_abs(U_3810),U_3811)),zero_zero(U_3810)))
        | ~ sP294(U_3810,U_3811,U_3812) )
    & ! [U_3810,U_3811,U_3812] :
        ( sP294(U_3810,U_3811,U_3812)
        | ~ ordere142940540dd_abs(U_3810) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP294])],[f_978_3]) ).

cnf(f_978_5,plain,
    ( sP294(U_3810,U_3811,U_3812)
    | ~ ordere142940540dd_abs(U_3810) ),
    inference(clausify,[status(thm)],[f_978_4]) ).

cnf(f_978_6,plain,
    ( ti(U_3810,U_3811) = zero_zero(U_3810)
    | ~ hBOOL(hAPP(U_3810,bool,hAPP(U_3810,fun(U_3810,bool),ord_less_eq(U_3810),hAPP(U_3810,U_3810,abs_abs(U_3810),U_3811)),zero_zero(U_3810)))
    | ~ sP294(U_3810,U_3811,U_3812) ),
    inference(clausify,[status(thm)],[f_978_4]) ).

cnf(f_978_7,plain,
    ( hBOOL(hAPP(U_3810,bool,hAPP(U_3810,fun(U_3810,bool),ord_less_eq(U_3810),hAPP(U_3810,U_3810,abs_abs(U_3810),U_3812)),zero_zero(U_3810)))
    | ti(U_3810,U_3812) != zero_zero(U_3810)
    | ~ sP294(U_3810,U_3811,U_3812) ),
    inference(clausify,[status(thm)],[f_978_4]) ).

fof(f_979_1,plain,
    ! [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)),hAPP(X_a,X_a,abs_abs(X_a),A_1)))
      | ~ ordere142940540dd_abs(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_908_abs__ge__zero]) ).

fof(f_979_2,plain,
    ! [U_3814] :
      ( ! [U_3813] : hBOOL(hAPP(U_3814,bool,hAPP(U_3814,fun(U_3814,bool),ord_less_eq(U_3814),zero_zero(U_3814)),hAPP(U_3814,U_3814,abs_abs(U_3814),U_3813)))
      | ~ ordere142940540dd_abs(U_3814) ),
    inference(variable_rename,[status(thm)],[f_979_1]) ).

fof(f_979_3,plain,
    ! [U_3813,U_3814] :
      ( hBOOL(hAPP(U_3814,bool,hAPP(U_3814,fun(U_3814,bool),ord_less_eq(U_3814),zero_zero(U_3814)),hAPP(U_3814,U_3814,abs_abs(U_3814),U_3813)))
      | ~ ordere142940540dd_abs(U_3814) ),
    inference(definitional_conversion,[status(esa)],[f_979_2]) ).

cnf(f_979_4,plain,
    ( hBOOL(hAPP(U_3814,bool,hAPP(U_3814,fun(U_3814,bool),ord_less_eq(U_3814),zero_zero(U_3814)),hAPP(U_3814,U_3814,abs_abs(U_3814),U_3813)))
    | ~ ordere142940540dd_abs(U_3814) ),
    inference(clausify,[status(thm)],[f_979_3]) ).

fof(f_980_1,plain,
    ! [X_a] :
      ( ! [A_1] : ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),zero_zero(X_a)))
      | ~ ordere142940540dd_abs(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_909_abs__not__less__zero]) ).

fof(f_980_2,plain,
    ! [U_3816] :
      ( ! [U_3815] : ~ hBOOL(hAPP(U_3816,bool,hAPP(U_3816,fun(U_3816,bool),ord_less(U_3816),hAPP(U_3816,U_3816,abs_abs(U_3816),U_3815)),zero_zero(U_3816)))
      | ~ ordere142940540dd_abs(U_3816) ),
    inference(variable_rename,[status(thm)],[f_980_1]) ).

fof(f_980_3,plain,
    ! [U_3816,U_3815] :
      ( ~ hBOOL(hAPP(U_3816,bool,hAPP(U_3816,fun(U_3816,bool),ord_less(U_3816),hAPP(U_3816,U_3816,abs_abs(U_3816),U_3815)),zero_zero(U_3816)))
      | ~ ordere142940540dd_abs(U_3816) ),
    inference(definitional_conversion,[status(esa)],[f_980_2]) ).

cnf(f_980_4,plain,
    ( ~ hBOOL(hAPP(U_3816,bool,hAPP(U_3816,fun(U_3816,bool),ord_less(U_3816),hAPP(U_3816,U_3816,abs_abs(U_3816),U_3815)),zero_zero(U_3816)))
    | ~ ordere142940540dd_abs(U_3816) ),
    inference(clausify,[status(thm)],[f_980_3]) ).

fof(f_981_1,plain,
    ! [X_b] :
      ( ! [A_2] :
          ( ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),hAPP(X_b,X_b,abs_abs(X_b),A_2)))
            | ti(X_b,A_2) = zero_zero(X_b) )
          & ( ti(X_b,A_2) != zero_zero(X_b)
            | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),hAPP(X_b,X_b,abs_abs(X_b),A_2))) ) )
      | ~ ordere142940540dd_abs(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_910_zero__less__abs__iff]) ).

fof(f_981_2,plain,
    ! [U_3818] :
      ( ! [U_3817] :
          ( ( hBOOL(hAPP(U_3818,bool,hAPP(U_3818,fun(U_3818,bool),ord_less(U_3818),zero_zero(U_3818)),hAPP(U_3818,U_3818,abs_abs(U_3818),U_3817)))
            | ti(U_3818,U_3817) = zero_zero(U_3818) )
          & ( ti(U_3818,U_3817) != zero_zero(U_3818)
            | ~ hBOOL(hAPP(U_3818,bool,hAPP(U_3818,fun(U_3818,bool),ord_less(U_3818),zero_zero(U_3818)),hAPP(U_3818,U_3818,abs_abs(U_3818),U_3817))) ) )
      | ~ ordere142940540dd_abs(U_3818) ),
    inference(variable_rename,[status(thm)],[f_981_1]) ).

fof(f_981_3,plain,
    ! [U_3818] :
      ( ( ! [U_3820] :
            ( hBOOL(hAPP(U_3818,bool,hAPP(U_3818,fun(U_3818,bool),ord_less(U_3818),zero_zero(U_3818)),hAPP(U_3818,U_3818,abs_abs(U_3818),U_3820)))
            | ti(U_3818,U_3820) = zero_zero(U_3818) )
        & ! [U_3819] :
            ( ti(U_3818,U_3819) != zero_zero(U_3818)
            | ~ hBOOL(hAPP(U_3818,bool,hAPP(U_3818,fun(U_3818,bool),ord_less(U_3818),zero_zero(U_3818)),hAPP(U_3818,U_3818,abs_abs(U_3818),U_3819))) ) )
      | ~ ordere142940540dd_abs(U_3818) ),
    inference(miniscope,[status(thm)],[f_981_2]) ).

fof(f_981_4,plain,
    ( ! [U_3818,U_3819,U_3820] :
        ( hBOOL(hAPP(U_3818,bool,hAPP(U_3818,fun(U_3818,bool),ord_less(U_3818),zero_zero(U_3818)),hAPP(U_3818,U_3818,abs_abs(U_3818),U_3820)))
        | ti(U_3818,U_3820) = zero_zero(U_3818)
        | ~ sP295(U_3818,U_3819,U_3820) )
    & ! [U_3818,U_3819,U_3820] :
        ( ti(U_3818,U_3819) != zero_zero(U_3818)
        | ~ hBOOL(hAPP(U_3818,bool,hAPP(U_3818,fun(U_3818,bool),ord_less(U_3818),zero_zero(U_3818)),hAPP(U_3818,U_3818,abs_abs(U_3818),U_3819)))
        | ~ sP295(U_3818,U_3819,U_3820) )
    & ! [U_3818,U_3819,U_3820] :
        ( sP295(U_3818,U_3819,U_3820)
        | ~ ordere142940540dd_abs(U_3818) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP295])],[f_981_3]) ).

cnf(f_981_5,plain,
    ( sP295(U_3818,U_3819,U_3820)
    | ~ ordere142940540dd_abs(U_3818) ),
    inference(clausify,[status(thm)],[f_981_4]) ).

cnf(f_981_6,plain,
    ( ti(U_3818,U_3819) != zero_zero(U_3818)
    | ~ hBOOL(hAPP(U_3818,bool,hAPP(U_3818,fun(U_3818,bool),ord_less(U_3818),zero_zero(U_3818)),hAPP(U_3818,U_3818,abs_abs(U_3818),U_3819)))
    | ~ sP295(U_3818,U_3819,U_3820) ),
    inference(clausify,[status(thm)],[f_981_4]) ).

cnf(f_981_7,plain,
    ( hBOOL(hAPP(U_3818,bool,hAPP(U_3818,fun(U_3818,bool),ord_less(U_3818),zero_zero(U_3818)),hAPP(U_3818,U_3818,abs_abs(U_3818),U_3820)))
    | ti(U_3818,U_3820) = zero_zero(U_3818)
    | ~ sP295(U_3818,U_3819,U_3820) ),
    inference(clausify,[status(thm)],[f_981_4]) ).

fof(f_982_1,plain,
    ! [X_a] :
      ( ! [A_1] :
          ( hAPP(X_a,X_a,abs_abs(X_a),A_1) = ti(X_a,A_1)
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) )
      | ~ ordere142940540dd_abs(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_911_abs__of__pos]) ).

fof(f_982_2,plain,
    ! [U_3822] :
      ( ! [U_3821] :
          ( hAPP(U_3822,U_3822,abs_abs(U_3822),U_3821) = ti(U_3822,U_3821)
          | ~ hBOOL(hAPP(U_3822,bool,hAPP(U_3822,fun(U_3822,bool),ord_less(U_3822),zero_zero(U_3822)),U_3821)) )
      | ~ ordere142940540dd_abs(U_3822) ),
    inference(variable_rename,[status(thm)],[f_982_1]) ).

fof(f_982_3,plain,
    ! [U_3822,U_3821] :
      ( hAPP(U_3822,U_3822,abs_abs(U_3822),U_3821) = ti(U_3822,U_3821)
      | ~ hBOOL(hAPP(U_3822,bool,hAPP(U_3822,fun(U_3822,bool),ord_less(U_3822),zero_zero(U_3822)),U_3821))
      | ~ ordere142940540dd_abs(U_3822) ),
    inference(definitional_conversion,[status(esa)],[f_982_2]) ).

cnf(f_982_4,plain,
    ( hAPP(U_3822,U_3822,abs_abs(U_3822),U_3821) = ti(U_3822,U_3821)
    | ~ hBOOL(hAPP(U_3822,bool,hAPP(U_3822,fun(U_3822,bool),ord_less(U_3822),zero_zero(U_3822)),U_3821))
    | ~ ordere142940540dd_abs(U_3822) ),
    inference(clausify,[status(thm)],[f_982_3]) ).

fof(f_983_1,plain,
    ! [X_a] :
      ( ! [A_1,B] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B)))),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B))))
      | ~ ordere142940540dd_abs(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_912_abs__triangle__ineq3]) ).

fof(f_983_2,plain,
    ! [U_3825] :
      ( ! [U_3824,U_3823] : hBOOL(hAPP(U_3825,bool,hAPP(U_3825,fun(U_3825,bool),ord_less_eq(U_3825),hAPP(U_3825,U_3825,abs_abs(U_3825),hAPP(U_3825,U_3825,hAPP(U_3825,fun(U_3825,U_3825),minus_minus(U_3825),hAPP(U_3825,U_3825,abs_abs(U_3825),U_3824)),hAPP(U_3825,U_3825,abs_abs(U_3825),U_3823)))),hAPP(U_3825,U_3825,abs_abs(U_3825),hAPP(U_3825,U_3825,hAPP(U_3825,fun(U_3825,U_3825),minus_minus(U_3825),U_3824),U_3823))))
      | ~ ordere142940540dd_abs(U_3825) ),
    inference(variable_rename,[status(thm)],[f_983_1]) ).

fof(f_983_3,plain,
    ! [U_3823,U_3825,U_3824] :
      ( hBOOL(hAPP(U_3825,bool,hAPP(U_3825,fun(U_3825,bool),ord_less_eq(U_3825),hAPP(U_3825,U_3825,abs_abs(U_3825),hAPP(U_3825,U_3825,hAPP(U_3825,fun(U_3825,U_3825),minus_minus(U_3825),hAPP(U_3825,U_3825,abs_abs(U_3825),U_3824)),hAPP(U_3825,U_3825,abs_abs(U_3825),U_3823)))),hAPP(U_3825,U_3825,abs_abs(U_3825),hAPP(U_3825,U_3825,hAPP(U_3825,fun(U_3825,U_3825),minus_minus(U_3825),U_3824),U_3823))))
      | ~ ordere142940540dd_abs(U_3825) ),
    inference(definitional_conversion,[status(esa)],[f_983_2]) ).

cnf(f_983_4,plain,
    ( hBOOL(hAPP(U_3825,bool,hAPP(U_3825,fun(U_3825,bool),ord_less_eq(U_3825),hAPP(U_3825,U_3825,abs_abs(U_3825),hAPP(U_3825,U_3825,hAPP(U_3825,fun(U_3825,U_3825),minus_minus(U_3825),hAPP(U_3825,U_3825,abs_abs(U_3825),U_3824)),hAPP(U_3825,U_3825,abs_abs(U_3825),U_3823)))),hAPP(U_3825,U_3825,abs_abs(U_3825),hAPP(U_3825,U_3825,hAPP(U_3825,fun(U_3825,U_3825),minus_minus(U_3825),U_3824),U_3823))))
    | ~ ordere142940540dd_abs(U_3825) ),
    inference(clausify,[status(thm)],[f_983_3]) ).

fof(f_984_1,plain,
    ! [X_a] :
      ( ! [A_1,B] : 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),minus_minus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B))),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B))))
      | ~ ordere142940540dd_abs(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_913_abs__triangle__ineq2]) ).

fof(f_984_2,plain,
    ! [U_3828] :
      ( ! [U_3827,U_3826] : hBOOL(hAPP(U_3828,bool,hAPP(U_3828,fun(U_3828,bool),ord_less_eq(U_3828),hAPP(U_3828,U_3828,hAPP(U_3828,fun(U_3828,U_3828),minus_minus(U_3828),hAPP(U_3828,U_3828,abs_abs(U_3828),U_3827)),hAPP(U_3828,U_3828,abs_abs(U_3828),U_3826))),hAPP(U_3828,U_3828,abs_abs(U_3828),hAPP(U_3828,U_3828,hAPP(U_3828,fun(U_3828,U_3828),minus_minus(U_3828),U_3827),U_3826))))
      | ~ ordere142940540dd_abs(U_3828) ),
    inference(variable_rename,[status(thm)],[f_984_1]) ).

fof(f_984_3,plain,
    ! [U_3828,U_3826,U_3827] :
      ( hBOOL(hAPP(U_3828,bool,hAPP(U_3828,fun(U_3828,bool),ord_less_eq(U_3828),hAPP(U_3828,U_3828,hAPP(U_3828,fun(U_3828,U_3828),minus_minus(U_3828),hAPP(U_3828,U_3828,abs_abs(U_3828),U_3827)),hAPP(U_3828,U_3828,abs_abs(U_3828),U_3826))),hAPP(U_3828,U_3828,abs_abs(U_3828),hAPP(U_3828,U_3828,hAPP(U_3828,fun(U_3828,U_3828),minus_minus(U_3828),U_3827),U_3826))))
      | ~ ordere142940540dd_abs(U_3828) ),
    inference(definitional_conversion,[status(esa)],[f_984_2]) ).

cnf(f_984_4,plain,
    ( hBOOL(hAPP(U_3828,bool,hAPP(U_3828,fun(U_3828,bool),ord_less_eq(U_3828),hAPP(U_3828,U_3828,hAPP(U_3828,fun(U_3828,U_3828),minus_minus(U_3828),hAPP(U_3828,U_3828,abs_abs(U_3828),U_3827)),hAPP(U_3828,U_3828,abs_abs(U_3828),U_3826))),hAPP(U_3828,U_3828,abs_abs(U_3828),hAPP(U_3828,U_3828,hAPP(U_3828,fun(U_3828,U_3828),minus_minus(U_3828),U_3827),U_3826))))
    | ~ ordere142940540dd_abs(U_3828) ),
    inference(clausify,[status(thm)],[f_984_3]) ).

fof(f_985_1,plain,
    ! [X_a] :
      ( ! [A_1,B] : 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),minus_minus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B))),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B),A_1))))
      | ~ ordere142940540dd_abs(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_914_abs__triangle__ineq2__sym]) ).

fof(f_985_2,plain,
    ! [U_3831] :
      ( ! [U_3830,U_3829] : hBOOL(hAPP(U_3831,bool,hAPP(U_3831,fun(U_3831,bool),ord_less_eq(U_3831),hAPP(U_3831,U_3831,hAPP(U_3831,fun(U_3831,U_3831),minus_minus(U_3831),hAPP(U_3831,U_3831,abs_abs(U_3831),U_3830)),hAPP(U_3831,U_3831,abs_abs(U_3831),U_3829))),hAPP(U_3831,U_3831,abs_abs(U_3831),hAPP(U_3831,U_3831,hAPP(U_3831,fun(U_3831,U_3831),minus_minus(U_3831),U_3829),U_3830))))
      | ~ ordere142940540dd_abs(U_3831) ),
    inference(variable_rename,[status(thm)],[f_985_1]) ).

fof(f_985_3,plain,
    ! [U_3829,U_3831,U_3830] :
      ( hBOOL(hAPP(U_3831,bool,hAPP(U_3831,fun(U_3831,bool),ord_less_eq(U_3831),hAPP(U_3831,U_3831,hAPP(U_3831,fun(U_3831,U_3831),minus_minus(U_3831),hAPP(U_3831,U_3831,abs_abs(U_3831),U_3830)),hAPP(U_3831,U_3831,abs_abs(U_3831),U_3829))),hAPP(U_3831,U_3831,abs_abs(U_3831),hAPP(U_3831,U_3831,hAPP(U_3831,fun(U_3831,U_3831),minus_minus(U_3831),U_3829),U_3830))))
      | ~ ordere142940540dd_abs(U_3831) ),
    inference(definitional_conversion,[status(esa)],[f_985_2]) ).

cnf(f_985_4,plain,
    ( hBOOL(hAPP(U_3831,bool,hAPP(U_3831,fun(U_3831,bool),ord_less_eq(U_3831),hAPP(U_3831,U_3831,hAPP(U_3831,fun(U_3831,U_3831),minus_minus(U_3831),hAPP(U_3831,U_3831,abs_abs(U_3831),U_3830)),hAPP(U_3831,U_3831,abs_abs(U_3831),U_3829))),hAPP(U_3831,U_3831,abs_abs(U_3831),hAPP(U_3831,U_3831,hAPP(U_3831,fun(U_3831,U_3831),minus_minus(U_3831),U_3829),U_3830))))
    | ~ ordere142940540dd_abs(U_3831) ),
    inference(clausify,[status(thm)],[f_985_3]) ).

fof(f_986_1,plain,
    ! [X_a] :
      ( ! [B,D,A_1,C] :
          ( 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),times_times(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(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,abs_abs(X_a),B)),D))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),C)) )
      | ~ linordered_idom(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_915_abs__mult__less]) ).

fof(f_986_2,plain,
    ! [U_3836] :
      ( ! [U_3835,U_3834,U_3833,U_3832] :
          ( hBOOL(hAPP(U_3836,bool,hAPP(U_3836,fun(U_3836,bool),ord_less(U_3836),hAPP(U_3836,U_3836,hAPP(U_3836,fun(U_3836,U_3836),times_times(U_3836),hAPP(U_3836,U_3836,abs_abs(U_3836),U_3833)),hAPP(U_3836,U_3836,abs_abs(U_3836),U_3835))),hAPP(U_3836,U_3836,hAPP(U_3836,fun(U_3836,U_3836),times_times(U_3836),U_3832),U_3834)))
          | ~ hBOOL(hAPP(U_3836,bool,hAPP(U_3836,fun(U_3836,bool),ord_less(U_3836),hAPP(U_3836,U_3836,abs_abs(U_3836),U_3835)),U_3834))
          | ~ hBOOL(hAPP(U_3836,bool,hAPP(U_3836,fun(U_3836,bool),ord_less(U_3836),hAPP(U_3836,U_3836,abs_abs(U_3836),U_3833)),U_3832)) )
      | ~ linordered_idom(U_3836) ),
    inference(variable_rename,[status(thm)],[f_986_1]) ).

fof(f_986_3,plain,
    ! [U_3836,U_3832,U_3834,U_3833,U_3835] :
      ( hBOOL(hAPP(U_3836,bool,hAPP(U_3836,fun(U_3836,bool),ord_less(U_3836),hAPP(U_3836,U_3836,hAPP(U_3836,fun(U_3836,U_3836),times_times(U_3836),hAPP(U_3836,U_3836,abs_abs(U_3836),U_3833)),hAPP(U_3836,U_3836,abs_abs(U_3836),U_3835))),hAPP(U_3836,U_3836,hAPP(U_3836,fun(U_3836,U_3836),times_times(U_3836),U_3832),U_3834)))
      | ~ hBOOL(hAPP(U_3836,bool,hAPP(U_3836,fun(U_3836,bool),ord_less(U_3836),hAPP(U_3836,U_3836,abs_abs(U_3836),U_3835)),U_3834))
      | ~ hBOOL(hAPP(U_3836,bool,hAPP(U_3836,fun(U_3836,bool),ord_less(U_3836),hAPP(U_3836,U_3836,abs_abs(U_3836),U_3833)),U_3832))
      | ~ linordered_idom(U_3836) ),
    inference(definitional_conversion,[status(esa)],[f_986_2]) ).

cnf(f_986_4,plain,
    ( hBOOL(hAPP(U_3836,bool,hAPP(U_3836,fun(U_3836,bool),ord_less(U_3836),hAPP(U_3836,U_3836,hAPP(U_3836,fun(U_3836,U_3836),times_times(U_3836),hAPP(U_3836,U_3836,abs_abs(U_3836),U_3833)),hAPP(U_3836,U_3836,abs_abs(U_3836),U_3835))),hAPP(U_3836,U_3836,hAPP(U_3836,fun(U_3836,U_3836),times_times(U_3836),U_3832),U_3834)))
    | ~ hBOOL(hAPP(U_3836,bool,hAPP(U_3836,fun(U_3836,bool),ord_less(U_3836),hAPP(U_3836,U_3836,abs_abs(U_3836),U_3835)),U_3834))
    | ~ hBOOL(hAPP(U_3836,bool,hAPP(U_3836,fun(U_3836,bool),ord_less(U_3836),hAPP(U_3836,U_3836,abs_abs(U_3836),U_3833)),U_3832))
    | ~ linordered_idom(U_3836) ),
    inference(clausify,[status(thm)],[f_986_3]) ).

fof(f_987_1,plain,
    ! [X_a] :
      ( ! [A_1,B] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B))))
      | ~ ordere142940540dd_abs(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_916_abs__triangle__ineq]) ).

fof(f_987_2,plain,
    ! [U_3839] :
      ( ! [U_3838,U_3837] : hBOOL(hAPP(U_3839,bool,hAPP(U_3839,fun(U_3839,bool),ord_less_eq(U_3839),hAPP(U_3839,U_3839,abs_abs(U_3839),hAPP(U_3839,U_3839,hAPP(U_3839,fun(U_3839,U_3839),plus_plus(U_3839),U_3838),U_3837))),hAPP(U_3839,U_3839,hAPP(U_3839,fun(U_3839,U_3839),plus_plus(U_3839),hAPP(U_3839,U_3839,abs_abs(U_3839),U_3838)),hAPP(U_3839,U_3839,abs_abs(U_3839),U_3837))))
      | ~ ordere142940540dd_abs(U_3839) ),
    inference(variable_rename,[status(thm)],[f_987_1]) ).

fof(f_987_3,plain,
    ! [U_3837,U_3839,U_3838] :
      ( hBOOL(hAPP(U_3839,bool,hAPP(U_3839,fun(U_3839,bool),ord_less_eq(U_3839),hAPP(U_3839,U_3839,abs_abs(U_3839),hAPP(U_3839,U_3839,hAPP(U_3839,fun(U_3839,U_3839),plus_plus(U_3839),U_3838),U_3837))),hAPP(U_3839,U_3839,hAPP(U_3839,fun(U_3839,U_3839),plus_plus(U_3839),hAPP(U_3839,U_3839,abs_abs(U_3839),U_3838)),hAPP(U_3839,U_3839,abs_abs(U_3839),U_3837))))
      | ~ ordere142940540dd_abs(U_3839) ),
    inference(definitional_conversion,[status(esa)],[f_987_2]) ).

cnf(f_987_4,plain,
    ( hBOOL(hAPP(U_3839,bool,hAPP(U_3839,fun(U_3839,bool),ord_less_eq(U_3839),hAPP(U_3839,U_3839,abs_abs(U_3839),hAPP(U_3839,U_3839,hAPP(U_3839,fun(U_3839,U_3839),plus_plus(U_3839),U_3838),U_3837))),hAPP(U_3839,U_3839,hAPP(U_3839,fun(U_3839,U_3839),plus_plus(U_3839),hAPP(U_3839,U_3839,abs_abs(U_3839),U_3838)),hAPP(U_3839,U_3839,abs_abs(U_3839),U_3837))))
    | ~ ordere142940540dd_abs(U_3839) ),
    inference(clausify,[status(thm)],[f_987_3]) ).

fof(f_988_1,plain,
    ! [X_a] :
      ( ! [A_1,B] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),B)) )
      | ~ ordere142940540dd_abs(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_917_abs__le__D1]) ).

fof(f_988_2,plain,
    ! [U_3842] :
      ( ! [U_3841,U_3840] :
          ( hBOOL(hAPP(U_3842,bool,hAPP(U_3842,fun(U_3842,bool),ord_less_eq(U_3842),U_3841),U_3840))
          | ~ hBOOL(hAPP(U_3842,bool,hAPP(U_3842,fun(U_3842,bool),ord_less_eq(U_3842),hAPP(U_3842,U_3842,abs_abs(U_3842),U_3841)),U_3840)) )
      | ~ ordere142940540dd_abs(U_3842) ),
    inference(variable_rename,[status(thm)],[f_988_1]) ).

fof(f_988_3,plain,
    ! [U_3840,U_3842,U_3841] :
      ( hBOOL(hAPP(U_3842,bool,hAPP(U_3842,fun(U_3842,bool),ord_less_eq(U_3842),U_3841),U_3840))
      | ~ hBOOL(hAPP(U_3842,bool,hAPP(U_3842,fun(U_3842,bool),ord_less_eq(U_3842),hAPP(U_3842,U_3842,abs_abs(U_3842),U_3841)),U_3840))
      | ~ ordere142940540dd_abs(U_3842) ),
    inference(definitional_conversion,[status(esa)],[f_988_2]) ).

cnf(f_988_4,plain,
    ( hBOOL(hAPP(U_3842,bool,hAPP(U_3842,fun(U_3842,bool),ord_less_eq(U_3842),U_3841),U_3840))
    | ~ hBOOL(hAPP(U_3842,bool,hAPP(U_3842,fun(U_3842,bool),ord_less_eq(U_3842),hAPP(U_3842,U_3842,abs_abs(U_3842),U_3841)),U_3840))
    | ~ ordere142940540dd_abs(U_3842) ),
    inference(clausify,[status(thm)],[f_988_3]) ).

fof(f_989_1,plain,
    ! [X_a] :
      ( ! [A_1] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),hAPP(X_a,X_a,abs_abs(X_a),A_1)))
      | ~ ordere142940540dd_abs(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_918_abs__ge__self]) ).

fof(f_989_2,plain,
    ! [U_3844] :
      ( ! [U_3843] : hBOOL(hAPP(U_3844,bool,hAPP(U_3844,fun(U_3844,bool),ord_less_eq(U_3844),U_3843),hAPP(U_3844,U_3844,abs_abs(U_3844),U_3843)))
      | ~ ordere142940540dd_abs(U_3844) ),
    inference(variable_rename,[status(thm)],[f_989_1]) ).

fof(f_989_3,plain,
    ! [U_3844,U_3843] :
      ( hBOOL(hAPP(U_3844,bool,hAPP(U_3844,fun(U_3844,bool),ord_less_eq(U_3844),U_3843),hAPP(U_3844,U_3844,abs_abs(U_3844),U_3843)))
      | ~ ordere142940540dd_abs(U_3844) ),
    inference(definitional_conversion,[status(esa)],[f_989_2]) ).

cnf(f_989_4,plain,
    ( hBOOL(hAPP(U_3844,bool,hAPP(U_3844,fun(U_3844,bool),ord_less_eq(U_3844),U_3843),hAPP(U_3844,U_3844,abs_abs(U_3844),U_3843)))
    | ~ ordere142940540dd_abs(U_3844) ),
    inference(clausify,[status(thm)],[f_989_3]) ).

fof(f_990_1,plain,
    ! [X_a] :
      ( ! [B,A_1] :
          ( hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B))
          | ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),zero_zero(X_a)))
            & ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B)) )
          | ( ~ 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),zero_zero(X_a)),A_1)) ) )
      | ~ ordered_ring_abs(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_919_abs__eq__mult]) ).

fof(f_990_2,plain,
    ! [U_3847] :
      ( ! [U_3846,U_3845] :
          ( hAPP(U_3847,U_3847,abs_abs(U_3847),hAPP(U_3847,U_3847,hAPP(U_3847,fun(U_3847,U_3847),times_times(U_3847),U_3845),U_3846)) = hAPP(U_3847,U_3847,hAPP(U_3847,fun(U_3847,U_3847),times_times(U_3847),hAPP(U_3847,U_3847,abs_abs(U_3847),U_3845)),hAPP(U_3847,U_3847,abs_abs(U_3847),U_3846))
          | ( ~ hBOOL(hAPP(U_3847,bool,hAPP(U_3847,fun(U_3847,bool),ord_less_eq(U_3847),U_3846),zero_zero(U_3847)))
            & ~ hBOOL(hAPP(U_3847,bool,hAPP(U_3847,fun(U_3847,bool),ord_less_eq(U_3847),zero_zero(U_3847)),U_3846)) )
          | ( ~ hBOOL(hAPP(U_3847,bool,hAPP(U_3847,fun(U_3847,bool),ord_less_eq(U_3847),U_3845),zero_zero(U_3847)))
            & ~ hBOOL(hAPP(U_3847,bool,hAPP(U_3847,fun(U_3847,bool),ord_less_eq(U_3847),zero_zero(U_3847)),U_3845)) ) )
      | ~ ordered_ring_abs(U_3847) ),
    inference(variable_rename,[status(thm)],[f_990_1]) ).

fof(f_990_3,plain,
    ( ! [U_3846,U_3847] :
        ( ~ hBOOL(hAPP(U_3847,bool,hAPP(U_3847,fun(U_3847,bool),ord_less_eq(U_3847),U_3846),zero_zero(U_3847)))
        | ~ sP297(U_3846,U_3847) )
    & ! [U_3846,U_3847] :
        ( ~ hBOOL(hAPP(U_3847,bool,hAPP(U_3847,fun(U_3847,bool),ord_less_eq(U_3847),zero_zero(U_3847)),U_3846))
        | ~ sP297(U_3846,U_3847) )
    & ! [U_3847,U_3845] :
        ( ~ hBOOL(hAPP(U_3847,bool,hAPP(U_3847,fun(U_3847,bool),ord_less_eq(U_3847),U_3845),zero_zero(U_3847)))
        | ~ sP296(U_3847,U_3845) )
    & ! [U_3847,U_3845] :
        ( ~ hBOOL(hAPP(U_3847,bool,hAPP(U_3847,fun(U_3847,bool),ord_less_eq(U_3847),zero_zero(U_3847)),U_3845))
        | ~ sP296(U_3847,U_3845) )
    & ! [U_3846,U_3847,U_3845] :
        ( hAPP(U_3847,U_3847,abs_abs(U_3847),hAPP(U_3847,U_3847,hAPP(U_3847,fun(U_3847,U_3847),times_times(U_3847),U_3845),U_3846)) = hAPP(U_3847,U_3847,hAPP(U_3847,fun(U_3847,U_3847),times_times(U_3847),hAPP(U_3847,U_3847,abs_abs(U_3847),U_3845)),hAPP(U_3847,U_3847,abs_abs(U_3847),U_3846))
        | sP297(U_3846,U_3847)
        | sP296(U_3847,U_3845)
        | ~ ordered_ring_abs(U_3847) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP296,sP297])],[f_990_2]) ).

cnf(f_990_4,plain,
    ( hAPP(U_3847,U_3847,abs_abs(U_3847),hAPP(U_3847,U_3847,hAPP(U_3847,fun(U_3847,U_3847),times_times(U_3847),U_3845),U_3846)) = hAPP(U_3847,U_3847,hAPP(U_3847,fun(U_3847,U_3847),times_times(U_3847),hAPP(U_3847,U_3847,abs_abs(U_3847),U_3845)),hAPP(U_3847,U_3847,abs_abs(U_3847),U_3846))
    | sP297(U_3846,U_3847)
    | sP296(U_3847,U_3845)
    | ~ ordered_ring_abs(U_3847) ),
    inference(clausify,[status(thm)],[f_990_3]) ).

cnf(f_990_5,plain,
    ( ~ hBOOL(hAPP(U_3847,bool,hAPP(U_3847,fun(U_3847,bool),ord_less_eq(U_3847),zero_zero(U_3847)),U_3845))
    | ~ sP296(U_3847,U_3845) ),
    inference(clausify,[status(thm)],[f_990_3]) ).

cnf(f_990_6,plain,
    ( ~ hBOOL(hAPP(U_3847,bool,hAPP(U_3847,fun(U_3847,bool),ord_less_eq(U_3847),U_3845),zero_zero(U_3847)))
    | ~ sP296(U_3847,U_3845) ),
    inference(clausify,[status(thm)],[f_990_3]) ).

cnf(f_990_7,plain,
    ( ~ hBOOL(hAPP(U_3847,bool,hAPP(U_3847,fun(U_3847,bool),ord_less_eq(U_3847),zero_zero(U_3847)),U_3846))
    | ~ sP297(U_3846,U_3847) ),
    inference(clausify,[status(thm)],[f_990_3]) ).

cnf(f_990_8,plain,
    ( ~ hBOOL(hAPP(U_3847,bool,hAPP(U_3847,fun(U_3847,bool),ord_less_eq(U_3847),U_3846),zero_zero(U_3847)))
    | ~ sP297(U_3846,U_3847) ),
    inference(clausify,[status(thm)],[f_990_3]) ).

fof(f_991_1,plain,
    ! [X_a] :
      ( ! [Y,X] :
          ( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,abs_abs(X_a),Y)),X) = hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),X))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X)) )
      | ~ linordered_idom(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_920_abs__mult__pos]) ).

fof(f_991_2,plain,
    ! [U_3850] :
      ( ! [U_3849,U_3848] :
          ( hAPP(U_3850,U_3850,hAPP(U_3850,fun(U_3850,U_3850),times_times(U_3850),hAPP(U_3850,U_3850,abs_abs(U_3850),U_3849)),U_3848) = hAPP(U_3850,U_3850,abs_abs(U_3850),hAPP(U_3850,U_3850,hAPP(U_3850,fun(U_3850,U_3850),times_times(U_3850),U_3849),U_3848))
          | ~ hBOOL(hAPP(U_3850,bool,hAPP(U_3850,fun(U_3850,bool),ord_less_eq(U_3850),zero_zero(U_3850)),U_3848)) )
      | ~ linordered_idom(U_3850) ),
    inference(variable_rename,[status(thm)],[f_991_1]) ).

fof(f_991_3,plain,
    ! [U_3849,U_3850,U_3848] :
      ( hAPP(U_3850,U_3850,hAPP(U_3850,fun(U_3850,U_3850),times_times(U_3850),hAPP(U_3850,U_3850,abs_abs(U_3850),U_3849)),U_3848) = hAPP(U_3850,U_3850,abs_abs(U_3850),hAPP(U_3850,U_3850,hAPP(U_3850,fun(U_3850,U_3850),times_times(U_3850),U_3849),U_3848))
      | ~ hBOOL(hAPP(U_3850,bool,hAPP(U_3850,fun(U_3850,bool),ord_less_eq(U_3850),zero_zero(U_3850)),U_3848))
      | ~ linordered_idom(U_3850) ),
    inference(definitional_conversion,[status(esa)],[f_991_2]) ).

cnf(f_991_4,plain,
    ( hAPP(U_3850,U_3850,hAPP(U_3850,fun(U_3850,U_3850),times_times(U_3850),hAPP(U_3850,U_3850,abs_abs(U_3850),U_3849)),U_3848) = hAPP(U_3850,U_3850,abs_abs(U_3850),hAPP(U_3850,U_3850,hAPP(U_3850,fun(U_3850,U_3850),times_times(U_3850),U_3849),U_3848))
    | ~ hBOOL(hAPP(U_3850,bool,hAPP(U_3850,fun(U_3850,bool),ord_less_eq(U_3850),zero_zero(U_3850)),U_3848))
    | ~ linordered_idom(U_3850) ),
    inference(clausify,[status(thm)],[f_991_3]) ).

fof(f_992_1,plain,
    ! [X_a] :
      ( ! [A_1,B] : hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B))
      | ~ linordered_idom(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_921_abs__mult]) ).

fof(f_992_2,plain,
    ! [U_3853] :
      ( ! [U_3852,U_3851] : hAPP(U_3853,U_3853,abs_abs(U_3853),hAPP(U_3853,U_3853,hAPP(U_3853,fun(U_3853,U_3853),times_times(U_3853),U_3852),U_3851)) = hAPP(U_3853,U_3853,hAPP(U_3853,fun(U_3853,U_3853),times_times(U_3853),hAPP(U_3853,U_3853,abs_abs(U_3853),U_3852)),hAPP(U_3853,U_3853,abs_abs(U_3853),U_3851))
      | ~ linordered_idom(U_3853) ),
    inference(variable_rename,[status(thm)],[f_992_1]) ).

fof(f_992_3,plain,
    ! [U_3853,U_3851,U_3852] :
      ( hAPP(U_3853,U_3853,abs_abs(U_3853),hAPP(U_3853,U_3853,hAPP(U_3853,fun(U_3853,U_3853),times_times(U_3853),U_3852),U_3851)) = hAPP(U_3853,U_3853,hAPP(U_3853,fun(U_3853,U_3853),times_times(U_3853),hAPP(U_3853,U_3853,abs_abs(U_3853),U_3852)),hAPP(U_3853,U_3853,abs_abs(U_3853),U_3851))
      | ~ linordered_idom(U_3853) ),
    inference(definitional_conversion,[status(esa)],[f_992_2]) ).

cnf(f_992_4,plain,
    ( hAPP(U_3853,U_3853,abs_abs(U_3853),hAPP(U_3853,U_3853,hAPP(U_3853,fun(U_3853,U_3853),times_times(U_3853),U_3852),U_3851)) = hAPP(U_3853,U_3853,hAPP(U_3853,fun(U_3853,U_3853),times_times(U_3853),hAPP(U_3853,U_3853,abs_abs(U_3853),U_3852)),hAPP(U_3853,U_3853,abs_abs(U_3853),U_3851))
    | ~ linordered_idom(U_3853) ),
    inference(clausify,[status(thm)],[f_992_3]) ).

fof(f_993_1,plain,
    ! [X_a] :
      ( ! [A_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),A_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),A_1)
      | ~ linordered_idom(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_922_abs__mult__self]) ).

fof(f_993_2,plain,
    ! [U_3855] :
      ( ! [U_3854] : hAPP(U_3855,U_3855,hAPP(U_3855,fun(U_3855,U_3855),times_times(U_3855),hAPP(U_3855,U_3855,abs_abs(U_3855),U_3854)),hAPP(U_3855,U_3855,abs_abs(U_3855),U_3854)) = hAPP(U_3855,U_3855,hAPP(U_3855,fun(U_3855,U_3855),times_times(U_3855),U_3854),U_3854)
      | ~ linordered_idom(U_3855) ),
    inference(variable_rename,[status(thm)],[f_993_1]) ).

fof(f_993_3,plain,
    ! [U_3854,U_3855] :
      ( hAPP(U_3855,U_3855,hAPP(U_3855,fun(U_3855,U_3855),times_times(U_3855),hAPP(U_3855,U_3855,abs_abs(U_3855),U_3854)),hAPP(U_3855,U_3855,abs_abs(U_3855),U_3854)) = hAPP(U_3855,U_3855,hAPP(U_3855,fun(U_3855,U_3855),times_times(U_3855),U_3854),U_3854)
      | ~ linordered_idom(U_3855) ),
    inference(definitional_conversion,[status(esa)],[f_993_2]) ).

cnf(f_993_4,plain,
    ( hAPP(U_3855,U_3855,hAPP(U_3855,fun(U_3855,U_3855),times_times(U_3855),hAPP(U_3855,U_3855,abs_abs(U_3855),U_3854)),hAPP(U_3855,U_3855,abs_abs(U_3855),U_3854)) = hAPP(U_3855,U_3855,hAPP(U_3855,fun(U_3855,U_3855),times_times(U_3855),U_3854),U_3854)
    | ~ linordered_idom(U_3855) ),
    inference(clausify,[status(thm)],[f_993_3]) ).

fof(f_994_1,plain,
    ! [X_a] :
      ( ! [A_1,B] : hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)) = hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B),A_1))
      | ~ ordere142940540dd_abs(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_923_abs__minus__commute]) ).

fof(f_994_2,plain,
    ! [U_3858] :
      ( ! [U_3857,U_3856] : hAPP(U_3858,U_3858,abs_abs(U_3858),hAPP(U_3858,U_3858,hAPP(U_3858,fun(U_3858,U_3858),minus_minus(U_3858),U_3857),U_3856)) = hAPP(U_3858,U_3858,abs_abs(U_3858),hAPP(U_3858,U_3858,hAPP(U_3858,fun(U_3858,U_3858),minus_minus(U_3858),U_3856),U_3857))
      | ~ ordere142940540dd_abs(U_3858) ),
    inference(variable_rename,[status(thm)],[f_994_1]) ).

fof(f_994_3,plain,
    ! [U_3856,U_3858,U_3857] :
      ( hAPP(U_3858,U_3858,abs_abs(U_3858),hAPP(U_3858,U_3858,hAPP(U_3858,fun(U_3858,U_3858),minus_minus(U_3858),U_3857),U_3856)) = hAPP(U_3858,U_3858,abs_abs(U_3858),hAPP(U_3858,U_3858,hAPP(U_3858,fun(U_3858,U_3858),minus_minus(U_3858),U_3856),U_3857))
      | ~ ordere142940540dd_abs(U_3858) ),
    inference(definitional_conversion,[status(esa)],[f_994_2]) ).

cnf(f_994_4,plain,
    ( hAPP(U_3858,U_3858,abs_abs(U_3858),hAPP(U_3858,U_3858,hAPP(U_3858,fun(U_3858,U_3858),minus_minus(U_3858),U_3857),U_3856)) = hAPP(U_3858,U_3858,abs_abs(U_3858),hAPP(U_3858,U_3858,hAPP(U_3858,fun(U_3858,U_3858),minus_minus(U_3858),U_3856),U_3857))
    | ~ ordere142940540dd_abs(U_3858) ),
    inference(clausify,[status(thm)],[f_994_3]) ).

fof(f_995_1,plain,
    ! [X_a] :
      ( ! [A_1,B] : hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B))
      | ~ ordere142940540dd_abs(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_924_abs__add__abs]) ).

fof(f_995_2,plain,
    ! [U_3861] :
      ( ! [U_3860,U_3859] : hAPP(U_3861,U_3861,abs_abs(U_3861),hAPP(U_3861,U_3861,hAPP(U_3861,fun(U_3861,U_3861),plus_plus(U_3861),hAPP(U_3861,U_3861,abs_abs(U_3861),U_3860)),hAPP(U_3861,U_3861,abs_abs(U_3861),U_3859))) = hAPP(U_3861,U_3861,hAPP(U_3861,fun(U_3861,U_3861),plus_plus(U_3861),hAPP(U_3861,U_3861,abs_abs(U_3861),U_3860)),hAPP(U_3861,U_3861,abs_abs(U_3861),U_3859))
      | ~ ordere142940540dd_abs(U_3861) ),
    inference(variable_rename,[status(thm)],[f_995_1]) ).

fof(f_995_3,plain,
    ! [U_3861,U_3859,U_3860] :
      ( hAPP(U_3861,U_3861,abs_abs(U_3861),hAPP(U_3861,U_3861,hAPP(U_3861,fun(U_3861,U_3861),plus_plus(U_3861),hAPP(U_3861,U_3861,abs_abs(U_3861),U_3860)),hAPP(U_3861,U_3861,abs_abs(U_3861),U_3859))) = hAPP(U_3861,U_3861,hAPP(U_3861,fun(U_3861,U_3861),plus_plus(U_3861),hAPP(U_3861,U_3861,abs_abs(U_3861),U_3860)),hAPP(U_3861,U_3861,abs_abs(U_3861),U_3859))
      | ~ ordere142940540dd_abs(U_3861) ),
    inference(definitional_conversion,[status(esa)],[f_995_2]) ).

cnf(f_995_4,plain,
    ( hAPP(U_3861,U_3861,abs_abs(U_3861),hAPP(U_3861,U_3861,hAPP(U_3861,fun(U_3861,U_3861),plus_plus(U_3861),hAPP(U_3861,U_3861,abs_abs(U_3861),U_3860)),hAPP(U_3861,U_3861,abs_abs(U_3861),U_3859))) = hAPP(U_3861,U_3861,hAPP(U_3861,fun(U_3861,U_3861),plus_plus(U_3861),hAPP(U_3861,U_3861,abs_abs(U_3861),U_3860)),hAPP(U_3861,U_3861,abs_abs(U_3861),U_3859))
    | ~ ordere142940540dd_abs(U_3861) ),
    inference(clausify,[status(thm)],[f_995_3]) ).

fof(f_996_1,plain,
    ! [X_a] :
      ( ! [A_1] : hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)) = hAPP(X_a,X_a,abs_abs(X_a),A_1)
      | ~ ordere142940540dd_abs(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_925_abs__idempotent]) ).

fof(f_996_2,plain,
    ! [U_3863] :
      ( ! [U_3862] : hAPP(U_3863,U_3863,abs_abs(U_3863),hAPP(U_3863,U_3863,abs_abs(U_3863),U_3862)) = hAPP(U_3863,U_3863,abs_abs(U_3863),U_3862)
      | ~ ordere142940540dd_abs(U_3863) ),
    inference(variable_rename,[status(thm)],[f_996_1]) ).

fof(f_996_3,plain,
    ! [U_3863,U_3862] :
      ( hAPP(U_3863,U_3863,abs_abs(U_3863),hAPP(U_3863,U_3863,abs_abs(U_3863),U_3862)) = hAPP(U_3863,U_3863,abs_abs(U_3863),U_3862)
      | ~ ordere142940540dd_abs(U_3863) ),
    inference(definitional_conversion,[status(esa)],[f_996_2]) ).

cnf(f_996_4,plain,
    ( hAPP(U_3863,U_3863,abs_abs(U_3863),hAPP(U_3863,U_3863,abs_abs(U_3863),U_3862)) = hAPP(U_3863,U_3863,abs_abs(U_3863),U_3862)
    | ~ ordere142940540dd_abs(U_3863) ),
    inference(clausify,[status(thm)],[f_996_3]) ).

fof(f_997_1,plain,
    ~ hBOOL(hAPP(int,bool,nat_neg,one_one(int))),
    inference(fof_nnf,[status(thm)],[fact_926_not__neg__1]) ).

fof(f_997_2,plain,
    ~ hBOOL(hAPP(int,bool,nat_neg,one_one(int))),
    inference(definitional_conversion,[status(esa)],[f_997_1]) ).

cnf(f_997_3,plain,
    ~ hBOOL(hAPP(int,bool,nat_neg,one_one(int))),
    inference(clausify,[status(thm)],[f_997_2]) ).

fof(f_998_1,plain,
    ! [X_a] :
      ( hAPP(X_a,X_a,abs_abs(X_a),one_one(X_a)) = one_one(X_a)
      | ~ linordered_idom(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_927_abs__one]) ).

fof(f_998_2,plain,
    ! [U_3864] :
      ( hAPP(U_3864,U_3864,abs_abs(U_3864),one_one(U_3864)) = one_one(U_3864)
      | ~ linordered_idom(U_3864) ),
    inference(variable_rename,[status(thm)],[f_998_1]) ).

fof(f_998_3,plain,
    ! [U_3864] :
      ( hAPP(U_3864,U_3864,abs_abs(U_3864),one_one(U_3864)) = one_one(U_3864)
      | ~ linordered_idom(U_3864) ),
    inference(definitional_conversion,[status(esa)],[f_998_2]) ).

cnf(f_998_4,plain,
    ( hAPP(U_3864,U_3864,abs_abs(U_3864),one_one(U_3864)) = one_one(U_3864)
    | ~ linordered_idom(U_3864) ),
    inference(clausify,[status(thm)],[f_998_3]) ).

fof(f_999_1,plain,
    ~ hBOOL(hAPP(int,bool,nat_neg,zero_zero(int))),
    inference(fof_nnf,[status(thm)],[fact_928_not__neg__0]) ).

fof(f_999_2,plain,
    ~ hBOOL(hAPP(int,bool,nat_neg,zero_zero(int))),
    inference(definitional_conversion,[status(esa)],[f_999_1]) ).

cnf(f_999_3,plain,
    ~ hBOOL(hAPP(int,bool,nat_neg,zero_zero(int))),
    inference(clausify,[status(thm)],[f_999_2]) ).

fof(f_1000_1,plain,
    ! [X_b] :
      ( ! [A_2] :
          ( ( hAPP(X_b,X_b,abs_abs(X_b),A_2) = zero_zero(X_b)
            | ti(X_b,A_2) != zero_zero(X_b) )
          & ( ti(X_b,A_2) = zero_zero(X_b)
            | hAPP(X_b,X_b,abs_abs(X_b),A_2) != zero_zero(X_b) ) )
      | ~ ordere142940540dd_abs(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_929_abs__eq__0]) ).

fof(f_1000_2,plain,
    ! [U_3866] :
      ( ! [U_3865] :
          ( ( hAPP(U_3866,U_3866,abs_abs(U_3866),U_3865) = zero_zero(U_3866)
            | ti(U_3866,U_3865) != zero_zero(U_3866) )
          & ( ti(U_3866,U_3865) = zero_zero(U_3866)
            | hAPP(U_3866,U_3866,abs_abs(U_3866),U_3865) != zero_zero(U_3866) ) )
      | ~ ordere142940540dd_abs(U_3866) ),
    inference(variable_rename,[status(thm)],[f_1000_1]) ).

fof(f_1000_3,plain,
    ! [U_3866] :
      ( ( ! [U_3868] :
            ( hAPP(U_3866,U_3866,abs_abs(U_3866),U_3868) = zero_zero(U_3866)
            | ti(U_3866,U_3868) != zero_zero(U_3866) )
        & ! [U_3867] :
            ( ti(U_3866,U_3867) = zero_zero(U_3866)
            | hAPP(U_3866,U_3866,abs_abs(U_3866),U_3867) != zero_zero(U_3866) ) )
      | ~ ordere142940540dd_abs(U_3866) ),
    inference(miniscope,[status(thm)],[f_1000_2]) ).

fof(f_1000_4,plain,
    ( ! [U_3866,U_3868,U_3867] :
        ( hAPP(U_3866,U_3866,abs_abs(U_3866),U_3868) = zero_zero(U_3866)
        | ti(U_3866,U_3868) != zero_zero(U_3866)
        | ~ sP298(U_3866,U_3868,U_3867) )
    & ! [U_3866,U_3868,U_3867] :
        ( ti(U_3866,U_3867) = zero_zero(U_3866)
        | hAPP(U_3866,U_3866,abs_abs(U_3866),U_3867) != zero_zero(U_3866)
        | ~ sP298(U_3866,U_3868,U_3867) )
    & ! [U_3866,U_3868,U_3867] :
        ( sP298(U_3866,U_3868,U_3867)
        | ~ ordere142940540dd_abs(U_3866) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP298])],[f_1000_3]) ).

cnf(f_1000_5,plain,
    ( sP298(U_3866,U_3868,U_3867)
    | ~ ordere142940540dd_abs(U_3866) ),
    inference(clausify,[status(thm)],[f_1000_4]) ).

cnf(f_1000_6,plain,
    ( ti(U_3866,U_3867) = zero_zero(U_3866)
    | hAPP(U_3866,U_3866,abs_abs(U_3866),U_3867) != zero_zero(U_3866)
    | ~ sP298(U_3866,U_3868,U_3867) ),
    inference(clausify,[status(thm)],[f_1000_4]) ).

cnf(f_1000_7,plain,
    ( hAPP(U_3866,U_3866,abs_abs(U_3866),U_3868) = zero_zero(U_3866)
    | ti(U_3866,U_3868) != zero_zero(U_3866)
    | ~ sP298(U_3866,U_3868,U_3867) ),
    inference(clausify,[status(thm)],[f_1000_4]) ).

fof(f_1001_1,plain,
    ! [X_a] :
      ( hAPP(X_a,X_a,abs_abs(X_a),zero_zero(X_a)) = zero_zero(X_a)
      | ~ ordere142940540dd_abs(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_930_abs__zero]) ).

fof(f_1001_2,plain,
    ! [U_3869] :
      ( hAPP(U_3869,U_3869,abs_abs(U_3869),zero_zero(U_3869)) = zero_zero(U_3869)
      | ~ ordere142940540dd_abs(U_3869) ),
    inference(variable_rename,[status(thm)],[f_1001_1]) ).

fof(f_1001_3,plain,
    ! [U_3869] :
      ( hAPP(U_3869,U_3869,abs_abs(U_3869),zero_zero(U_3869)) = zero_zero(U_3869)
      | ~ ordere142940540dd_abs(U_3869) ),
    inference(definitional_conversion,[status(esa)],[f_1001_2]) ).

cnf(f_1001_4,plain,
    ( hAPP(U_3869,U_3869,abs_abs(U_3869),zero_zero(U_3869)) = zero_zero(U_3869)
    | ~ ordere142940540dd_abs(U_3869) ),
    inference(clausify,[status(thm)],[f_1001_3]) ).

fof(f_1002_1,plain,
    ! [M_1,N] :
      ( hAPP(int,int,abs_abs(int),M_1) = one_one(int)
      | hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M_1),N)) != one_one(int) ),
    inference(fof_nnf,[status(thm)],[fact_931_abs__zmult__eq__1]) ).

fof(f_1002_2,plain,
    ! [U_3871,U_3870] :
      ( hAPP(int,int,abs_abs(int),U_3871) = one_one(int)
      | hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3871),U_3870)) != one_one(int) ),
    inference(variable_rename,[status(thm)],[f_1002_1]) ).

fof(f_1002_3,plain,
    ! [U_3871] :
      ( ! [U_3870] : hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3871),U_3870)) != one_one(int)
      | hAPP(int,int,abs_abs(int),U_3871) = one_one(int) ),
    inference(miniscope,[status(thm)],[f_1002_2]) ).

fof(f_1002_4,plain,
    ! [U_3870,U_3871] :
      ( hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3871),U_3870)) != one_one(int)
      | hAPP(int,int,abs_abs(int),U_3871) = one_one(int) ),
    inference(definitional_conversion,[status(esa)],[f_1002_3]) ).

cnf(f_1002_5,plain,
    ( hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),U_3871),U_3870)) != one_one(int)
    | hAPP(int,int,abs_abs(int),U_3871) = one_one(int) ),
    inference(clausify,[status(thm)],[f_1002_4]) ).

fof(f_1003_1,plain,
    ! [X_a] :
      ( ! [N] : hAPP(X_a,X_a,abs_abs(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N)) = hAPP(nat,X_a,semiring_1_of_nat(X_a),N)
      | ~ linordered_idom(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_932_abs__of__nat]) ).

fof(f_1003_2,plain,
    ! [U_3873] :
      ( ! [U_3872] : hAPP(U_3873,U_3873,abs_abs(U_3873),hAPP(nat,U_3873,semiring_1_of_nat(U_3873),U_3872)) = hAPP(nat,U_3873,semiring_1_of_nat(U_3873),U_3872)
      | ~ linordered_idom(U_3873) ),
    inference(variable_rename,[status(thm)],[f_1003_1]) ).

fof(f_1003_3,plain,
    ! [U_3872,U_3873] :
      ( hAPP(U_3873,U_3873,abs_abs(U_3873),hAPP(nat,U_3873,semiring_1_of_nat(U_3873),U_3872)) = hAPP(nat,U_3873,semiring_1_of_nat(U_3873),U_3872)
      | ~ linordered_idom(U_3873) ),
    inference(definitional_conversion,[status(esa)],[f_1003_2]) ).

cnf(f_1003_4,plain,
    ( hAPP(U_3873,U_3873,abs_abs(U_3873),hAPP(nat,U_3873,semiring_1_of_nat(U_3873),U_3872)) = hAPP(nat,U_3873,semiring_1_of_nat(U_3873),U_3872)
    | ~ linordered_idom(U_3873) ),
    inference(clausify,[status(thm)],[f_1003_3]) ).

fof(f_1004_1,plain,
    ! [N] : ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(nat,int,semiring_1_of_nat(int),N))),
    inference(fof_nnf,[status(thm)],[fact_933_not__neg__int]) ).

fof(f_1004_2,plain,
    ! [U_3874] : ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(nat,int,semiring_1_of_nat(int),U_3874))),
    inference(variable_rename,[status(thm)],[f_1004_1]) ).

fof(f_1004_3,plain,
    ! [U_3874] : ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(nat,int,semiring_1_of_nat(int),U_3874))),
    inference(definitional_conversion,[status(esa)],[f_1004_2]) ).

cnf(f_1004_4,plain,
    ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(nat,int,semiring_1_of_nat(int),U_3874))),
    inference(clausify,[status(thm)],[f_1004_3]) ).

fof(f_1005_1,plain,
    ! [M_1] : hAPP(int,int,abs_abs(int),hAPP(nat,int,semiring_1_of_nat(int),M_1)) = hAPP(nat,int,semiring_1_of_nat(int),M_1),
    inference(fof_nnf,[status(thm)],[fact_934_abs__int__eq]) ).

fof(f_1005_2,plain,
    ! [U_3875] : hAPP(int,int,abs_abs(int),hAPP(nat,int,semiring_1_of_nat(int),U_3875)) = hAPP(nat,int,semiring_1_of_nat(int),U_3875),
    inference(variable_rename,[status(thm)],[f_1005_1]) ).

fof(f_1005_3,plain,
    ! [U_3875] : hAPP(int,int,abs_abs(int),hAPP(nat,int,semiring_1_of_nat(int),U_3875)) = hAPP(nat,int,semiring_1_of_nat(int),U_3875),
    inference(definitional_conversion,[status(esa)],[f_1005_2]) ).

cnf(f_1005_4,plain,
    hAPP(int,int,abs_abs(int),hAPP(nat,int,semiring_1_of_nat(int),U_3875)) = hAPP(nat,int,semiring_1_of_nat(int),U_3875),
    inference(clausify,[status(thm)],[f_1005_3]) ).

fof(f_1006_1,plain,
    ! [V] :
      ( hAPP(int,nat,number_number_of(nat),V) = zero_zero(nat)
      | ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) ),
    inference(fof_nnf,[status(thm)],[fact_935_neg__imp__number__of__eq__0]) ).

fof(f_1006_2,plain,
    ! [U_3876] :
      ( hAPP(int,nat,number_number_of(nat),U_3876) = zero_zero(nat)
      | ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3876))) ),
    inference(variable_rename,[status(thm)],[f_1006_1]) ).

fof(f_1006_3,plain,
    ! [U_3876] :
      ( hAPP(int,nat,number_number_of(nat),U_3876) = zero_zero(nat)
      | ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3876))) ),
    inference(definitional_conversion,[status(esa)],[f_1006_2]) ).

cnf(f_1006_4,plain,
    ( hAPP(int,nat,number_number_of(nat),U_3876) = zero_zero(nat)
    | ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3876))) ),
    inference(clausify,[status(thm)],[f_1006_3]) ).

fof(f_1007_1,plain,
    ! [V_3,V_2] :
      ( ( hAPP(int,nat,number_number_of(nat),V_3) = hAPP(int,nat,number_number_of(nat),V_2)
        | ( ( ( V_3 != V_2
              & ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_2))) )
            | ( hAPP(int,int,number_number_of(int),V_3) != zero_zero(int)
              & hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_2))) ) )
          & ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_3))) )
        | ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),V_2)),zero_zero(int)))
          & hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_3))) ) )
      & ( ( ( ( ( V_3 = V_2
                | hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_2))) )
              & ( hAPP(int,int,number_number_of(int),V_3) = zero_zero(int)
                | ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_2))) ) )
            | hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_3))) )
          & ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),V_2)),zero_zero(int)))
            | ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_3))) ) )
        | hAPP(int,nat,number_number_of(nat),V_3) != hAPP(int,nat,number_number_of(nat),V_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_936_eq__nat__number__of]) ).

fof(f_1007_2,plain,
    ! [U_3878,U_3877] :
      ( ( hAPP(int,nat,number_number_of(nat),U_3878) = hAPP(int,nat,number_number_of(nat),U_3877)
        | ( ( ( U_3878 != U_3877
              & ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3877))) )
            | ( hAPP(int,int,number_number_of(int),U_3878) != zero_zero(int)
              & hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3877))) ) )
          & ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3878))) )
        | ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),U_3877)),zero_zero(int)))
          & hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3878))) ) )
      & ( ( ( ( ( U_3878 = U_3877
                | hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3877))) )
              & ( hAPP(int,int,number_number_of(int),U_3878) = zero_zero(int)
                | ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3877))) ) )
            | hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3878))) )
          & ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),U_3877)),zero_zero(int)))
            | ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3878))) ) )
        | hAPP(int,nat,number_number_of(nat),U_3878) != hAPP(int,nat,number_number_of(nat),U_3877) ) ),
    inference(variable_rename,[status(thm)],[f_1007_1]) ).

fof(f_1007_3,plain,
    ( ! [U_3882,U_3880] :
        ( hAPP(int,nat,number_number_of(nat),U_3882) = hAPP(int,nat,number_number_of(nat),U_3880)
        | ( ( ( U_3882 != U_3880
              & ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3880))) )
            | ( hAPP(int,int,number_number_of(int),U_3882) != zero_zero(int)
              & hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3880))) ) )
          & ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3882))) )
        | ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),U_3880)),zero_zero(int)))
          & hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3882))) ) )
    & ! [U_3881,U_3879] :
        ( ( ( ( ( U_3881 = U_3879
                | hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3879))) )
              & ( hAPP(int,int,number_number_of(int),U_3881) = zero_zero(int)
                | ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3879))) ) )
            | hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3881))) )
          & ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),U_3879)),zero_zero(int)))
            | ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3881))) ) )
        | hAPP(int,nat,number_number_of(nat),U_3881) != hAPP(int,nat,number_number_of(nat),U_3879) ) ),
    inference(miniscope,[status(thm)],[f_1007_2]) ).

fof(f_1007_4,plain,
    ( ! [U_3880,U_3882] :
        ( U_3882 != U_3880
        | ~ sP303(U_3880,U_3882) )
    & ! [U_3880,U_3882] :
        ( ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3880)))
        | ~ sP303(U_3880,U_3882) )
    & ! [U_3880,U_3882] :
        ( hAPP(int,int,number_number_of(int),U_3882) != zero_zero(int)
        | ~ sP302(U_3880,U_3882) )
    & ! [U_3880,U_3882] :
        ( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3880)))
        | ~ sP302(U_3880,U_3882) )
    & ! [U_3880,U_3882] :
        ( sP303(U_3880,U_3882)
        | sP302(U_3880,U_3882)
        | ~ sP304(U_3880,U_3882) )
    & ! [U_3880,U_3882] :
        ( ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3882)))
        | ~ sP304(U_3880,U_3882) )
    & ! [U_3880,U_3882] :
        ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),U_3880)),zero_zero(int)))
        | ~ sP301(U_3880,U_3882) )
    & ! [U_3880,U_3882] :
        ( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3882)))
        | ~ sP301(U_3880,U_3882) )
    & ! [U_3879,U_3881] :
        ( U_3881 = U_3879
        | hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3879)))
        | ~ sP299(U_3879,U_3881) )
    & ! [U_3879,U_3881] :
        ( hAPP(int,int,number_number_of(int),U_3881) = zero_zero(int)
        | ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3879)))
        | ~ sP299(U_3879,U_3881) )
    & ! [U_3879,U_3881] :
        ( sP299(U_3879,U_3881)
        | hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3881)))
        | ~ sP300(U_3879,U_3881) )
    & ! [U_3879,U_3881] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),U_3879)),zero_zero(int)))
        | ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3881)))
        | ~ sP300(U_3879,U_3881) )
    & ! [U_3880,U_3882] :
        ( hAPP(int,nat,number_number_of(nat),U_3882) = hAPP(int,nat,number_number_of(nat),U_3880)
        | sP304(U_3880,U_3882)
        | sP301(U_3880,U_3882) )
    & ! [U_3879,U_3881] :
        ( sP300(U_3879,U_3881)
        | hAPP(int,nat,number_number_of(nat),U_3881) != hAPP(int,nat,number_number_of(nat),U_3879) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP299,sP300,sP301,sP302,sP303,sP304])],[f_1007_3]) ).

cnf(f_1007_5,plain,
    ( sP300(U_3879,U_3881)
    | hAPP(int,nat,number_number_of(nat),U_3881) != hAPP(int,nat,number_number_of(nat),U_3879) ),
    inference(clausify,[status(thm)],[f_1007_4]) ).

cnf(f_1007_6,plain,
    ( hAPP(int,nat,number_number_of(nat),U_3882) = hAPP(int,nat,number_number_of(nat),U_3880)
    | sP304(U_3880,U_3882)
    | sP301(U_3880,U_3882) ),
    inference(clausify,[status(thm)],[f_1007_4]) ).

cnf(f_1007_7,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),U_3879)),zero_zero(int)))
    | ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3881)))
    | ~ sP300(U_3879,U_3881) ),
    inference(clausify,[status(thm)],[f_1007_4]) ).

cnf(f_1007_8,plain,
    ( sP299(U_3879,U_3881)
    | hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3881)))
    | ~ sP300(U_3879,U_3881) ),
    inference(clausify,[status(thm)],[f_1007_4]) ).

cnf(f_1007_9,plain,
    ( hAPP(int,int,number_number_of(int),U_3881) = zero_zero(int)
    | ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3879)))
    | ~ sP299(U_3879,U_3881) ),
    inference(clausify,[status(thm)],[f_1007_4]) ).

cnf(f_1007_10,plain,
    ( U_3881 = U_3879
    | hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3879)))
    | ~ sP299(U_3879,U_3881) ),
    inference(clausify,[status(thm)],[f_1007_4]) ).

cnf(f_1007_11,plain,
    ( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3882)))
    | ~ sP301(U_3880,U_3882) ),
    inference(clausify,[status(thm)],[f_1007_4]) ).

cnf(f_1007_12,plain,
    ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),U_3880)),zero_zero(int)))
    | ~ sP301(U_3880,U_3882) ),
    inference(clausify,[status(thm)],[f_1007_4]) ).

cnf(f_1007_13,plain,
    ( ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3882)))
    | ~ sP304(U_3880,U_3882) ),
    inference(clausify,[status(thm)],[f_1007_4]) ).

cnf(f_1007_14,plain,
    ( sP303(U_3880,U_3882)
    | sP302(U_3880,U_3882)
    | ~ sP304(U_3880,U_3882) ),
    inference(clausify,[status(thm)],[f_1007_4]) ).

cnf(f_1007_15,plain,
    ( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3880)))
    | ~ sP302(U_3880,U_3882) ),
    inference(clausify,[status(thm)],[f_1007_4]) ).

cnf(f_1007_16,plain,
    ( hAPP(int,int,number_number_of(int),U_3882) != zero_zero(int)
    | ~ sP302(U_3880,U_3882) ),
    inference(clausify,[status(thm)],[f_1007_4]) ).

cnf(f_1007_17,plain,
    ( ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3880)))
    | ~ sP303(U_3880,U_3882) ),
    inference(clausify,[status(thm)],[f_1007_4]) ).

cnf(f_1007_18,plain,
    ( U_3882 != U_3880
    | ~ sP303(U_3880,U_3882) ),
    inference(clausify,[status(thm)],[f_1007_4]) ).

fof(f_1008_1,plain,
    ! [V_1,K_1,V] :
      ( ( ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V_1)),K_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),V_1))),K_1)
            | hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_1))) )
          & ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V_1)),K_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),K_1)
            | ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_1))) ) )
        | hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) )
      & ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V_1)),K_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V_1)),K_1)
        | ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) ) ),
    inference(fof_nnf,[status(thm)],[fact_937_nat__number__of__add__left]) ).

fof(f_1008_2,plain,
    ! [U_3885,U_3884,U_3883] :
      ( ( ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),U_3883)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),U_3885)),U_3884)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3883),U_3885))),U_3884)
            | hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3885))) )
          & ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),U_3883)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),U_3885)),U_3884)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),U_3883)),U_3884)
            | ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3885))) ) )
        | hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3883))) )
      & ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),U_3883)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),U_3885)),U_3884)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),U_3885)),U_3884)
        | ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3883))) ) ),
    inference(variable_rename,[status(thm)],[f_1008_1]) ).

fof(f_1008_3,plain,
    ( ! [U_3891,U_3889,U_3887] :
        ( ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),U_3887)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),U_3891)),U_3889)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3887),U_3891))),U_3889)
            | hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3891))) )
          & ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),U_3887)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),U_3891)),U_3889)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),U_3887)),U_3889)
            | ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3891))) ) )
        | hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3887))) )
    & ! [U_3890,U_3888,U_3886] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),U_3886)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),U_3890)),U_3888)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),U_3890)),U_3888)
        | ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3886))) ) ),
    inference(miniscope,[status(thm)],[f_1008_2]) ).

fof(f_1008_4,plain,
    ( ! [U_3887,U_3891,U_3889] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),U_3887)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),U_3891)),U_3889)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3887),U_3891))),U_3889)
        | hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3891)))
        | ~ sP305(U_3887,U_3891,U_3889) )
    & ! [U_3887,U_3891,U_3889] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),U_3887)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),U_3891)),U_3889)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),U_3887)),U_3889)
        | ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3891)))
        | ~ sP305(U_3887,U_3891,U_3889) )
    & ! [U_3887,U_3891,U_3889] :
        ( sP305(U_3887,U_3891,U_3889)
        | hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3887))) )
    & ! [U_3890,U_3886,U_3888] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),U_3886)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),U_3890)),U_3888)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),U_3890)),U_3888)
        | ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3886))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP305])],[f_1008_3]) ).

cnf(f_1008_5,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),U_3886)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),U_3890)),U_3888)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),U_3890)),U_3888)
    | ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3886))) ),
    inference(clausify,[status(thm)],[f_1008_4]) ).

cnf(f_1008_6,plain,
    ( sP305(U_3887,U_3891,U_3889)
    | hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3887))) ),
    inference(clausify,[status(thm)],[f_1008_4]) ).

cnf(f_1008_7,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),U_3887)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),U_3891)),U_3889)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),U_3887)),U_3889)
    | ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3891)))
    | ~ sP305(U_3887,U_3891,U_3889) ),
    inference(clausify,[status(thm)],[f_1008_4]) ).

cnf(f_1008_8,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),U_3887)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),U_3891)),U_3889)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3887),U_3891))),U_3889)
    | hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3891)))
    | ~ sP305(U_3887,U_3891,U_3889) ),
    inference(clausify,[status(thm)],[f_1008_4]) ).

fof(f_1009_1,plain,
    ! [V] :
      ( ( hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),V)) = hAPP(int,int,number_number_of(int),V)
        | hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) )
      & ( hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),V)) = zero_zero(int)
        | ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) ) ),
    inference(fof_nnf,[status(thm)],[fact_938_int__nat__number__of]) ).

fof(f_1009_2,plain,
    ! [U_3892] :
      ( ( hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),U_3892)) = hAPP(int,int,number_number_of(int),U_3892)
        | hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3892))) )
      & ( hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),U_3892)) = zero_zero(int)
        | ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3892))) ) ),
    inference(variable_rename,[status(thm)],[f_1009_1]) ).

fof(f_1009_3,plain,
    ( ! [U_3894] :
        ( hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),U_3894)) = hAPP(int,int,number_number_of(int),U_3894)
        | hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3894))) )
    & ! [U_3893] :
        ( hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),U_3893)) = zero_zero(int)
        | ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3893))) ) ),
    inference(miniscope,[status(thm)],[f_1009_2]) ).

fof(f_1009_4,plain,
    ( ! [U_3894] :
        ( hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),U_3894)) = hAPP(int,int,number_number_of(int),U_3894)
        | hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3894))) )
    & ! [U_3893] :
        ( hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),U_3893)) = zero_zero(int)
        | ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3893))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1009_3]) ).

cnf(f_1009_5,plain,
    ( hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),U_3893)) = zero_zero(int)
    | ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3893))) ),
    inference(clausify,[status(thm)],[f_1009_4]) ).

cnf(f_1009_6,plain,
    ( hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),U_3894)) = hAPP(int,int,number_number_of(int),U_3894)
    | hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3894))) ),
    inference(clausify,[status(thm)],[f_1009_4]) ).

fof(f_1010_1,plain,
    ! [Z,X,D] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X),Z))),one_one(int))),D))))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D)) ),
    inference(fof_nnf,[status(thm)],[fact_939_incr__lemma]) ).

fof(f_1010_2,plain,
    ! [U_3897,U_3896,U_3895] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3897),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3896),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3896),U_3897))),one_one(int))),U_3895))))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3895)) ),
    inference(variable_rename,[status(thm)],[f_1010_1]) ).

fof(f_1010_3,plain,
    ! [U_3895,U_3897,U_3896] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3897),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3896),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3896),U_3897))),one_one(int))),U_3895))))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3895)) ),
    inference(definitional_conversion,[status(esa)],[f_1010_2]) ).

cnf(f_1010_4,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3897),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3896),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3896),U_3897))),one_one(int))),U_3895))))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),U_3895)) ),
    inference(clausify,[status(thm)],[f_1010_3]) ).

fof(f_1011_1,plain,
    ! [K,F,Na] :
      ( ? [I] :
          ( hAPP(nat,int,F,I) = K
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),Na)) )
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),hAPP(nat,int,F,Na)))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,F,zero_zero(nat))),K))
      | ? [I] :
          ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),one_one(nat)))),hAPP(nat,int,F,I)))),one_one(int)))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_940_int__val__lemma]) ).

fof(f_1011_2,plain,
    ! [U_3902,U_3901,U_3900] :
      ( ? [U_3899] :
          ( hAPP(nat,int,U_3901,U_3899) = U_3902
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3899),U_3900)) )
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3902),hAPP(nat,int,U_3901,U_3900)))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,U_3901,zero_zero(nat))),U_3902))
      | ? [U_3898] :
          ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,U_3901,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_3898),one_one(nat)))),hAPP(nat,int,U_3901,U_3898)))),one_one(int)))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3898),U_3900)) ) ),
    inference(variable_rename,[status(thm)],[f_1011_1]) ).

fof(f_1011_3,plain,
    ! [U_3902,U_3901,U_3900] :
      ( ? [U_3899] :
          ( hAPP(nat,int,U_3901,U_3899) = U_3902
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3899),U_3900)) )
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3902),hAPP(nat,int,U_3901,U_3900)))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,U_3901,zero_zero(nat))),U_3902))
      | ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,U_3901,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),sK147(U_3902,U_3901,U_3900)),one_one(nat)))),hAPP(nat,int,U_3901,sK147(U_3902,U_3901,U_3900))))),one_one(int)))
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK147(U_3902,U_3901,U_3900)),U_3900)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK147]),skolemize(U_3898,sK147(U_3902,U_3901,U_3900))],[f_1011_2]) ).

fof(f_1011_4,plain,
    ! [U_3902,U_3901,U_3900] :
      ( ( hAPP(nat,int,U_3901,sK148(U_3902,U_3901,U_3900)) = U_3902
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sK148(U_3902,U_3901,U_3900)),U_3900)) )
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3902),hAPP(nat,int,U_3901,U_3900)))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,U_3901,zero_zero(nat))),U_3902))
      | ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,U_3901,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),sK147(U_3902,U_3901,U_3900)),one_one(nat)))),hAPP(nat,int,U_3901,sK147(U_3902,U_3901,U_3900))))),one_one(int)))
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK147(U_3902,U_3901,U_3900)),U_3900)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK148]),skolemize(U_3899,sK148(U_3902,U_3901,U_3900))],[f_1011_3]) ).

fof(f_1011_5,plain,
    ( ! [U_3900,U_3902,U_3901] :
        ( hAPP(nat,int,U_3901,sK148(U_3902,U_3901,U_3900)) = U_3902
        | ~ sP307(U_3900,U_3902,U_3901) )
    & ! [U_3900,U_3902,U_3901] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sK148(U_3902,U_3901,U_3900)),U_3900))
        | ~ sP307(U_3900,U_3902,U_3901) )
    & ! [U_3900,U_3902,U_3901] :
        ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,U_3901,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),sK147(U_3902,U_3901,U_3900)),one_one(nat)))),hAPP(nat,int,U_3901,sK147(U_3902,U_3901,U_3900))))),one_one(int)))
        | ~ sP306(U_3900,U_3902,U_3901) )
    & ! [U_3900,U_3902,U_3901] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK147(U_3902,U_3901,U_3900)),U_3900))
        | ~ sP306(U_3900,U_3902,U_3901) )
    & ! [U_3900,U_3902,U_3901] :
        ( sP307(U_3900,U_3902,U_3901)
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3902),hAPP(nat,int,U_3901,U_3900)))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,U_3901,zero_zero(nat))),U_3902))
        | sP306(U_3900,U_3902,U_3901) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP306,sP307])],[f_1011_4]) ).

cnf(f_1011_6,plain,
    ( sP307(U_3900,U_3902,U_3901)
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3902),hAPP(nat,int,U_3901,U_3900)))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,U_3901,zero_zero(nat))),U_3902))
    | sP306(U_3900,U_3902,U_3901) ),
    inference(clausify,[status(thm)],[f_1011_5]) ).

cnf(f_1011_7,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK147(U_3902,U_3901,U_3900)),U_3900))
    | ~ sP306(U_3900,U_3902,U_3901) ),
    inference(clausify,[status(thm)],[f_1011_5]) ).

cnf(f_1011_8,plain,
    ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,U_3901,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),sK147(U_3902,U_3901,U_3900)),one_one(nat)))),hAPP(nat,int,U_3901,sK147(U_3902,U_3901,U_3900))))),one_one(int)))
    | ~ sP306(U_3900,U_3902,U_3901) ),
    inference(clausify,[status(thm)],[f_1011_5]) ).

cnf(f_1011_9,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sK148(U_3902,U_3901,U_3900)),U_3900))
    | ~ sP307(U_3900,U_3902,U_3901) ),
    inference(clausify,[status(thm)],[f_1011_5]) ).

cnf(f_1011_10,plain,
    ( hAPP(nat,int,U_3901,sK148(U_3902,U_3901,U_3900)) = U_3902
    | ~ sP307(U_3900,U_3902,U_3901) ),
    inference(clausify,[status(thm)],[f_1011_5]) ).

fof(f_1012_1,plain,
    ! [K,F,Na] :
      ( ? [I] :
          ( hAPP(nat,int,F,I) = K
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),Na)) )
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),hAPP(nat,int,F,Na)))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,F,zero_zero(nat))),K))
      | ? [I] :
          ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),one_one(nat)))),hAPP(nat,int,F,I)))),one_one(int)))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_941_nat0__intermed__int__val]) ).

fof(f_1012_2,plain,
    ! [U_3907,U_3906,U_3905] :
      ( ? [U_3904] :
          ( hAPP(nat,int,U_3906,U_3904) = U_3907
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3904),U_3905)) )
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3907),hAPP(nat,int,U_3906,U_3905)))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,U_3906,zero_zero(nat))),U_3907))
      | ? [U_3903] :
          ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,U_3906,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_3903),one_one(nat)))),hAPP(nat,int,U_3906,U_3903)))),one_one(int)))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3903),U_3905)) ) ),
    inference(variable_rename,[status(thm)],[f_1012_1]) ).

fof(f_1012_3,plain,
    ! [U_3907,U_3906,U_3905] :
      ( ? [U_3904] :
          ( hAPP(nat,int,U_3906,U_3904) = U_3907
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3904),U_3905)) )
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3907),hAPP(nat,int,U_3906,U_3905)))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,U_3906,zero_zero(nat))),U_3907))
      | ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,U_3906,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),sK149(U_3907,U_3906,U_3905)),one_one(nat)))),hAPP(nat,int,U_3906,sK149(U_3907,U_3906,U_3905))))),one_one(int)))
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK149(U_3907,U_3906,U_3905)),U_3905)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK149]),skolemize(U_3903,sK149(U_3907,U_3906,U_3905))],[f_1012_2]) ).

fof(f_1012_4,plain,
    ! [U_3907,U_3906,U_3905] :
      ( ( hAPP(nat,int,U_3906,sK150(U_3907,U_3906,U_3905)) = U_3907
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sK150(U_3907,U_3906,U_3905)),U_3905)) )
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3907),hAPP(nat,int,U_3906,U_3905)))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,U_3906,zero_zero(nat))),U_3907))
      | ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,U_3906,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),sK149(U_3907,U_3906,U_3905)),one_one(nat)))),hAPP(nat,int,U_3906,sK149(U_3907,U_3906,U_3905))))),one_one(int)))
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK149(U_3907,U_3906,U_3905)),U_3905)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK150]),skolemize(U_3904,sK150(U_3907,U_3906,U_3905))],[f_1012_3]) ).

fof(f_1012_5,plain,
    ( ! [U_3905,U_3907,U_3906] :
        ( hAPP(nat,int,U_3906,sK150(U_3907,U_3906,U_3905)) = U_3907
        | ~ sP309(U_3905,U_3907,U_3906) )
    & ! [U_3905,U_3907,U_3906] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sK150(U_3907,U_3906,U_3905)),U_3905))
        | ~ sP309(U_3905,U_3907,U_3906) )
    & ! [U_3905,U_3907,U_3906] :
        ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,U_3906,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),sK149(U_3907,U_3906,U_3905)),one_one(nat)))),hAPP(nat,int,U_3906,sK149(U_3907,U_3906,U_3905))))),one_one(int)))
        | ~ sP308(U_3905,U_3907,U_3906) )
    & ! [U_3905,U_3907,U_3906] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK149(U_3907,U_3906,U_3905)),U_3905))
        | ~ sP308(U_3905,U_3907,U_3906) )
    & ! [U_3905,U_3907,U_3906] :
        ( sP309(U_3905,U_3907,U_3906)
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3907),hAPP(nat,int,U_3906,U_3905)))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,U_3906,zero_zero(nat))),U_3907))
        | sP308(U_3905,U_3907,U_3906) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP308,sP309])],[f_1012_4]) ).

cnf(f_1012_6,plain,
    ( sP309(U_3905,U_3907,U_3906)
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3907),hAPP(nat,int,U_3906,U_3905)))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,U_3906,zero_zero(nat))),U_3907))
    | sP308(U_3905,U_3907,U_3906) ),
    inference(clausify,[status(thm)],[f_1012_5]) ).

cnf(f_1012_7,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK149(U_3907,U_3906,U_3905)),U_3905))
    | ~ sP308(U_3905,U_3907,U_3906) ),
    inference(clausify,[status(thm)],[f_1012_5]) ).

cnf(f_1012_8,plain,
    ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,U_3906,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),sK149(U_3907,U_3906,U_3905)),one_one(nat)))),hAPP(nat,int,U_3906,sK149(U_3907,U_3906,U_3905))))),one_one(int)))
    | ~ sP308(U_3905,U_3907,U_3906) ),
    inference(clausify,[status(thm)],[f_1012_5]) ).

cnf(f_1012_9,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sK150(U_3907,U_3906,U_3905)),U_3905))
    | ~ sP309(U_3905,U_3907,U_3906) ),
    inference(clausify,[status(thm)],[f_1012_5]) ).

cnf(f_1012_10,plain,
    ( hAPP(nat,int,U_3906,sK150(U_3907,U_3906,U_3905)) = U_3907
    | ~ sP309(U_3905,U_3907,U_3906) ),
    inference(clausify,[status(thm)],[f_1012_5]) ).

fof(f_1013_1,plain,
    ! [K,F,Na,M] :
      ( ? [I] :
          ( hAPP(nat,int,F,I) = K
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),Na))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),I)) )
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),hAPP(nat,int,F,Na)))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,F,M)),K))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))
      | ? [I] :
          ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),one_one(nat)))),hAPP(nat,int,F,I)))),one_one(int)))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),Na))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),I)) ) ),
    inference(fof_nnf,[status(thm)],[fact_942_nat__intermed__int__val]) ).

fof(f_1013_2,plain,
    ! [U_3913,U_3912,U_3911,U_3910] :
      ( ? [U_3909] :
          ( hAPP(nat,int,U_3912,U_3909) = U_3913
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3909),U_3911))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3910),U_3909)) )
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3913),hAPP(nat,int,U_3912,U_3911)))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,U_3912,U_3910)),U_3913))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3910),U_3911))
      | ? [U_3908] :
          ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,U_3912,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_3908),one_one(nat)))),hAPP(nat,int,U_3912,U_3908)))),one_one(int)))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3908),U_3911))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3910),U_3908)) ) ),
    inference(variable_rename,[status(thm)],[f_1013_1]) ).

fof(f_1013_3,plain,
    ! [U_3913,U_3912,U_3911,U_3910] :
      ( ? [U_3909] :
          ( hAPP(nat,int,U_3912,U_3909) = U_3913
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3909),U_3911))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3910),U_3909)) )
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3913),hAPP(nat,int,U_3912,U_3911)))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,U_3912,U_3910)),U_3913))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3910),U_3911))
      | ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,U_3912,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),sK151(U_3913,U_3912,U_3911,U_3910)),one_one(nat)))),hAPP(nat,int,U_3912,sK151(U_3913,U_3912,U_3911,U_3910))))),one_one(int)))
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK151(U_3913,U_3912,U_3911,U_3910)),U_3911))
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3910),sK151(U_3913,U_3912,U_3911,U_3910))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK151]),skolemize(U_3908,sK151(U_3913,U_3912,U_3911,U_3910))],[f_1013_2]) ).

fof(f_1013_4,plain,
    ! [U_3913,U_3912,U_3911,U_3910] :
      ( ( hAPP(nat,int,U_3912,sK152(U_3913,U_3912,U_3911,U_3910)) = U_3913
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sK152(U_3913,U_3912,U_3911,U_3910)),U_3911))
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3910),sK152(U_3913,U_3912,U_3911,U_3910))) )
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3913),hAPP(nat,int,U_3912,U_3911)))
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,U_3912,U_3910)),U_3913))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3910),U_3911))
      | ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,U_3912,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),sK151(U_3913,U_3912,U_3911,U_3910)),one_one(nat)))),hAPP(nat,int,U_3912,sK151(U_3913,U_3912,U_3911,U_3910))))),one_one(int)))
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK151(U_3913,U_3912,U_3911,U_3910)),U_3911))
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3910),sK151(U_3913,U_3912,U_3911,U_3910))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK152]),skolemize(U_3909,sK152(U_3913,U_3912,U_3911,U_3910))],[f_1013_3]) ).

fof(f_1013_5,plain,
    ( ! [U_3910,U_3911,U_3913,U_3912] :
        ( hAPP(nat,int,U_3912,sK152(U_3913,U_3912,U_3911,U_3910)) = U_3913
        | ~ sP311(U_3910,U_3911,U_3913,U_3912) )
    & ! [U_3910,U_3911,U_3913,U_3912] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sK152(U_3913,U_3912,U_3911,U_3910)),U_3911))
        | ~ sP311(U_3910,U_3911,U_3913,U_3912) )
    & ! [U_3910,U_3911,U_3913,U_3912] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3910),sK152(U_3913,U_3912,U_3911,U_3910)))
        | ~ sP311(U_3910,U_3911,U_3913,U_3912) )
    & ! [U_3910,U_3911,U_3913,U_3912] :
        ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,U_3912,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),sK151(U_3913,U_3912,U_3911,U_3910)),one_one(nat)))),hAPP(nat,int,U_3912,sK151(U_3913,U_3912,U_3911,U_3910))))),one_one(int)))
        | ~ sP310(U_3910,U_3911,U_3913,U_3912) )
    & ! [U_3910,U_3911,U_3913,U_3912] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK151(U_3913,U_3912,U_3911,U_3910)),U_3911))
        | ~ sP310(U_3910,U_3911,U_3913,U_3912) )
    & ! [U_3910,U_3911,U_3913,U_3912] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3910),sK151(U_3913,U_3912,U_3911,U_3910)))
        | ~ sP310(U_3910,U_3911,U_3913,U_3912) )
    & ! [U_3910,U_3911,U_3913,U_3912] :
        ( sP311(U_3910,U_3911,U_3913,U_3912)
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3913),hAPP(nat,int,U_3912,U_3911)))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,U_3912,U_3910)),U_3913))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3910),U_3911))
        | sP310(U_3910,U_3911,U_3913,U_3912) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP310,sP311])],[f_1013_4]) ).

cnf(f_1013_6,plain,
    ( sP311(U_3910,U_3911,U_3913,U_3912)
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3913),hAPP(nat,int,U_3912,U_3911)))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,U_3912,U_3910)),U_3913))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3910),U_3911))
    | sP310(U_3910,U_3911,U_3913,U_3912) ),
    inference(clausify,[status(thm)],[f_1013_5]) ).

cnf(f_1013_7,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3910),sK151(U_3913,U_3912,U_3911,U_3910)))
    | ~ sP310(U_3910,U_3911,U_3913,U_3912) ),
    inference(clausify,[status(thm)],[f_1013_5]) ).

cnf(f_1013_8,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK151(U_3913,U_3912,U_3911,U_3910)),U_3911))
    | ~ sP310(U_3910,U_3911,U_3913,U_3912) ),
    inference(clausify,[status(thm)],[f_1013_5]) ).

cnf(f_1013_9,plain,
    ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,U_3912,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),sK151(U_3913,U_3912,U_3911,U_3910)),one_one(nat)))),hAPP(nat,int,U_3912,sK151(U_3913,U_3912,U_3911,U_3910))))),one_one(int)))
    | ~ sP310(U_3910,U_3911,U_3913,U_3912) ),
    inference(clausify,[status(thm)],[f_1013_5]) ).

cnf(f_1013_10,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3910),sK152(U_3913,U_3912,U_3911,U_3910)))
    | ~ sP311(U_3910,U_3911,U_3913,U_3912) ),
    inference(clausify,[status(thm)],[f_1013_5]) ).

cnf(f_1013_11,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sK152(U_3913,U_3912,U_3911,U_3910)),U_3911))
    | ~ sP311(U_3910,U_3911,U_3913,U_3912) ),
    inference(clausify,[status(thm)],[f_1013_5]) ).

cnf(f_1013_12,plain,
    ( hAPP(nat,int,U_3912,sK152(U_3913,U_3912,U_3911,U_3910)) = U_3913
    | ~ sP311(U_3910,U_3911,U_3913,U_3912) ),
    inference(clausify,[status(thm)],[f_1013_5]) ).

fof(f_1014_1,plain,
    ! [N,V] :
      ( ( hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,V))),N)
        | hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) )
      & ( hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),N)
        | ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) ) ),
    inference(fof_nnf,[status(thm)],[fact_943_Suc__nat__number__of__add]) ).

fof(f_1014_2,plain,
    ! [U_3915,U_3914] :
      ( ( hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),U_3914)),U_3915)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,U_3914))),U_3915)
        | hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3914))) )
      & ( hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),U_3914)),U_3915)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),U_3915)
        | ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3914))) ) ),
    inference(variable_rename,[status(thm)],[f_1014_1]) ).

fof(f_1014_3,plain,
    ( ! [U_3919,U_3917] :
        ( hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),U_3917)),U_3919)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,U_3917))),U_3919)
        | hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3917))) )
    & ! [U_3918,U_3916] :
        ( hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),U_3916)),U_3918)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),U_3918)
        | ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3916))) ) ),
    inference(miniscope,[status(thm)],[f_1014_2]) ).

fof(f_1014_4,plain,
    ( ! [U_3919,U_3917] :
        ( hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),U_3917)),U_3919)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,U_3917))),U_3919)
        | hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3917))) )
    & ! [U_3918,U_3916] :
        ( hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),U_3916)),U_3918)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),U_3918)
        | ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3916))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1014_3]) ).

cnf(f_1014_5,plain,
    ( hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),U_3916)),U_3918)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),U_3918)
    | ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3916))) ),
    inference(clausify,[status(thm)],[f_1014_4]) ).

cnf(f_1014_6,plain,
    ( hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),U_3917)),U_3919)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,U_3917))),U_3919)
    | hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3917))) ),
    inference(clausify,[status(thm)],[f_1014_4]) ).

fof(f_1015_1,plain,
    ! [K_1] : hAPP(int,int,succ,K_1) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_1),one_one(int)),
    inference(fof_nnf,[status(thm)],[fact_944_succ__def]) ).

fof(f_1015_2,plain,
    ! [U_3920] : hAPP(int,int,succ,U_3920) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3920),one_one(int)),
    inference(variable_rename,[status(thm)],[f_1015_1]) ).

fof(f_1015_3,plain,
    ! [U_3920] : hAPP(int,int,succ,U_3920) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3920),one_one(int)),
    inference(definitional_conversion,[status(esa)],[f_1015_2]) ).

cnf(f_1015_4,plain,
    hAPP(int,int,succ,U_3920) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3920),one_one(int)),
    inference(clausify,[status(thm)],[f_1015_3]) ).

fof(f_1016_1,plain,
    ! [X_a] :
      ( ! [K_1] : hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,succ,K_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),hAPP(int,X_a,number_number_of(X_a),K_1))
      | ~ number_ring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_945_number__of__succ]) ).

fof(f_1016_2,plain,
    ! [U_3922] :
      ( ! [U_3921] : hAPP(int,U_3922,number_number_of(U_3922),hAPP(int,int,succ,U_3921)) = hAPP(U_3922,U_3922,hAPP(U_3922,fun(U_3922,U_3922),plus_plus(U_3922),one_one(U_3922)),hAPP(int,U_3922,number_number_of(U_3922),U_3921))
      | ~ number_ring(U_3922) ),
    inference(variable_rename,[status(thm)],[f_1016_1]) ).

fof(f_1016_3,plain,
    ! [U_3922,U_3921] :
      ( hAPP(int,U_3922,number_number_of(U_3922),hAPP(int,int,succ,U_3921)) = hAPP(U_3922,U_3922,hAPP(U_3922,fun(U_3922,U_3922),plus_plus(U_3922),one_one(U_3922)),hAPP(int,U_3922,number_number_of(U_3922),U_3921))
      | ~ number_ring(U_3922) ),
    inference(definitional_conversion,[status(esa)],[f_1016_2]) ).

cnf(f_1016_4,plain,
    ( hAPP(int,U_3922,number_number_of(U_3922),hAPP(int,int,succ,U_3921)) = hAPP(U_3922,U_3922,hAPP(U_3922,fun(U_3922,U_3922),plus_plus(U_3922),one_one(U_3922)),hAPP(int,U_3922,number_number_of(U_3922),U_3921))
    | ~ number_ring(U_3922) ),
    inference(clausify,[status(thm)],[f_1016_3]) ).

fof(f_1017_1,plain,
    ! [V] :
      ( ( hAPP(nat,nat,suc,hAPP(int,nat,number_number_of(nat),V)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,V))
        | hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) )
      & ( hAPP(nat,nat,suc,hAPP(int,nat,number_number_of(nat),V)) = one_one(nat)
        | ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) ) ),
    inference(fof_nnf,[status(thm)],[fact_946_Suc__nat__number__of]) ).

fof(f_1017_2,plain,
    ! [U_3923] :
      ( ( hAPP(nat,nat,suc,hAPP(int,nat,number_number_of(nat),U_3923)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,U_3923))
        | hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3923))) )
      & ( hAPP(nat,nat,suc,hAPP(int,nat,number_number_of(nat),U_3923)) = one_one(nat)
        | ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3923))) ) ),
    inference(variable_rename,[status(thm)],[f_1017_1]) ).

fof(f_1017_3,plain,
    ( ! [U_3925] :
        ( hAPP(nat,nat,suc,hAPP(int,nat,number_number_of(nat),U_3925)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,U_3925))
        | hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3925))) )
    & ! [U_3924] :
        ( hAPP(nat,nat,suc,hAPP(int,nat,number_number_of(nat),U_3924)) = one_one(nat)
        | ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3924))) ) ),
    inference(miniscope,[status(thm)],[f_1017_2]) ).

fof(f_1017_4,plain,
    ( ! [U_3925] :
        ( hAPP(nat,nat,suc,hAPP(int,nat,number_number_of(nat),U_3925)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,U_3925))
        | hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3925))) )
    & ! [U_3924] :
        ( hAPP(nat,nat,suc,hAPP(int,nat,number_number_of(nat),U_3924)) = one_one(nat)
        | ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3924))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1017_3]) ).

cnf(f_1017_5,plain,
    ( hAPP(nat,nat,suc,hAPP(int,nat,number_number_of(nat),U_3924)) = one_one(nat)
    | ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3924))) ),
    inference(clausify,[status(thm)],[f_1017_4]) ).

cnf(f_1017_6,plain,
    ( hAPP(nat,nat,suc,hAPP(int,nat,number_number_of(nat),U_3925)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,U_3925))
    | hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3925))) ),
    inference(clausify,[status(thm)],[f_1017_4]) ).

fof(f_1018_1,plain,
    ! [W] :
      ( ( hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,W)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),W)),hAPP(int,nat,number_number_of(nat),W)))
        | hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),W))) )
      & ( hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,W)) = zero_zero(nat)
        | ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),W))) ) ),
    inference(fof_nnf,[status(thm)],[fact_947_nat__number__of__Bit1]) ).

fof(f_1018_2,plain,
    ! [U_3926] :
      ( ( hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,U_3926)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),U_3926)),hAPP(int,nat,number_number_of(nat),U_3926)))
        | hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3926))) )
      & ( hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,U_3926)) = zero_zero(nat)
        | ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3926))) ) ),
    inference(variable_rename,[status(thm)],[f_1018_1]) ).

fof(f_1018_3,plain,
    ( ! [U_3928] :
        ( hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,U_3928)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),U_3928)),hAPP(int,nat,number_number_of(nat),U_3928)))
        | hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3928))) )
    & ! [U_3927] :
        ( hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,U_3927)) = zero_zero(nat)
        | ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3927))) ) ),
    inference(miniscope,[status(thm)],[f_1018_2]) ).

fof(f_1018_4,plain,
    ( ! [U_3928] :
        ( hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,U_3928)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),U_3928)),hAPP(int,nat,number_number_of(nat),U_3928)))
        | hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3928))) )
    & ! [U_3927] :
        ( hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,U_3927)) = zero_zero(nat)
        | ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3927))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1018_3]) ).

cnf(f_1018_5,plain,
    ( hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,U_3927)) = zero_zero(nat)
    | ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3927))) ),
    inference(clausify,[status(thm)],[f_1018_4]) ).

cnf(f_1018_6,plain,
    ( hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,U_3928)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),U_3928)),hAPP(int,nat,number_number_of(nat),U_3928)))
    | hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3928))) ),
    inference(clausify,[status(thm)],[f_1018_4]) ).

fof(f_1019_1,plain,
    ! [V] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(int,nat,number_number_of(nat),V)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,V))
        | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls)) )
      & ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(int,nat,number_number_of(nat),V)) = one_one(nat)
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls)) ) ),
    inference(fof_nnf,[status(thm)],[fact_948_nat__1__add__number__of]) ).

fof(f_1019_2,plain,
    ! [U_3929] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(int,nat,number_number_of(nat),U_3929)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,U_3929))
        | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3929),pls)) )
      & ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(int,nat,number_number_of(nat),U_3929)) = one_one(nat)
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3929),pls)) ) ),
    inference(variable_rename,[status(thm)],[f_1019_1]) ).

fof(f_1019_3,plain,
    ( ! [U_3931] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(int,nat,number_number_of(nat),U_3931)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,U_3931))
        | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3931),pls)) )
    & ! [U_3930] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(int,nat,number_number_of(nat),U_3930)) = one_one(nat)
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3930),pls)) ) ),
    inference(miniscope,[status(thm)],[f_1019_2]) ).

fof(f_1019_4,plain,
    ( ! [U_3931] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(int,nat,number_number_of(nat),U_3931)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,U_3931))
        | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3931),pls)) )
    & ! [U_3930] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(int,nat,number_number_of(nat),U_3930)) = one_one(nat)
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3930),pls)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1019_3]) ).

cnf(f_1019_5,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(int,nat,number_number_of(nat),U_3930)) = one_one(nat)
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3930),pls)) ),
    inference(clausify,[status(thm)],[f_1019_4]) ).

cnf(f_1019_6,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(int,nat,number_number_of(nat),U_3931)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,U_3931))
    | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3931),pls)) ),
    inference(clausify,[status(thm)],[f_1019_4]) ).

fof(f_1020_1,plain,
    hAPP(int,int,succ,pls) = hAPP(int,int,bit1,pls),
    inference(fof_nnf,[status(thm)],[fact_949_succ__Pls]) ).

fof(f_1020_2,plain,
    hAPP(int,int,succ,pls) = hAPP(int,int,bit1,pls),
    inference(definitional_conversion,[status(esa)],[f_1020_1]) ).

cnf(f_1020_3,plain,
    hAPP(int,int,succ,pls) = hAPP(int,int,bit1,pls),
    inference(clausify,[status(thm)],[f_1020_2]) ).

fof(f_1021_1,plain,
    ! [W_1] :
      ( ( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,W_1))))
        | ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),W_1))) )
      & ( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),W_1)))
        | ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,W_1)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_950_neg__number__of__Bit1]) ).

fof(f_1021_2,plain,
    ! [U_3932] :
      ( ( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,U_3932))))
        | ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3932))) )
      & ( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3932)))
        | ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,U_3932)))) ) ),
    inference(variable_rename,[status(thm)],[f_1021_1]) ).

fof(f_1021_3,plain,
    ( ! [U_3934] :
        ( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,U_3934))))
        | ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3934))) )
    & ! [U_3933] :
        ( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3933)))
        | ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,U_3933)))) ) ),
    inference(miniscope,[status(thm)],[f_1021_2]) ).

fof(f_1021_4,plain,
    ( ! [U_3934] :
        ( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,U_3934))))
        | ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3934))) )
    & ! [U_3933] :
        ( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3933)))
        | ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,U_3933)))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1021_3]) ).

cnf(f_1021_5,plain,
    ( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3933)))
    | ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,U_3933)))) ),
    inference(clausify,[status(thm)],[f_1021_4]) ).

cnf(f_1021_6,plain,
    ( hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,U_3934))))
    | ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),U_3934))) ),
    inference(clausify,[status(thm)],[f_1021_4]) ).

fof(f_1022_1,plain,
    ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),pls))),
    inference(fof_nnf,[status(thm)],[fact_951_not__neg__number__of__Pls]) ).

fof(f_1022_2,plain,
    ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),pls))),
    inference(definitional_conversion,[status(esa)],[f_1022_1]) ).

cnf(f_1022_3,plain,
    ~ hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),pls))),
    inference(clausify,[status(thm)],[f_1022_2]) ).

fof(f_1023_1,plain,
    hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),
    inference(fof_nnf,[status(thm)],[fact_952_transfer__int__nat__numerals_I4_J]) ).

fof(f_1023_2,plain,
    hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),
    inference(definitional_conversion,[status(esa)],[f_1023_1]) ).

cnf(f_1023_3,plain,
    hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),
    inference(clausify,[status(thm)],[f_1023_2]) ).

fof(f_1024_1,plain,
    ! [X_a] :
      ( ! [W] : hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,W)) = 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),one_one(X_a)),hAPP(int,X_a,number_number_of(X_a),W))),hAPP(int,X_a,number_number_of(X_a),W))
      | ~ number_ring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_953_number__of__Bit1]) ).

fof(f_1024_2,plain,
    ! [U_3936] :
      ( ! [U_3935] : hAPP(int,U_3936,number_number_of(U_3936),hAPP(int,int,bit1,U_3935)) = hAPP(U_3936,U_3936,hAPP(U_3936,fun(U_3936,U_3936),plus_plus(U_3936),hAPP(U_3936,U_3936,hAPP(U_3936,fun(U_3936,U_3936),plus_plus(U_3936),one_one(U_3936)),hAPP(int,U_3936,number_number_of(U_3936),U_3935))),hAPP(int,U_3936,number_number_of(U_3936),U_3935))
      | ~ number_ring(U_3936) ),
    inference(variable_rename,[status(thm)],[f_1024_1]) ).

fof(f_1024_3,plain,
    ! [U_3935,U_3936] :
      ( hAPP(int,U_3936,number_number_of(U_3936),hAPP(int,int,bit1,U_3935)) = hAPP(U_3936,U_3936,hAPP(U_3936,fun(U_3936,U_3936),plus_plus(U_3936),hAPP(U_3936,U_3936,hAPP(U_3936,fun(U_3936,U_3936),plus_plus(U_3936),one_one(U_3936)),hAPP(int,U_3936,number_number_of(U_3936),U_3935))),hAPP(int,U_3936,number_number_of(U_3936),U_3935))
      | ~ number_ring(U_3936) ),
    inference(definitional_conversion,[status(esa)],[f_1024_2]) ).

cnf(f_1024_4,plain,
    ( hAPP(int,U_3936,number_number_of(U_3936),hAPP(int,int,bit1,U_3935)) = hAPP(U_3936,U_3936,hAPP(U_3936,fun(U_3936,U_3936),plus_plus(U_3936),hAPP(U_3936,U_3936,hAPP(U_3936,fun(U_3936,U_3936),plus_plus(U_3936),one_one(U_3936)),hAPP(int,U_3936,number_number_of(U_3936),U_3935))),hAPP(int,U_3936,number_number_of(U_3936),U_3935))
    | ~ number_ring(U_3936) ),
    inference(clausify,[status(thm)],[f_1024_3]) ).

fof(f_1025_1,plain,
    hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,pls)) = hAPP(nat,nat,suc,zero_zero(nat)),
    inference(fof_nnf,[status(thm)],[fact_954_numeral__1__eq__Suc__0]) ).

fof(f_1025_2,plain,
    hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,pls)) = hAPP(nat,nat,suc,zero_zero(nat)),
    inference(definitional_conversion,[status(esa)],[f_1025_1]) ).

cnf(f_1025_3,plain,
    hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,pls)) = hAPP(nat,nat,suc,zero_zero(nat)),
    inference(clausify,[status(thm)],[f_1025_2]) ).

fof(f_1026_1,plain,
    hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))) = hAPP(nat,nat,suc,hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))),
    inference(fof_nnf,[status(thm)],[fact_955_numeral__3__eq__3]) ).

fof(f_1026_2,plain,
    hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))) = hAPP(nat,nat,suc,hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))),
    inference(definitional_conversion,[status(esa)],[f_1026_1]) ).

cnf(f_1026_3,plain,
    hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))) = hAPP(nat,nat,suc,hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))),
    inference(clausify,[status(thm)],[f_1026_2]) ).

fof(f_1027_1,plain,
    ! [N] : hAPP(nat,nat,suc,hAPP(nat,nat,suc,hAPP(nat,nat,suc,N))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),N),
    inference(fof_nnf,[status(thm)],[fact_956_Suc3__eq__add__3]) ).

fof(f_1027_2,plain,
    ! [U_3937] : hAPP(nat,nat,suc,hAPP(nat,nat,suc,hAPP(nat,nat,suc,U_3937))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),U_3937),
    inference(variable_rename,[status(thm)],[f_1027_1]) ).

fof(f_1027_3,plain,
    ! [U_3937] : hAPP(nat,nat,suc,hAPP(nat,nat,suc,hAPP(nat,nat,suc,U_3937))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),U_3937),
    inference(definitional_conversion,[status(esa)],[f_1027_2]) ).

cnf(f_1027_4,plain,
    hAPP(nat,nat,suc,hAPP(nat,nat,suc,hAPP(nat,nat,suc,U_3937))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),U_3937),
    inference(clausify,[status(thm)],[f_1027_3]) ).

fof(f_1028_1,plain,
    ! [X_a] :
      ( one_one(X_a) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,pls))
      | ~ number_ring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_957_semiring__norm_I110_J]) ).

fof(f_1028_2,plain,
    ! [U_3938] :
      ( one_one(U_3938) = hAPP(int,U_3938,number_number_of(U_3938),hAPP(int,int,bit1,pls))
      | ~ number_ring(U_3938) ),
    inference(variable_rename,[status(thm)],[f_1028_1]) ).

fof(f_1028_3,plain,
    ! [U_3938] :
      ( one_one(U_3938) = hAPP(int,U_3938,number_number_of(U_3938),hAPP(int,int,bit1,pls))
      | ~ number_ring(U_3938) ),
    inference(definitional_conversion,[status(esa)],[f_1028_2]) ).

cnf(f_1028_4,plain,
    ( one_one(U_3938) = hAPP(int,U_3938,number_number_of(U_3938),hAPP(int,int,bit1,pls))
    | ~ number_ring(U_3938) ),
    inference(clausify,[status(thm)],[f_1028_3]) ).

fof(f_1029_1,plain,
    one_one(nat) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,pls)),
    inference(fof_nnf,[status(thm)],[fact_958_Numeral1__eq1__nat]) ).

fof(f_1029_2,plain,
    one_one(nat) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,pls)),
    inference(definitional_conversion,[status(esa)],[f_1029_1]) ).

cnf(f_1029_3,plain,
    one_one(nat) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,pls)),
    inference(clausify,[status(thm)],[f_1029_2]) ).

fof(f_1030_1,plain,
    hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,pls)) = one_one(nat),
    inference(fof_nnf,[status(thm)],[fact_959_nat__numeral__1__eq__1]) ).

fof(f_1030_2,plain,
    hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,pls)) = one_one(nat),
    inference(definitional_conversion,[status(esa)],[f_1030_1]) ).

cnf(f_1030_3,plain,
    hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,pls)) = one_one(nat),
    inference(clausify,[status(thm)],[f_1030_2]) ).

fof(f_1031_1,plain,
    one_one(int) = hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,pls)),
    inference(fof_nnf,[status(thm)],[fact_960_one__is__num__one]) ).

fof(f_1031_2,plain,
    one_one(int) = hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,pls)),
    inference(definitional_conversion,[status(esa)],[f_1031_1]) ).

cnf(f_1031_3,plain,
    one_one(int) = hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,pls)),
    inference(clausify,[status(thm)],[f_1031_2]) ).

fof(f_1032_1,plain,
    ! [X_a] :
      ( hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,pls)) = one_one(X_a)
      | ~ number_ring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_961_numeral__1__eq__1]) ).

fof(f_1032_2,plain,
    ! [U_3939] :
      ( hAPP(int,U_3939,number_number_of(U_3939),hAPP(int,int,bit1,pls)) = one_one(U_3939)
      | ~ number_ring(U_3939) ),
    inference(variable_rename,[status(thm)],[f_1032_1]) ).

fof(f_1032_3,plain,
    ! [U_3939] :
      ( hAPP(int,U_3939,number_number_of(U_3939),hAPP(int,int,bit1,pls)) = one_one(U_3939)
      | ~ number_ring(U_3939) ),
    inference(definitional_conversion,[status(esa)],[f_1032_2]) ).

cnf(f_1032_4,plain,
    ( hAPP(int,U_3939,number_number_of(U_3939),hAPP(int,int,bit1,pls)) = one_one(U_3939)
    | ~ number_ring(U_3939) ),
    inference(clausify,[status(thm)],[f_1032_3]) ).

fof(f_1033_1,plain,
    ! [X_a] :
      ( hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,pls)) = one_one(X_a)
      | ~ number_semiring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_962_semiring__numeral__1__eq__1]) ).

fof(f_1033_2,plain,
    ! [U_3940] :
      ( hAPP(int,U_3940,number_number_of(U_3940),hAPP(int,int,bit1,pls)) = one_one(U_3940)
      | ~ number_semiring(U_3940) ),
    inference(variable_rename,[status(thm)],[f_1033_1]) ).

fof(f_1033_3,plain,
    ! [U_3940] :
      ( hAPP(int,U_3940,number_number_of(U_3940),hAPP(int,int,bit1,pls)) = one_one(U_3940)
      | ~ number_semiring(U_3940) ),
    inference(definitional_conversion,[status(esa)],[f_1033_2]) ).

cnf(f_1033_4,plain,
    ( hAPP(int,U_3940,number_number_of(U_3940),hAPP(int,int,bit1,pls)) = one_one(U_3940)
    | ~ number_semiring(U_3940) ),
    inference(clausify,[status(thm)],[f_1033_3]) ).

fof(f_1034_1,plain,
    ! [X_a] :
      ( ! [A_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,pls))) = ti(X_a,A_1)
      | ~ number_ring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_963_mult__numeral__1__right]) ).

fof(f_1034_2,plain,
    ! [U_3942] :
      ( ! [U_3941] : hAPP(U_3942,U_3942,hAPP(U_3942,fun(U_3942,U_3942),times_times(U_3942),U_3941),hAPP(int,U_3942,number_number_of(U_3942),hAPP(int,int,bit1,pls))) = ti(U_3942,U_3941)
      | ~ number_ring(U_3942) ),
    inference(variable_rename,[status(thm)],[f_1034_1]) ).

fof(f_1034_3,plain,
    ! [U_3942,U_3941] :
      ( hAPP(U_3942,U_3942,hAPP(U_3942,fun(U_3942,U_3942),times_times(U_3942),U_3941),hAPP(int,U_3942,number_number_of(U_3942),hAPP(int,int,bit1,pls))) = ti(U_3942,U_3941)
      | ~ number_ring(U_3942) ),
    inference(definitional_conversion,[status(esa)],[f_1034_2]) ).

cnf(f_1034_4,plain,
    ( hAPP(U_3942,U_3942,hAPP(U_3942,fun(U_3942,U_3942),times_times(U_3942),U_3941),hAPP(int,U_3942,number_number_of(U_3942),hAPP(int,int,bit1,pls))) = ti(U_3942,U_3941)
    | ~ number_ring(U_3942) ),
    inference(clausify,[status(thm)],[f_1034_3]) ).

fof(f_1035_1,plain,
    ! [X_a] :
      ( ! [A_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,pls))),A_1) = ti(X_a,A_1)
      | ~ number_ring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_964_mult__numeral__1]) ).

fof(f_1035_2,plain,
    ! [U_3944] :
      ( ! [U_3943] : hAPP(U_3944,U_3944,hAPP(U_3944,fun(U_3944,U_3944),times_times(U_3944),hAPP(int,U_3944,number_number_of(U_3944),hAPP(int,int,bit1,pls))),U_3943) = ti(U_3944,U_3943)
      | ~ number_ring(U_3944) ),
    inference(variable_rename,[status(thm)],[f_1035_1]) ).

fof(f_1035_3,plain,
    ! [U_3944,U_3943] :
      ( hAPP(U_3944,U_3944,hAPP(U_3944,fun(U_3944,U_3944),times_times(U_3944),hAPP(int,U_3944,number_number_of(U_3944),hAPP(int,int,bit1,pls))),U_3943) = ti(U_3944,U_3943)
      | ~ number_ring(U_3944) ),
    inference(definitional_conversion,[status(esa)],[f_1035_2]) ).

cnf(f_1035_4,plain,
    ( hAPP(U_3944,U_3944,hAPP(U_3944,fun(U_3944,U_3944),times_times(U_3944),hAPP(int,U_3944,number_number_of(U_3944),hAPP(int,int,bit1,pls))),U_3943) = ti(U_3944,U_3943)
    | ~ number_ring(U_3944) ),
    inference(clausify,[status(thm)],[f_1035_3]) ).

fof(f_1036_1,plain,
    ! [X_a] :
      ( ! [V] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),one_one(X_a)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),hAPP(int,int,bit1,pls)))
      | ~ number_ring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_965_add__special_I3_J]) ).

fof(f_1036_2,plain,
    ! [U_3946] :
      ( ! [U_3945] : hAPP(U_3946,U_3946,hAPP(U_3946,fun(U_3946,U_3946),plus_plus(U_3946),hAPP(int,U_3946,number_number_of(U_3946),U_3945)),one_one(U_3946)) = hAPP(int,U_3946,number_number_of(U_3946),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3945),hAPP(int,int,bit1,pls)))
      | ~ number_ring(U_3946) ),
    inference(variable_rename,[status(thm)],[f_1036_1]) ).

fof(f_1036_3,plain,
    ! [U_3946,U_3945] :
      ( hAPP(U_3946,U_3946,hAPP(U_3946,fun(U_3946,U_3946),plus_plus(U_3946),hAPP(int,U_3946,number_number_of(U_3946),U_3945)),one_one(U_3946)) = hAPP(int,U_3946,number_number_of(U_3946),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3945),hAPP(int,int,bit1,pls)))
      | ~ number_ring(U_3946) ),
    inference(definitional_conversion,[status(esa)],[f_1036_2]) ).

cnf(f_1036_4,plain,
    ( hAPP(U_3946,U_3946,hAPP(U_3946,fun(U_3946,U_3946),plus_plus(U_3946),hAPP(int,U_3946,number_number_of(U_3946),U_3945)),one_one(U_3946)) = hAPP(int,U_3946,number_number_of(U_3946),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3945),hAPP(int,int,bit1,pls)))
    | ~ number_ring(U_3946) ),
    inference(clausify,[status(thm)],[f_1036_3]) ).

fof(f_1037_1,plain,
    ! [X_a] :
      ( ! [W] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),hAPP(int,X_a,number_number_of(X_a),W)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit1,pls)),W))
      | ~ number_ring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_966_add__special_I2_J]) ).

fof(f_1037_2,plain,
    ! [U_3948] :
      ( ! [U_3947] : hAPP(U_3948,U_3948,hAPP(U_3948,fun(U_3948,U_3948),plus_plus(U_3948),one_one(U_3948)),hAPP(int,U_3948,number_number_of(U_3948),U_3947)) = hAPP(int,U_3948,number_number_of(U_3948),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit1,pls)),U_3947))
      | ~ number_ring(U_3948) ),
    inference(variable_rename,[status(thm)],[f_1037_1]) ).

fof(f_1037_3,plain,
    ! [U_3948,U_3947] :
      ( hAPP(U_3948,U_3948,hAPP(U_3948,fun(U_3948,U_3948),plus_plus(U_3948),one_one(U_3948)),hAPP(int,U_3948,number_number_of(U_3948),U_3947)) = hAPP(int,U_3948,number_number_of(U_3948),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit1,pls)),U_3947))
      | ~ number_ring(U_3948) ),
    inference(definitional_conversion,[status(esa)],[f_1037_2]) ).

cnf(f_1037_4,plain,
    ( hAPP(U_3948,U_3948,hAPP(U_3948,fun(U_3948,U_3948),plus_plus(U_3948),one_one(U_3948)),hAPP(int,U_3948,number_number_of(U_3948),U_3947)) = hAPP(int,U_3948,number_number_of(U_3948),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit1,pls)),U_3947))
    | ~ number_ring(U_3948) ),
    inference(clausify,[status(thm)],[f_1037_3]) ).

fof(f_1038_1,plain,
    zero_zero(int) = hAPP(int,int,number_number_of(int),pls),
    inference(fof_nnf,[status(thm)],[fact_967_zero__is__num__zero]) ).

fof(f_1038_2,plain,
    zero_zero(int) = hAPP(int,int,number_number_of(int),pls),
    inference(definitional_conversion,[status(esa)],[f_1038_1]) ).

cnf(f_1038_3,plain,
    zero_zero(int) = hAPP(int,int,number_number_of(int),pls),
    inference(clausify,[status(thm)],[f_1038_2]) ).

fof(f_1039_1,plain,
    ! [K_1] : hAPP(int,int,bit1,K_1) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),K_1)),K_1),
    inference(fof_nnf,[status(thm)],[fact_968_Bit1__def]) ).

fof(f_1039_2,plain,
    ! [U_3949] : hAPP(int,int,bit1,U_3949) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),U_3949)),U_3949),
    inference(variable_rename,[status(thm)],[f_1039_1]) ).

fof(f_1039_3,plain,
    ! [U_3949] : hAPP(int,int,bit1,U_3949) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),U_3949)),U_3949),
    inference(definitional_conversion,[status(esa)],[f_1039_2]) ).

cnf(f_1039_4,plain,
    hAPP(int,int,bit1,U_3949) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),U_3949)),U_3949),
    inference(clausify,[status(thm)],[f_1039_3]) ).

fof(f_1040_1,plain,
    ! [X_a] :
      ( hAPP(int,X_a,number_number_of(X_a),pls) = zero_zero(X_a)
      | ~ number_semiring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_969_semiring__numeral__0__eq__0]) ).

fof(f_1040_2,plain,
    ! [U_3950] :
      ( hAPP(int,U_3950,number_number_of(U_3950),pls) = zero_zero(U_3950)
      | ~ number_semiring(U_3950) ),
    inference(variable_rename,[status(thm)],[f_1040_1]) ).

fof(f_1040_3,plain,
    ! [U_3950] :
      ( hAPP(int,U_3950,number_number_of(U_3950),pls) = zero_zero(U_3950)
      | ~ number_semiring(U_3950) ),
    inference(definitional_conversion,[status(esa)],[f_1040_2]) ).

cnf(f_1040_4,plain,
    ( hAPP(int,U_3950,number_number_of(U_3950),pls) = zero_zero(U_3950)
    | ~ number_semiring(U_3950) ),
    inference(clausify,[status(thm)],[f_1040_3]) ).

fof(f_1041_1,plain,
    ! [X_a] :
      ( hAPP(int,X_a,number_number_of(X_a),pls) = zero_zero(X_a)
      | ~ number_ring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_970_number__of__Pls]) ).

fof(f_1041_2,plain,
    ! [U_3951] :
      ( hAPP(int,U_3951,number_number_of(U_3951),pls) = zero_zero(U_3951)
      | ~ number_ring(U_3951) ),
    inference(variable_rename,[status(thm)],[f_1041_1]) ).

fof(f_1041_3,plain,
    ! [U_3951] :
      ( hAPP(int,U_3951,number_number_of(U_3951),pls) = zero_zero(U_3951)
      | ~ number_ring(U_3951) ),
    inference(definitional_conversion,[status(esa)],[f_1041_2]) ).

cnf(f_1041_4,plain,
    ( hAPP(int,U_3951,number_number_of(U_3951),pls) = zero_zero(U_3951)
    | ~ number_ring(U_3951) ),
    inference(clausify,[status(thm)],[f_1041_3]) ).

fof(f_1042_1,plain,
    ! [X_a] :
      ( zero_zero(X_a) = hAPP(int,X_a,number_number_of(X_a),pls)
      | ~ number_ring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_971_semiring__norm_I112_J]) ).

fof(f_1042_2,plain,
    ! [U_3952] :
      ( zero_zero(U_3952) = hAPP(int,U_3952,number_number_of(U_3952),pls)
      | ~ number_ring(U_3952) ),
    inference(variable_rename,[status(thm)],[f_1042_1]) ).

fof(f_1042_3,plain,
    ! [U_3952] :
      ( zero_zero(U_3952) = hAPP(int,U_3952,number_number_of(U_3952),pls)
      | ~ number_ring(U_3952) ),
    inference(definitional_conversion,[status(esa)],[f_1042_2]) ).

cnf(f_1042_4,plain,
    ( zero_zero(U_3952) = hAPP(int,U_3952,number_number_of(U_3952),pls)
    | ~ number_ring(U_3952) ),
    inference(clausify,[status(thm)],[f_1042_3]) ).

fof(f_1043_1,plain,
    ! [X_a] :
      ( ! [A_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),pls)),A_1) = ti(X_a,A_1)
      | ~ number_ring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_972_add__numeral__0]) ).

fof(f_1043_2,plain,
    ! [U_3954] :
      ( ! [U_3953] : hAPP(U_3954,U_3954,hAPP(U_3954,fun(U_3954,U_3954),plus_plus(U_3954),hAPP(int,U_3954,number_number_of(U_3954),pls)),U_3953) = ti(U_3954,U_3953)
      | ~ number_ring(U_3954) ),
    inference(variable_rename,[status(thm)],[f_1043_1]) ).

fof(f_1043_3,plain,
    ! [U_3953,U_3954] :
      ( hAPP(U_3954,U_3954,hAPP(U_3954,fun(U_3954,U_3954),plus_plus(U_3954),hAPP(int,U_3954,number_number_of(U_3954),pls)),U_3953) = ti(U_3954,U_3953)
      | ~ number_ring(U_3954) ),
    inference(definitional_conversion,[status(esa)],[f_1043_2]) ).

cnf(f_1043_4,plain,
    ( hAPP(U_3954,U_3954,hAPP(U_3954,fun(U_3954,U_3954),plus_plus(U_3954),hAPP(int,U_3954,number_number_of(U_3954),pls)),U_3953) = ti(U_3954,U_3953)
    | ~ number_ring(U_3954) ),
    inference(clausify,[status(thm)],[f_1043_3]) ).

fof(f_1044_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),hAPP(int,X_a,number_number_of(X_a),pls)) = ti(X_a,A_1)
      | ~ number_ring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_973_add__numeral__0__right]) ).

fof(f_1044_2,plain,
    ! [U_3956] :
      ( ! [U_3955] : hAPP(U_3956,U_3956,hAPP(U_3956,fun(U_3956,U_3956),plus_plus(U_3956),U_3955),hAPP(int,U_3956,number_number_of(U_3956),pls)) = ti(U_3956,U_3955)
      | ~ number_ring(U_3956) ),
    inference(variable_rename,[status(thm)],[f_1044_1]) ).

fof(f_1044_3,plain,
    ! [U_3955,U_3956] :
      ( hAPP(U_3956,U_3956,hAPP(U_3956,fun(U_3956,U_3956),plus_plus(U_3956),U_3955),hAPP(int,U_3956,number_number_of(U_3956),pls)) = ti(U_3956,U_3955)
      | ~ number_ring(U_3956) ),
    inference(definitional_conversion,[status(esa)],[f_1044_2]) ).

cnf(f_1044_4,plain,
    ( hAPP(U_3956,U_3956,hAPP(U_3956,fun(U_3956,U_3956),plus_plus(U_3956),U_3955),hAPP(int,U_3956,number_number_of(U_3956),pls)) = ti(U_3956,U_3955)
    | ~ number_ring(U_3956) ),
    inference(clausify,[status(thm)],[f_1044_3]) ).

fof(f_1045_1,plain,
    hAPP(int,nat,number_number_of(nat),pls) = zero_zero(nat),
    inference(fof_nnf,[status(thm)],[fact_974_nat__number__of__Pls]) ).

fof(f_1045_2,plain,
    hAPP(int,nat,number_number_of(nat),pls) = zero_zero(nat),
    inference(definitional_conversion,[status(esa)],[f_1045_1]) ).

cnf(f_1045_3,plain,
    hAPP(int,nat,number_number_of(nat),pls) = zero_zero(nat),
    inference(clausify,[status(thm)],[f_1045_2]) ).

fof(f_1046_1,plain,
    zero_zero(nat) = hAPP(int,nat,number_number_of(nat),pls),
    inference(fof_nnf,[status(thm)],[fact_975_semiring__norm_I113_J]) ).

fof(f_1046_2,plain,
    zero_zero(nat) = hAPP(int,nat,number_number_of(nat),pls),
    inference(definitional_conversion,[status(esa)],[f_1046_1]) ).

cnf(f_1046_3,plain,
    zero_zero(nat) = hAPP(int,nat,number_number_of(nat),pls),
    inference(clausify,[status(thm)],[f_1046_2]) ).

fof(f_1047_1,plain,
    pls = zero_zero(int),
    inference(fof_nnf,[status(thm)],[fact_976_Pls__def]) ).

fof(f_1047_2,plain,
    pls = zero_zero(int),
    inference(definitional_conversion,[status(esa)],[f_1047_1]) ).

cnf(f_1047_3,plain,
    pls = zero_zero(int),
    inference(clausify,[status(thm)],[f_1047_2]) ).

fof(f_1048_1,plain,
    ! [K,L] :
      ( ( hAPP(int,int,bit1,K) = hAPP(int,int,bit1,L)
        | K != L )
      & ( K = L
        | hAPP(int,int,bit1,K) != hAPP(int,int,bit1,L) ) ),
    inference(fof_nnf,[status(thm)],[fact_977_rel__simps_I51_J]) ).

fof(f_1048_2,plain,
    ! [U_3958,U_3957] :
      ( ( hAPP(int,int,bit1,U_3958) = hAPP(int,int,bit1,U_3957)
        | U_3958 != U_3957 )
      & ( U_3958 = U_3957
        | hAPP(int,int,bit1,U_3958) != hAPP(int,int,bit1,U_3957) ) ),
    inference(variable_rename,[status(thm)],[f_1048_1]) ).

fof(f_1048_3,plain,
    ( ! [U_3962,U_3960] :
        ( hAPP(int,int,bit1,U_3962) = hAPP(int,int,bit1,U_3960)
        | U_3962 != U_3960 )
    & ! [U_3961,U_3959] :
        ( U_3961 = U_3959
        | hAPP(int,int,bit1,U_3961) != hAPP(int,int,bit1,U_3959) ) ),
    inference(miniscope,[status(thm)],[f_1048_2]) ).

fof(f_1048_4,plain,
    ( ! [U_3960,U_3962] :
        ( hAPP(int,int,bit1,U_3962) = hAPP(int,int,bit1,U_3960)
        | U_3962 != U_3960 )
    & ! [U_3959,U_3961] :
        ( U_3961 = U_3959
        | hAPP(int,int,bit1,U_3961) != hAPP(int,int,bit1,U_3959) ) ),
    inference(definitional_conversion,[status(esa)],[f_1048_3]) ).

cnf(f_1048_5,plain,
    ( U_3961 = U_3959
    | hAPP(int,int,bit1,U_3961) != hAPP(int,int,bit1,U_3959) ),
    inference(clausify,[status(thm)],[f_1048_4]) ).

cnf(f_1048_6,plain,
    ( hAPP(int,int,bit1,U_3962) = hAPP(int,int,bit1,U_3960)
    | U_3962 != U_3960 ),
    inference(clausify,[status(thm)],[f_1048_4]) ).

fof(f_1049_1,plain,
    ! [K_1] : hAPP(int,int,bit1,K_1) != pls,
    inference(fof_nnf,[status(thm)],[fact_978_rel__simps_I46_J]) ).

fof(f_1049_2,plain,
    ! [U_3963] : hAPP(int,int,bit1,U_3963) != pls,
    inference(variable_rename,[status(thm)],[f_1049_1]) ).

fof(f_1049_3,plain,
    ! [U_3963] : hAPP(int,int,bit1,U_3963) != pls,
    inference(definitional_conversion,[status(esa)],[f_1049_2]) ).

cnf(f_1049_4,plain,
    hAPP(int,int,bit1,U_3963) != pls,
    inference(clausify,[status(thm)],[f_1049_3]) ).

fof(f_1050_1,plain,
    ! [L_1] : pls != hAPP(int,int,bit1,L_1),
    inference(fof_nnf,[status(thm)],[fact_979_rel__simps_I39_J]) ).

fof(f_1050_2,plain,
    ! [U_3964] : pls != hAPP(int,int,bit1,U_3964),
    inference(variable_rename,[status(thm)],[f_1050_1]) ).

fof(f_1050_3,plain,
    ! [U_3964] : pls != hAPP(int,int,bit1,U_3964),
    inference(definitional_conversion,[status(esa)],[f_1050_2]) ).

cnf(f_1050_4,plain,
    pls != hAPP(int,int,bit1,U_3964),
    inference(clausify,[status(thm)],[f_1050_3]) ).

fof(f_1051_1,plain,
    ! [K_1] : hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K_1),pls) = K_1,
    inference(fof_nnf,[status(thm)],[fact_980_diff__bin__simps_I1_J]) ).

fof(f_1051_2,plain,
    ! [U_3965] : hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3965),pls) = U_3965,
    inference(variable_rename,[status(thm)],[f_1051_1]) ).

fof(f_1051_3,plain,
    ! [U_3965] : hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3965),pls) = U_3965,
    inference(definitional_conversion,[status(esa)],[f_1051_2]) ).

cnf(f_1051_4,plain,
    hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_3965),pls) = U_3965,
    inference(clausify,[status(thm)],[f_1051_3]) ).

fof(f_1052_1,plain,
    ! [K_1] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),pls),K_1) = K_1,
    inference(fof_nnf,[status(thm)],[fact_981_add__Pls]) ).

fof(f_1052_2,plain,
    ! [U_3966] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),pls),U_3966) = U_3966,
    inference(variable_rename,[status(thm)],[f_1052_1]) ).

fof(f_1052_3,plain,
    ! [U_3966] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),pls),U_3966) = U_3966,
    inference(definitional_conversion,[status(esa)],[f_1052_2]) ).

cnf(f_1052_4,plain,
    hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),pls),U_3966) = U_3966,
    inference(clausify,[status(thm)],[f_1052_3]) ).

fof(f_1053_1,plain,
    ! [K_1] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_1),pls) = K_1,
    inference(fof_nnf,[status(thm)],[fact_982_add__Pls__right]) ).

fof(f_1053_2,plain,
    ! [U_3967] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3967),pls) = U_3967,
    inference(variable_rename,[status(thm)],[f_1053_1]) ).

fof(f_1053_3,plain,
    ! [U_3967] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3967),pls) = U_3967,
    inference(definitional_conversion,[status(esa)],[f_1053_2]) ).

cnf(f_1053_4,plain,
    hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_3967),pls) = U_3967,
    inference(clausify,[status(thm)],[f_1053_3]) ).

fof(f_1054_1,plain,
    ! [W] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),W) = pls,
    inference(fof_nnf,[status(thm)],[fact_983_mult__Pls]) ).

fof(f_1054_2,plain,
    ! [U_3968] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),U_3968) = pls,
    inference(variable_rename,[status(thm)],[f_1054_1]) ).

fof(f_1054_3,plain,
    ! [U_3968] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),U_3968) = pls,
    inference(definitional_conversion,[status(esa)],[f_1054_2]) ).

cnf(f_1054_4,plain,
    hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),U_3968) = pls,
    inference(clausify,[status(thm)],[f_1054_3]) ).

fof(f_1055_1,plain,
    hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))))),
    inference(fof_nnf,[status(thm)],[fact_984_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J]) ).

fof(f_1055_2,plain,
    hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))))),
    inference(definitional_conversion,[status(esa)],[f_1055_1]) ).

cnf(f_1055_3,plain,
    hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))))),
    inference(clausify,[status(thm)],[f_1055_2]) ).

fof(f_1056_1,plain,
    hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),pls)),
    inference(fof_nnf,[status(thm)],[fact_985_rel__simps_I19_J]) ).

fof(f_1056_2,plain,
    hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),pls)),
    inference(definitional_conversion,[status(esa)],[f_1056_1]) ).

cnf(f_1056_3,plain,
    hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),pls)),
    inference(clausify,[status(thm)],[f_1056_2]) ).

fof(f_1057_1,plain,
    ! [K] :
      ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),hAPP(int,int,bit1,K)))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),K)) )
      & ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),K))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),hAPP(int,int,bit1,K))) ) ),
    inference(fof_nnf,[status(thm)],[fact_986_rel__simps_I22_J]) ).

fof(f_1057_2,plain,
    ! [U_3969] :
      ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),hAPP(int,int,bit1,U_3969)))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),U_3969)) )
      & ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),U_3969))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),hAPP(int,int,bit1,U_3969))) ) ),
    inference(variable_rename,[status(thm)],[f_1057_1]) ).

fof(f_1057_3,plain,
    ( ! [U_3971] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),hAPP(int,int,bit1,U_3971)))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),U_3971)) )
    & ! [U_3970] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),U_3970))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),hAPP(int,int,bit1,U_3970))) ) ),
    inference(miniscope,[status(thm)],[f_1057_2]) ).

fof(f_1057_4,plain,
    ( ! [U_3971] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),hAPP(int,int,bit1,U_3971)))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),U_3971)) )
    & ! [U_3970] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),U_3970))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),hAPP(int,int,bit1,U_3970))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1057_3]) ).

cnf(f_1057_5,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),U_3970))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),hAPP(int,int,bit1,U_3970))) ),
    inference(clausify,[status(thm)],[f_1057_4]) ).

cnf(f_1057_6,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),hAPP(int,int,bit1,U_3971)))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),U_3971)) ),
    inference(clausify,[status(thm)],[f_1057_4]) ).

fof(f_1058_1,plain,
    ! [K,L] :
      ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,K)),hAPP(int,int,bit1,L)))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),L)) )
      & ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),L))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,K)),hAPP(int,int,bit1,L))) ) ),
    inference(fof_nnf,[status(thm)],[fact_987_rel__simps_I34_J]) ).

fof(f_1058_2,plain,
    ! [U_3973,U_3972] :
      ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,U_3973)),hAPP(int,int,bit1,U_3972)))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3973),U_3972)) )
      & ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3973),U_3972))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,U_3973)),hAPP(int,int,bit1,U_3972))) ) ),
    inference(variable_rename,[status(thm)],[f_1058_1]) ).

fof(f_1058_3,plain,
    ( ! [U_3977,U_3975] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,U_3977)),hAPP(int,int,bit1,U_3975)))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3977),U_3975)) )
    & ! [U_3976,U_3974] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3976),U_3974))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,U_3976)),hAPP(int,int,bit1,U_3974))) ) ),
    inference(miniscope,[status(thm)],[f_1058_2]) ).

fof(f_1058_4,plain,
    ( ! [U_3977,U_3975] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,U_3977)),hAPP(int,int,bit1,U_3975)))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3977),U_3975)) )
    & ! [U_3976,U_3974] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3976),U_3974))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,U_3976)),hAPP(int,int,bit1,U_3974))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1058_3]) ).

cnf(f_1058_5,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3976),U_3974))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,U_3976)),hAPP(int,int,bit1,U_3974))) ),
    inference(clausify,[status(thm)],[f_1058_4]) ).

cnf(f_1058_6,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,U_3977)),hAPP(int,int,bit1,U_3975)))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3977),U_3975)) ),
    inference(clausify,[status(thm)],[f_1058_4]) ).

fof(f_1059_1,plain,
    ! [K1,K2] :
      ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,K1)),hAPP(int,int,bit1,K2)))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K1),K2)) )
      & ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K1),K2))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,K1)),hAPP(int,int,bit1,K2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_988_less__eq__int__code_I16_J]) ).

fof(f_1059_2,plain,
    ! [U_3979,U_3978] :
      ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,U_3979)),hAPP(int,int,bit1,U_3978)))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3979),U_3978)) )
      & ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3979),U_3978))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,U_3979)),hAPP(int,int,bit1,U_3978))) ) ),
    inference(variable_rename,[status(thm)],[f_1059_1]) ).

fof(f_1059_3,plain,
    ( ! [U_3983,U_3981] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,U_3983)),hAPP(int,int,bit1,U_3981)))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3983),U_3981)) )
    & ! [U_3982,U_3980] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3982),U_3980))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,U_3982)),hAPP(int,int,bit1,U_3980))) ) ),
    inference(miniscope,[status(thm)],[f_1059_2]) ).

fof(f_1059_4,plain,
    ( ! [U_3981,U_3983] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,U_3983)),hAPP(int,int,bit1,U_3981)))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3983),U_3981)) )
    & ! [U_3980,U_3982] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3982),U_3980))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,U_3982)),hAPP(int,int,bit1,U_3980))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1059_3]) ).

cnf(f_1059_5,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3982),U_3980))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,U_3982)),hAPP(int,int,bit1,U_3980))) ),
    inference(clausify,[status(thm)],[f_1059_4]) ).

cnf(f_1059_6,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,U_3983)),hAPP(int,int,bit1,U_3981)))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),U_3983),U_3981)) ),
    inference(clausify,[status(thm)],[f_1059_4]) ).

fof(f_1060_1,plain,
    ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)),
    inference(fof_nnf,[status(thm)],[fact_989_rel__simps_I2_J]) ).

fof(f_1060_2,plain,
    ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)),
    inference(definitional_conversion,[status(esa)],[f_1060_1]) ).

cnf(f_1060_3,plain,
    ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)),
    inference(clausify,[status(thm)],[f_1060_2]) ).

fof(f_1061_1,plain,
    ! [K] :
      ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K)),pls))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),pls)) )
      & ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),pls))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K)),pls)) ) ),
    inference(fof_nnf,[status(thm)],[fact_990_rel__simps_I12_J]) ).

fof(f_1061_2,plain,
    ! [U_3984] :
      ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,U_3984)),pls))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3984),pls)) )
      & ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3984),pls))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,U_3984)),pls)) ) ),
    inference(variable_rename,[status(thm)],[f_1061_1]) ).

fof(f_1061_3,plain,
    ( ! [U_3986] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,U_3986)),pls))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3986),pls)) )
    & ! [U_3985] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3985),pls))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,U_3985)),pls)) ) ),
    inference(miniscope,[status(thm)],[f_1061_2]) ).

fof(f_1061_4,plain,
    ( ! [U_3986] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,U_3986)),pls))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3986),pls)) )
    & ! [U_3985] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3985),pls))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,U_3985)),pls)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1061_3]) ).

cnf(f_1061_5,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3985),pls))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,U_3985)),pls)) ),
    inference(clausify,[status(thm)],[f_1061_4]) ).

cnf(f_1061_6,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,U_3986)),pls))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3986),pls)) ),
    inference(clausify,[status(thm)],[f_1061_4]) ).

fof(f_1062_1,plain,
    ! [K,L] :
      ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K)),hAPP(int,int,bit1,L)))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L)) )
      & ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K)),hAPP(int,int,bit1,L))) ) ),
    inference(fof_nnf,[status(thm)],[fact_991_rel__simps_I17_J]) ).

fof(f_1062_2,plain,
    ! [U_3988,U_3987] :
      ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,U_3988)),hAPP(int,int,bit1,U_3987)))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3988),U_3987)) )
      & ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3988),U_3987))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,U_3988)),hAPP(int,int,bit1,U_3987))) ) ),
    inference(variable_rename,[status(thm)],[f_1062_1]) ).

fof(f_1062_3,plain,
    ( ! [U_3992,U_3990] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,U_3992)),hAPP(int,int,bit1,U_3990)))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3992),U_3990)) )
    & ! [U_3991,U_3989] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3991),U_3989))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,U_3991)),hAPP(int,int,bit1,U_3989))) ) ),
    inference(miniscope,[status(thm)],[f_1062_2]) ).

fof(f_1062_4,plain,
    ( ! [U_3990,U_3992] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,U_3992)),hAPP(int,int,bit1,U_3990)))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3992),U_3990)) )
    & ! [U_3991,U_3989] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3991),U_3989))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,U_3991)),hAPP(int,int,bit1,U_3989))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1062_3]) ).

cnf(f_1062_5,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3991),U_3989))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,U_3991)),hAPP(int,int,bit1,U_3989))) ),
    inference(clausify,[status(thm)],[f_1062_4]) ).

cnf(f_1062_6,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,U_3992)),hAPP(int,int,bit1,U_3990)))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3992),U_3990)) ),
    inference(clausify,[status(thm)],[f_1062_4]) ).

fof(f_1063_1,plain,
    ! [K1,K2] :
      ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K1)),hAPP(int,int,bit1,K2)))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2)) )
      & ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K1)),hAPP(int,int,bit1,K2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_992_less__int__code_I16_J]) ).

fof(f_1063_2,plain,
    ! [U_3994,U_3993] :
      ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,U_3994)),hAPP(int,int,bit1,U_3993)))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3994),U_3993)) )
      & ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3994),U_3993))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,U_3994)),hAPP(int,int,bit1,U_3993))) ) ),
    inference(variable_rename,[status(thm)],[f_1063_1]) ).

fof(f_1063_3,plain,
    ( ! [U_3998,U_3996] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,U_3998)),hAPP(int,int,bit1,U_3996)))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3998),U_3996)) )
    & ! [U_3997,U_3995] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3997),U_3995))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,U_3997)),hAPP(int,int,bit1,U_3995))) ) ),
    inference(miniscope,[status(thm)],[f_1063_2]) ).

fof(f_1063_4,plain,
    ( ! [U_3996,U_3998] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,U_3998)),hAPP(int,int,bit1,U_3996)))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3998),U_3996)) )
    & ! [U_3995,U_3997] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3997),U_3995))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,U_3997)),hAPP(int,int,bit1,U_3995))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1063_3]) ).

cnf(f_1063_5,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3997),U_3995))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,U_3997)),hAPP(int,int,bit1,U_3995))) ),
    inference(clausify,[status(thm)],[f_1063_4]) ).

cnf(f_1063_6,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,U_3998)),hAPP(int,int,bit1,U_3996)))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3998),U_3996)) ),
    inference(clausify,[status(thm)],[f_1063_4]) ).

fof(f_1064_1,plain,
    ! [K] :
      ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,K)),pls))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),pls)) )
      & ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),pls))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,K)),pls)) ) ),
    inference(fof_nnf,[status(thm)],[fact_993_rel__simps_I29_J]) ).

fof(f_1064_2,plain,
    ! [U_3999] :
      ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,U_3999)),pls))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3999),pls)) )
      & ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_3999),pls))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,U_3999)),pls)) ) ),
    inference(variable_rename,[status(thm)],[f_1064_1]) ).

fof(f_1064_3,plain,
    ( ! [U_4001] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,U_4001)),pls))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_4001),pls)) )
    & ! [U_4000] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_4000),pls))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,U_4000)),pls)) ) ),
    inference(miniscope,[status(thm)],[f_1064_2]) ).

fof(f_1064_4,plain,
    ( ! [U_4001] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,U_4001)),pls))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_4001),pls)) )
    & ! [U_4000] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_4000),pls))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,U_4000)),pls)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1064_3]) ).

cnf(f_1064_5,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_4000),pls))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,U_4000)),pls)) ),
    inference(clausify,[status(thm)],[f_1064_4]) ).

cnf(f_1064_6,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,U_4001)),pls))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),U_4001),pls)) ),
    inference(clausify,[status(thm)],[f_1064_4]) ).

fof(f_1065_1,plain,
    ! [K] :
      ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit1,K)))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),K)) )
      & ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),K))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit1,K))) ) ),
    inference(fof_nnf,[status(thm)],[fact_994_rel__simps_I5_J]) ).

fof(f_1065_2,plain,
    ! [U_4002] :
      ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit1,U_4002)))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),U_4002)) )
      & ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),U_4002))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit1,U_4002))) ) ),
    inference(variable_rename,[status(thm)],[f_1065_1]) ).

fof(f_1065_3,plain,
    ( ! [U_4004] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit1,U_4004)))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),U_4004)) )
    & ! [U_4003] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),U_4003))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit1,U_4003))) ) ),
    inference(miniscope,[status(thm)],[f_1065_2]) ).

fof(f_1065_4,plain,
    ( ! [U_4004] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit1,U_4004)))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),U_4004)) )
    & ! [U_4003] :
        ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),U_4003))
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit1,U_4003))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1065_3]) ).

cnf(f_1065_5,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),U_4003))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit1,U_4003))) ),
    inference(clausify,[status(thm)],[f_1065_4]) ).

cnf(f_1065_6,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit1,U_4004)))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),U_4004)) ),
    inference(clausify,[status(thm)],[f_1065_4]) ).

fof(f_1066_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_1066_2,plain,
    ! [U_4006,U_4005] :
      ( preorder(fun(U_4006,U_4005))
      | ~ preorder(U_4005) ),
    inference(variable_rename,[status(thm)],[f_1066_1]) ).

fof(f_1066_3,plain,
    ! [U_4006,U_4005] :
      ( preorder(fun(U_4006,U_4005))
      | ~ preorder(U_4005) ),
    inference(definitional_conversion,[status(esa)],[f_1066_2]) ).

cnf(f_1066_4,plain,
    ( preorder(fun(U_4006,U_4005))
    | ~ preorder(U_4005) ),
    inference(clausify,[status(thm)],[f_1066_3]) ).

fof(f_1067_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_1067_2,plain,
    ! [U_4008,U_4007] :
      ( finite_finite_1(fun(U_4008,U_4007))
      | ~ finite_finite_1(U_4008)
      | ~ finite_finite_1(U_4007) ),
    inference(variable_rename,[status(thm)],[f_1067_1]) ).

fof(f_1067_3,plain,
    ! [U_4007,U_4008] :
      ( finite_finite_1(fun(U_4008,U_4007))
      | ~ finite_finite_1(U_4008)
      | ~ finite_finite_1(U_4007) ),
    inference(definitional_conversion,[status(esa)],[f_1067_2]) ).

cnf(f_1067_4,plain,
    ( finite_finite_1(fun(U_4008,U_4007))
    | ~ finite_finite_1(U_4008)
    | ~ finite_finite_1(U_4007) ),
    inference(clausify,[status(thm)],[f_1067_3]) ).

fof(f_1068_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_1068_2,plain,
    ! [U_4010,U_4009] :
      ( order(fun(U_4010,U_4009))
      | ~ order(U_4009) ),
    inference(variable_rename,[status(thm)],[f_1068_1]) ).

fof(f_1068_3,plain,
    ! [U_4010,U_4009] :
      ( order(fun(U_4010,U_4009))
      | ~ order(U_4009) ),
    inference(definitional_conversion,[status(esa)],[f_1068_2]) ).

cnf(f_1068_4,plain,
    ( order(fun(U_4010,U_4009))
    | ~ order(U_4009) ),
    inference(clausify,[status(thm)],[f_1068_3]) ).

fof(f_1069_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_1069_2,plain,
    ! [U_4012,U_4011] :
      ( ord(fun(U_4012,U_4011))
      | ~ ord(U_4011) ),
    inference(variable_rename,[status(thm)],[f_1069_1]) ).

fof(f_1069_3,plain,
    ! [U_4011,U_4012] :
      ( ord(fun(U_4012,U_4011))
      | ~ ord(U_4011) ),
    inference(definitional_conversion,[status(esa)],[f_1069_2]) ).

cnf(f_1069_4,plain,
    ( ord(fun(U_4012,U_4011))
    | ~ ord(U_4011) ),
    inference(clausify,[status(thm)],[f_1069_3]) ).

fof(f_1070_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_1070_2,plain,
    ! [U_4014,U_4013] :
      ( bot(fun(U_4014,U_4013))
      | ~ bot(U_4013) ),
    inference(variable_rename,[status(thm)],[f_1070_1]) ).

fof(f_1070_3,plain,
    ! [U_4013,U_4014] :
      ( bot(fun(U_4014,U_4013))
      | ~ bot(U_4013) ),
    inference(definitional_conversion,[status(esa)],[f_1070_2]) ).

cnf(f_1070_4,plain,
    ( bot(fun(U_4014,U_4013))
    | ~ bot(U_4013) ),
    inference(clausify,[status(thm)],[f_1070_3]) ).

fof(f_1071_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_1071_2,plain,
    ! [U_4016,U_4015] :
      ( minus(fun(U_4016,U_4015))
      | ~ minus(U_4015) ),
    inference(variable_rename,[status(thm)],[f_1071_1]) ).

fof(f_1071_3,plain,
    ! [U_4015,U_4016] :
      ( minus(fun(U_4016,U_4015))
      | ~ minus(U_4015) ),
    inference(definitional_conversion,[status(esa)],[f_1071_2]) ).

cnf(f_1071_4,plain,
    ( minus(fun(U_4016,U_4015))
    | ~ minus(U_4015) ),
    inference(clausify,[status(thm)],[f_1071_3]) ).

fof(f_1072_1,plain,
    semiri456707255roduct(int),
    inference(fof_nnf,[status(thm)],[arity_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc]) ).

fof(f_1072_2,plain,
    semiri456707255roduct(int),
    inference(definitional_conversion,[status(esa)],[f_1072_1]) ).

cnf(f_1072_3,plain,
    semiri456707255roduct(int),
    inference(clausify,[status(thm)],[f_1072_2]) ).

fof(f_1073_1,plain,
    ordere223160158up_add(int),
    inference(fof_nnf,[status(thm)],[arity_Int_Oint___Groups_Oordered__cancel__ab__semigroup__add]) ).

fof(f_1073_2,plain,
    ordere223160158up_add(int),
    inference(definitional_conversion,[status(esa)],[f_1073_1]) ).

cnf(f_1073_3,plain,
    ordere223160158up_add(int),
    inference(clausify,[status(thm)],[f_1073_2]) ).

fof(f_1074_1,plain,
    ordere236663937imp_le(int),
    inference(fof_nnf,[status(thm)],[arity_Int_Oint___Groups_Oordered__ab__semigroup__add__imp__le]) ).

fof(f_1074_2,plain,
    ordere236663937imp_le(int),
    inference(definitional_conversion,[status(esa)],[f_1074_1]) ).

cnf(f_1074_3,plain,
    ordere236663937imp_le(int),
    inference(clausify,[status(thm)],[f_1074_2]) ).

fof(f_1075_1,plain,
    linord893533164strict(int),
    inference(fof_nnf,[status(thm)],[arity_Int_Oint___Rings_Olinordered__comm__semiring__strict]) ).

fof(f_1075_2,plain,
    linord893533164strict(int),
    inference(definitional_conversion,[status(esa)],[f_1075_1]) ).

cnf(f_1075_3,plain,
    linord893533164strict(int),
    inference(clausify,[status(thm)],[f_1075_2]) ).

fof(f_1076_1,plain,
    linord626643107strict(int),
    inference(fof_nnf,[status(thm)],[arity_Int_Oint___Rings_Olinordered__semiring__1__strict]) ).

fof(f_1076_2,plain,
    linord626643107strict(int),
    inference(definitional_conversion,[status(esa)],[f_1076_1]) ).

cnf(f_1076_3,plain,
    linord626643107strict(int),
    inference(clausify,[status(thm)],[f_1076_2]) ).

fof(f_1077_1,plain,
    linord20386208strict(int),
    inference(fof_nnf,[status(thm)],[arity_Int_Oint___Rings_Olinordered__semiring__strict]) ).

fof(f_1077_2,plain,
    linord20386208strict(int),
    inference(definitional_conversion,[status(esa)],[f_1077_1]) ).

cnf(f_1077_3,plain,
    linord20386208strict(int),
    inference(clausify,[status(thm)],[f_1077_2]) ).

fof(f_1078_1,plain,
    ordere779506340up_add(int),
    inference(fof_nnf,[status(thm)],[arity_Int_Oint___Groups_Oordered__ab__semigroup__add]) ).

fof(f_1078_2,plain,
    ordere779506340up_add(int),
    inference(definitional_conversion,[status(esa)],[f_1078_1]) ).

cnf(f_1078_3,plain,
    ordere779506340up_add(int),
    inference(clausify,[status(thm)],[f_1078_2]) ).

fof(f_1079_1,plain,
    ordere142940540dd_abs(int),
    inference(fof_nnf,[status(thm)],[arity_Int_Oint___Groups_Oordered__ab__group__add__abs]) ).

fof(f_1079_2,plain,
    ordere142940540dd_abs(int),
    inference(definitional_conversion,[status(esa)],[f_1079_1]) ).

cnf(f_1079_3,plain,
    ordere142940540dd_abs(int),
    inference(clausify,[status(thm)],[f_1079_2]) ).

fof(f_1080_1,plain,
    ordere216010020id_add(int),
    inference(fof_nnf,[status(thm)],[arity_Int_Oint___Groups_Oordered__comm__monoid__add]) ).

fof(f_1080_2,plain,
    ordere216010020id_add(int),
    inference(definitional_conversion,[status(esa)],[f_1080_1]) ).

cnf(f_1080_3,plain,
    ordere216010020id_add(int),
    inference(clausify,[status(thm)],[f_1080_2]) ).

fof(f_1081_1,plain,
    linord219039673up_add(int),
    inference(fof_nnf,[status(thm)],[arity_Int_Oint___Groups_Olinordered__ab__group__add]) ).

fof(f_1081_2,plain,
    linord219039673up_add(int),
    inference(definitional_conversion,[status(esa)],[f_1081_1]) ).

cnf(f_1081_3,plain,
    linord219039673up_add(int),
    inference(clausify,[status(thm)],[f_1081_2]) ).

fof(f_1082_1,plain,
    cancel146912293up_add(int),
    inference(fof_nnf,[status(thm)],[arity_Int_Oint___Groups_Ocancel__ab__semigroup__add]) ).

fof(f_1082_2,plain,
    cancel146912293up_add(int),
    inference(definitional_conversion,[status(esa)],[f_1082_1]) ).

cnf(f_1082_3,plain,
    cancel146912293up_add(int),
    inference(clausify,[status(thm)],[f_1082_2]) ).

fof(f_1083_1,plain,
    ordere453448008miring(int),
    inference(fof_nnf,[status(thm)],[arity_Int_Oint___Rings_Oordered__cancel__semiring]) ).

fof(f_1083_2,plain,
    ordere453448008miring(int),
    inference(definitional_conversion,[status(esa)],[f_1083_1]) ).

cnf(f_1083_3,plain,
    ordere453448008miring(int),
    inference(clausify,[status(thm)],[f_1083_2]) ).

fof(f_1084_1,plain,
    linord581940658strict(int),
    inference(fof_nnf,[status(thm)],[arity_Int_Oint___Rings_Olinordered__ring__strict]) ).

fof(f_1084_2,plain,
    linord581940658strict(int),
    inference(definitional_conversion,[status(esa)],[f_1084_1]) ).

cnf(f_1084_3,plain,
    linord581940658strict(int),
    inference(clausify,[status(thm)],[f_1084_2]) ).

fof(f_1085_1,plain,
    ring_n68954251visors(int),
    inference(fof_nnf,[status(thm)],[arity_Int_Oint___Rings_Oring__no__zero__divisors]) ).

fof(f_1085_2,plain,
    ring_n68954251visors(int),
    inference(definitional_conversion,[status(esa)],[f_1085_1]) ).

cnf(f_1085_3,plain,
    ring_n68954251visors(int),
    inference(clausify,[status(thm)],[f_1085_2]) ).

fof(f_1086_1,plain,
    ordere1490568538miring(int),
    inference(fof_nnf,[status(thm)],[arity_Int_Oint___Rings_Oordered__comm__semiring]) ).

fof(f_1086_2,plain,
    ordere1490568538miring(int),
    inference(definitional_conversion,[status(esa)],[f_1086_1]) ).

cnf(f_1086_3,plain,
    ordere1490568538miring(int),
    inference(clausify,[status(thm)],[f_1086_2]) ).

fof(f_1087_1,plain,
    linord1278240602ring_1(int),
    inference(fof_nnf,[status(thm)],[arity_Int_Oint___Rings_Olinordered__semiring__1]) ).

fof(f_1087_2,plain,
    linord1278240602ring_1(int),
    inference(definitional_conversion,[status(esa)],[f_1087_1]) ).

cnf(f_1087_3,plain,
    linord1278240602ring_1(int),
    inference(clausify,[status(thm)],[f_1087_2]) ).

fof(f_1088_1,plain,
    ordered_ab_group_add(int),
    inference(fof_nnf,[status(thm)],[arity_Int_Oint___Groups_Oordered__ab__group__add]) ).

fof(f_1088_2,plain,
    ordered_ab_group_add(int),
    inference(definitional_conversion,[status(esa)],[f_1088_1]) ).

cnf(f_1088_3,plain,
    ordered_ab_group_add(int),
    inference(clausify,[status(thm)],[f_1088_2]) ).

fof(f_1089_1,plain,
    cancel_semigroup_add(int),
    inference(fof_nnf,[status(thm)],[arity_Int_Oint___Groups_Ocancel__semigroup__add]) ).

fof(f_1089_2,plain,
    cancel_semigroup_add(int),
    inference(definitional_conversion,[status(esa)],[f_1089_1]) ).

cnf(f_1089_3,plain,
    cancel_semigroup_add(int),
    inference(clausify,[status(thm)],[f_1089_2]) ).

fof(f_1090_1,plain,
    linordered_semiring(int),
    inference(fof_nnf,[status(thm)],[arity_Int_Oint___Rings_Olinordered__semiring]) ).

fof(f_1090_2,plain,
    linordered_semiring(int),
    inference(definitional_conversion,[status(esa)],[f_1090_1]) ).

cnf(f_1090_3,plain,
    linordered_semiring(int),
    inference(clausify,[status(thm)],[f_1090_2]) ).

fof(f_1091_1,plain,
    linordered_semidom(int),
    inference(fof_nnf,[status(thm)],[arity_Int_Oint___Rings_Olinordered__semidom]) ).

fof(f_1091_2,plain,
    linordered_semidom(int),
    inference(definitional_conversion,[status(esa)],[f_1091_1]) ).

cnf(f_1091_3,plain,
    linordered_semidom(int),
    inference(clausify,[status(thm)],[f_1091_2]) ).

fof(f_1092_1,plain,
    ab_semigroup_mult(int),
    inference(fof_nnf,[status(thm)],[arity_Int_Oint___Groups_Oab__semigroup__mult]) ).

fof(f_1092_2,plain,
    ab_semigroup_mult(int),
    inference(definitional_conversion,[status(esa)],[f_1092_1]) ).

cnf(f_1092_3,plain,
    ab_semigroup_mult(int),
    inference(clausify,[status(thm)],[f_1092_2]) ).

fof(f_1093_1,plain,
    comm_monoid_mult(int),
    inference(fof_nnf,[status(thm)],[arity_Int_Oint___Groups_Ocomm__monoid__mult]) ).

fof(f_1093_2,plain,
    comm_monoid_mult(int),
    inference(definitional_conversion,[status(esa)],[f_1093_1]) ).

cnf(f_1093_3,plain,
    comm_monoid_mult(int),
    inference(clausify,[status(thm)],[f_1093_2]) ).

fof(f_1094_1,plain,
    ab_semigroup_add(int),
    inference(fof_nnf,[status(thm)],[arity_Int_Oint___Groups_Oab__semigroup__add]) ).

fof(f_1094_2,plain,
    ab_semigroup_add(int),
    inference(definitional_conversion,[status(esa)],[f_1094_1]) ).

cnf(f_1094_3,plain,
    ab_semigroup_add(int),
    inference(clausify,[status(thm)],[f_1094_2]) ).

fof(f_1095_1,plain,
    ordered_semiring(int),
    inference(fof_nnf,[status(thm)],[arity_Int_Oint___Rings_Oordered__semiring]) ).

fof(f_1095_2,plain,
    ordered_semiring(int),
    inference(definitional_conversion,[status(esa)],[f_1095_1]) ).

cnf(f_1095_3,plain,
    ordered_semiring(int),
    inference(clausify,[status(thm)],[f_1095_2]) ).

fof(f_1096_1,plain,
    ordered_ring_abs(int),
    inference(fof_nnf,[status(thm)],[arity_Int_Oint___Rings_Oordered__ring__abs]) ).

fof(f_1096_2,plain,
    ordered_ring_abs(int),
    inference(definitional_conversion,[status(esa)],[f_1096_1]) ).

cnf(f_1096_3,plain,
    ordered_ring_abs(int),
    inference(clausify,[status(thm)],[f_1096_2]) ).

fof(f_1097_1,plain,
    no_zero_divisors(int),
    inference(fof_nnf,[status(thm)],[arity_Int_Oint___Rings_Ono__zero__divisors]) ).

fof(f_1097_2,plain,
    no_zero_divisors(int),
    inference(definitional_conversion,[status(esa)],[f_1097_1]) ).

cnf(f_1097_3,plain,
    no_zero_divisors(int),
    inference(clausify,[status(thm)],[f_1097_2]) ).

fof(f_1098_1,plain,
    comm_monoid_add(int),
    inference(fof_nnf,[status(thm)],[arity_Int_Oint___Groups_Ocomm__monoid__add]) ).

fof(f_1098_2,plain,
    comm_monoid_add(int),
    inference(definitional_conversion,[status(esa)],[f_1098_1]) ).

cnf(f_1098_3,plain,
    comm_monoid_add(int),
    inference(clausify,[status(thm)],[f_1098_2]) ).

fof(f_1099_1,plain,
    linordered_ring(int),
    inference(fof_nnf,[status(thm)],[arity_Int_Oint___Rings_Olinordered__ring]) ).

fof(f_1099_2,plain,
    linordered_ring(int),
    inference(definitional_conversion,[status(esa)],[f_1099_1]) ).

cnf(f_1099_3,plain,
    linordered_ring(int),
    inference(clausify,[status(thm)],[f_1099_2]) ).

fof(f_1100_1,plain,
    linordered_idom(int),
    inference(fof_nnf,[status(thm)],[arity_Int_Oint___Rings_Olinordered__idom]) ).

fof(f_1100_2,plain,
    linordered_idom(int),
    inference(definitional_conversion,[status(esa)],[f_1100_1]) ).

cnf(f_1100_3,plain,
    linordered_idom(int),
    inference(clausify,[status(thm)],[f_1100_2]) ).

fof(f_1101_1,plain,
    comm_semiring_1(int),
    inference(fof_nnf,[status(thm)],[arity_Int_Oint___Rings_Ocomm__semiring__1]) ).

fof(f_1101_2,plain,
    comm_semiring_1(int),
    inference(definitional_conversion,[status(esa)],[f_1101_1]) ).

cnf(f_1101_3,plain,
    comm_semiring_1(int),
    inference(clausify,[status(thm)],[f_1101_2]) ).

fof(f_1102_1,plain,
    comm_semiring(int),
    inference(fof_nnf,[status(thm)],[arity_Int_Oint___Rings_Ocomm__semiring]) ).

fof(f_1102_2,plain,
    comm_semiring(int),
    inference(definitional_conversion,[status(esa)],[f_1102_1]) ).

cnf(f_1102_3,plain,
    comm_semiring(int),
    inference(clausify,[status(thm)],[f_1102_2]) ).

fof(f_1103_1,plain,
    semiring_char_0(int),
    inference(fof_nnf,[status(thm)],[arity_Int_Oint___Nat_Osemiring__char__0]) ).

fof(f_1103_2,plain,
    semiring_char_0(int),
    inference(definitional_conversion,[status(esa)],[f_1103_1]) ).

cnf(f_1103_3,plain,
    semiring_char_0(int),
    inference(clausify,[status(thm)],[f_1103_2]) ).

fof(f_1104_1,plain,
    number_semiring(int),
    inference(fof_nnf,[status(thm)],[arity_Int_Oint___Int_Onumber__semiring]) ).

fof(f_1104_2,plain,
    number_semiring(int),
    inference(definitional_conversion,[status(esa)],[f_1104_1]) ).

cnf(f_1104_3,plain,
    number_semiring(int),
    inference(clausify,[status(thm)],[f_1104_2]) ).

fof(f_1105_1,plain,
    ab_group_add(int),
    inference(fof_nnf,[status(thm)],[arity_Int_Oint___Groups_Oab__group__add]) ).

fof(f_1105_2,plain,
    ab_group_add(int),
    inference(definitional_conversion,[status(esa)],[f_1105_1]) ).

cnf(f_1105_3,plain,
    ab_group_add(int),
    inference(clausify,[status(thm)],[f_1105_2]) ).

fof(f_1106_1,plain,
    zero_neq_one(int),
    inference(fof_nnf,[status(thm)],[arity_Int_Oint___Rings_Ozero__neq__one]) ).

fof(f_1106_2,plain,
    zero_neq_one(int),
    inference(definitional_conversion,[status(esa)],[f_1106_1]) ).

cnf(f_1106_3,plain,
    zero_neq_one(int),
    inference(clausify,[status(thm)],[f_1106_2]) ).

fof(f_1107_1,plain,
    ordered_ring(int),
    inference(fof_nnf,[status(thm)],[arity_Int_Oint___Rings_Oordered__ring]) ).

fof(f_1107_2,plain,
    ordered_ring(int),
    inference(definitional_conversion,[status(esa)],[f_1107_1]) ).

cnf(f_1107_3,plain,
    ordered_ring(int),
    inference(clausify,[status(thm)],[f_1107_2]) ).

fof(f_1108_1,plain,
    preorder(int),
    inference(fof_nnf,[status(thm)],[arity_Int_Oint___Orderings_Opreorder]) ).

fof(f_1108_2,plain,
    preorder(int),
    inference(definitional_conversion,[status(esa)],[f_1108_1]) ).

cnf(f_1108_3,plain,
    preorder(int),
    inference(clausify,[status(thm)],[f_1108_2]) ).

fof(f_1109_1,plain,
    linorder(int),
    inference(fof_nnf,[status(thm)],[arity_Int_Oint___Orderings_Olinorder]) ).

fof(f_1109_2,plain,
    linorder(int),
    inference(definitional_conversion,[status(esa)],[f_1109_1]) ).

cnf(f_1109_3,plain,
    linorder(int),
    inference(clausify,[status(thm)],[f_1109_2]) ).

fof(f_1110_1,plain,
    monoid_mult(int),
    inference(fof_nnf,[status(thm)],[arity_Int_Oint___Groups_Omonoid__mult]) ).

fof(f_1110_2,plain,
    monoid_mult(int),
    inference(definitional_conversion,[status(esa)],[f_1110_1]) ).

cnf(f_1110_3,plain,
    monoid_mult(int),
    inference(clausify,[status(thm)],[f_1110_2]) ).

fof(f_1111_1,plain,
    monoid_add(int),
    inference(fof_nnf,[status(thm)],[arity_Int_Oint___Groups_Omonoid__add]) ).

fof(f_1111_2,plain,
    monoid_add(int),
    inference(definitional_conversion,[status(esa)],[f_1111_1]) ).

cnf(f_1111_3,plain,
    monoid_add(int),
    inference(clausify,[status(thm)],[f_1111_2]) ).

fof(f_1112_1,plain,
    semiring_1(int),
    inference(fof_nnf,[status(thm)],[arity_Int_Oint___Rings_Osemiring__1]) ).

fof(f_1112_2,plain,
    semiring_1(int),
    inference(definitional_conversion,[status(esa)],[f_1112_1]) ).

cnf(f_1112_3,plain,
    semiring_1(int),
    inference(clausify,[status(thm)],[f_1112_2]) ).

fof(f_1113_1,plain,
    group_add(int),
    inference(fof_nnf,[status(thm)],[arity_Int_Oint___Groups_Ogroup__add]) ).

fof(f_1113_2,plain,
    group_add(int),
    inference(definitional_conversion,[status(esa)],[f_1113_1]) ).

cnf(f_1113_3,plain,
    group_add(int),
    inference(clausify,[status(thm)],[f_1113_2]) ).

fof(f_1114_1,plain,
    mult_zero(int),
    inference(fof_nnf,[status(thm)],[arity_Int_Oint___Rings_Omult__zero]) ).

fof(f_1114_2,plain,
    mult_zero(int),
    inference(definitional_conversion,[status(esa)],[f_1114_1]) ).

cnf(f_1114_3,plain,
    mult_zero(int),
    inference(clausify,[status(thm)],[f_1114_2]) ).

fof(f_1115_1,plain,
    order(int),
    inference(fof_nnf,[status(thm)],[arity_Int_Oint___Orderings_Oorder]) ).

fof(f_1115_2,plain,
    order(int),
    inference(definitional_conversion,[status(esa)],[f_1115_1]) ).

cnf(f_1115_3,plain,
    order(int),
    inference(clausify,[status(thm)],[f_1115_2]) ).

fof(f_1116_1,plain,
    ring_char_0(int),
    inference(fof_nnf,[status(thm)],[arity_Int_Oint___Int_Oring__char__0]) ).

fof(f_1116_2,plain,
    ring_char_0(int),
    inference(definitional_conversion,[status(esa)],[f_1116_1]) ).

cnf(f_1116_3,plain,
    ring_char_0(int),
    inference(clausify,[status(thm)],[f_1116_2]) ).

fof(f_1117_1,plain,
    number_ring(int),
    inference(fof_nnf,[status(thm)],[arity_Int_Oint___Int_Onumber__ring]) ).

fof(f_1117_2,plain,
    number_ring(int),
    inference(definitional_conversion,[status(esa)],[f_1117_1]) ).

cnf(f_1117_3,plain,
    number_ring(int),
    inference(clausify,[status(thm)],[f_1117_2]) ).

fof(f_1118_1,plain,
    semiring(int),
    inference(fof_nnf,[status(thm)],[arity_Int_Oint___Rings_Osemiring]) ).

fof(f_1118_2,plain,
    semiring(int),
    inference(definitional_conversion,[status(esa)],[f_1118_1]) ).

cnf(f_1118_3,plain,
    semiring(int),
    inference(clausify,[status(thm)],[f_1118_2]) ).

fof(f_1119_1,plain,
    ord(int),
    inference(fof_nnf,[status(thm)],[arity_Int_Oint___Orderings_Oord]) ).

fof(f_1119_2,plain,
    ord(int),
    inference(definitional_conversion,[status(esa)],[f_1119_1]) ).

cnf(f_1119_3,plain,
    ord(int),
    inference(clausify,[status(thm)],[f_1119_2]) ).

fof(f_1120_1,plain,
    ring_1(int),
    inference(fof_nnf,[status(thm)],[arity_Int_Oint___Rings_Oring__1]) ).

fof(f_1120_2,plain,
    ring_1(int),
    inference(definitional_conversion,[status(esa)],[f_1120_1]) ).

cnf(f_1120_3,plain,
    ring_1(int),
    inference(clausify,[status(thm)],[f_1120_2]) ).

fof(f_1121_1,plain,
    minus(int),
    inference(fof_nnf,[status(thm)],[arity_Int_Oint___Groups_Ominus]) ).

fof(f_1121_2,plain,
    minus(int),
    inference(definitional_conversion,[status(esa)],[f_1121_1]) ).

cnf(f_1121_3,plain,
    minus(int),
    inference(clausify,[status(thm)],[f_1121_2]) ).

fof(f_1122_1,plain,
    zero(int),
    inference(fof_nnf,[status(thm)],[arity_Int_Oint___Groups_Ozero]) ).

fof(f_1122_2,plain,
    zero(int),
    inference(definitional_conversion,[status(esa)],[f_1122_1]) ).

cnf(f_1122_3,plain,
    zero(int),
    inference(clausify,[status(thm)],[f_1122_2]) ).

fof(f_1123_1,plain,
    ring(int),
    inference(fof_nnf,[status(thm)],[arity_Int_Oint___Rings_Oring]) ).

fof(f_1123_2,plain,
    ring(int),
    inference(definitional_conversion,[status(esa)],[f_1123_1]) ).

cnf(f_1123_3,plain,
    ring(int),
    inference(clausify,[status(thm)],[f_1123_2]) ).

fof(f_1124_1,plain,
    number(int),
    inference(fof_nnf,[status(thm)],[arity_Int_Oint___Int_Onumber]) ).

fof(f_1124_2,plain,
    number(int),
    inference(definitional_conversion,[status(esa)],[f_1124_1]) ).

cnf(f_1124_3,plain,
    number(int),
    inference(clausify,[status(thm)],[f_1124_2]) ).

fof(f_1125_1,plain,
    one(int),
    inference(fof_nnf,[status(thm)],[arity_Int_Oint___Groups_Oone]) ).

fof(f_1125_2,plain,
    one(int),
    inference(definitional_conversion,[status(esa)],[f_1125_1]) ).

cnf(f_1125_3,plain,
    one(int),
    inference(clausify,[status(thm)],[f_1125_2]) ).

fof(f_1126_1,plain,
    semiri456707255roduct(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc]) ).

fof(f_1126_2,plain,
    semiri456707255roduct(nat),
    inference(definitional_conversion,[status(esa)],[f_1126_1]) ).

cnf(f_1126_3,plain,
    semiri456707255roduct(nat),
    inference(clausify,[status(thm)],[f_1126_2]) ).

fof(f_1127_1,plain,
    ordere223160158up_add(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add]) ).

fof(f_1127_2,plain,
    ordere223160158up_add(nat),
    inference(definitional_conversion,[status(esa)],[f_1127_1]) ).

cnf(f_1127_3,plain,
    ordere223160158up_add(nat),
    inference(clausify,[status(thm)],[f_1127_2]) ).

fof(f_1128_1,plain,
    ordere236663937imp_le(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le]) ).

fof(f_1128_2,plain,
    ordere236663937imp_le(nat),
    inference(definitional_conversion,[status(esa)],[f_1128_1]) ).

cnf(f_1128_3,plain,
    ordere236663937imp_le(nat),
    inference(clausify,[status(thm)],[f_1128_2]) ).

fof(f_1129_1,plain,
    linord893533164strict(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Rings_Olinordered__comm__semiring__strict]) ).

fof(f_1129_2,plain,
    linord893533164strict(nat),
    inference(definitional_conversion,[status(esa)],[f_1129_1]) ).

cnf(f_1129_3,plain,
    linord893533164strict(nat),
    inference(clausify,[status(thm)],[f_1129_2]) ).

fof(f_1130_1,plain,
    linord20386208strict(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Rings_Olinordered__semiring__strict]) ).

fof(f_1130_2,plain,
    linord20386208strict(nat),
    inference(definitional_conversion,[status(esa)],[f_1130_1]) ).

cnf(f_1130_3,plain,
    linord20386208strict(nat),
    inference(clausify,[status(thm)],[f_1130_2]) ).

fof(f_1131_1,plain,
    ordere779506340up_add(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Groups_Oordered__ab__semigroup__add]) ).

fof(f_1131_2,plain,
    ordere779506340up_add(nat),
    inference(definitional_conversion,[status(esa)],[f_1131_1]) ).

cnf(f_1131_3,plain,
    ordere779506340up_add(nat),
    inference(clausify,[status(thm)],[f_1131_2]) ).

fof(f_1132_1,plain,
    ordere216010020id_add(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Groups_Oordered__comm__monoid__add]) ).

fof(f_1132_2,plain,
    ordere216010020id_add(nat),
    inference(definitional_conversion,[status(esa)],[f_1132_1]) ).

cnf(f_1132_3,plain,
    ordere216010020id_add(nat),
    inference(clausify,[status(thm)],[f_1132_2]) ).

fof(f_1133_1,plain,
    cancel146912293up_add(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add]) ).

fof(f_1133_2,plain,
    cancel146912293up_add(nat),
    inference(definitional_conversion,[status(esa)],[f_1133_1]) ).

cnf(f_1133_3,plain,
    cancel146912293up_add(nat),
    inference(clausify,[status(thm)],[f_1133_2]) ).

fof(f_1134_1,plain,
    ordere453448008miring(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Rings_Oordered__cancel__semiring]) ).

fof(f_1134_2,plain,
    ordere453448008miring(nat),
    inference(definitional_conversion,[status(esa)],[f_1134_1]) ).

cnf(f_1134_3,plain,
    ordere453448008miring(nat),
    inference(clausify,[status(thm)],[f_1134_2]) ).

fof(f_1135_1,plain,
    ordere1490568538miring(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Rings_Oordered__comm__semiring]) ).

fof(f_1135_2,plain,
    ordere1490568538miring(nat),
    inference(definitional_conversion,[status(esa)],[f_1135_1]) ).

cnf(f_1135_3,plain,
    ordere1490568538miring(nat),
    inference(clausify,[status(thm)],[f_1135_2]) ).

fof(f_1136_1,plain,
    cancel_semigroup_add(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Groups_Ocancel__semigroup__add]) ).

fof(f_1136_2,plain,
    cancel_semigroup_add(nat),
    inference(definitional_conversion,[status(esa)],[f_1136_1]) ).

cnf(f_1136_3,plain,
    cancel_semigroup_add(nat),
    inference(clausify,[status(thm)],[f_1136_2]) ).

fof(f_1137_1,plain,
    linordered_semiring(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Rings_Olinordered__semiring]) ).

fof(f_1137_2,plain,
    linordered_semiring(nat),
    inference(definitional_conversion,[status(esa)],[f_1137_1]) ).

cnf(f_1137_3,plain,
    linordered_semiring(nat),
    inference(clausify,[status(thm)],[f_1137_2]) ).

fof(f_1138_1,plain,
    linordered_semidom(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Rings_Olinordered__semidom]) ).

fof(f_1138_2,plain,
    linordered_semidom(nat),
    inference(definitional_conversion,[status(esa)],[f_1138_1]) ).

cnf(f_1138_3,plain,
    linordered_semidom(nat),
    inference(clausify,[status(thm)],[f_1138_2]) ).

fof(f_1139_1,plain,
    ab_semigroup_mult(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Groups_Oab__semigroup__mult]) ).

fof(f_1139_2,plain,
    ab_semigroup_mult(nat),
    inference(definitional_conversion,[status(esa)],[f_1139_1]) ).

cnf(f_1139_3,plain,
    ab_semigroup_mult(nat),
    inference(clausify,[status(thm)],[f_1139_2]) ).

fof(f_1140_1,plain,
    comm_monoid_mult(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Groups_Ocomm__monoid__mult]) ).

fof(f_1140_2,plain,
    comm_monoid_mult(nat),
    inference(definitional_conversion,[status(esa)],[f_1140_1]) ).

cnf(f_1140_3,plain,
    comm_monoid_mult(nat),
    inference(clausify,[status(thm)],[f_1140_2]) ).

fof(f_1141_1,plain,
    ab_semigroup_add(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Groups_Oab__semigroup__add]) ).

fof(f_1141_2,plain,
    ab_semigroup_add(nat),
    inference(definitional_conversion,[status(esa)],[f_1141_1]) ).

cnf(f_1141_3,plain,
    ab_semigroup_add(nat),
    inference(clausify,[status(thm)],[f_1141_2]) ).

fof(f_1142_1,plain,
    ordered_semiring(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Rings_Oordered__semiring]) ).

fof(f_1142_2,plain,
    ordered_semiring(nat),
    inference(definitional_conversion,[status(esa)],[f_1142_1]) ).

cnf(f_1142_3,plain,
    ordered_semiring(nat),
    inference(clausify,[status(thm)],[f_1142_2]) ).

fof(f_1143_1,plain,
    no_zero_divisors(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Rings_Ono__zero__divisors]) ).

fof(f_1143_2,plain,
    no_zero_divisors(nat),
    inference(definitional_conversion,[status(esa)],[f_1143_1]) ).

cnf(f_1143_3,plain,
    no_zero_divisors(nat),
    inference(clausify,[status(thm)],[f_1143_2]) ).

fof(f_1144_1,plain,
    comm_monoid_add(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Groups_Ocomm__monoid__add]) ).

fof(f_1144_2,plain,
    comm_monoid_add(nat),
    inference(definitional_conversion,[status(esa)],[f_1144_1]) ).

cnf(f_1144_3,plain,
    comm_monoid_add(nat),
    inference(clausify,[status(thm)],[f_1144_2]) ).

fof(f_1145_1,plain,
    comm_semiring_1(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Rings_Ocomm__semiring__1]) ).

fof(f_1145_2,plain,
    comm_semiring_1(nat),
    inference(definitional_conversion,[status(esa)],[f_1145_1]) ).

cnf(f_1145_3,plain,
    comm_semiring_1(nat),
    inference(clausify,[status(thm)],[f_1145_2]) ).

fof(f_1146_1,plain,
    comm_semiring(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Rings_Ocomm__semiring]) ).

fof(f_1146_2,plain,
    comm_semiring(nat),
    inference(definitional_conversion,[status(esa)],[f_1146_1]) ).

cnf(f_1146_3,plain,
    comm_semiring(nat),
    inference(clausify,[status(thm)],[f_1146_2]) ).

fof(f_1147_1,plain,
    semiring_char_0(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Nat_Osemiring__char__0]) ).

fof(f_1147_2,plain,
    semiring_char_0(nat),
    inference(definitional_conversion,[status(esa)],[f_1147_1]) ).

cnf(f_1147_3,plain,
    semiring_char_0(nat),
    inference(clausify,[status(thm)],[f_1147_2]) ).

fof(f_1148_1,plain,
    number_semiring(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Int_Onumber__semiring]) ).

fof(f_1148_2,plain,
    number_semiring(nat),
    inference(definitional_conversion,[status(esa)],[f_1148_1]) ).

cnf(f_1148_3,plain,
    number_semiring(nat),
    inference(clausify,[status(thm)],[f_1148_2]) ).

fof(f_1149_1,plain,
    zero_neq_one(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Rings_Ozero__neq__one]) ).

fof(f_1149_2,plain,
    zero_neq_one(nat),
    inference(definitional_conversion,[status(esa)],[f_1149_1]) ).

cnf(f_1149_3,plain,
    zero_neq_one(nat),
    inference(clausify,[status(thm)],[f_1149_2]) ).

fof(f_1150_1,plain,
    preorder(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Orderings_Opreorder]) ).

fof(f_1150_2,plain,
    preorder(nat),
    inference(definitional_conversion,[status(esa)],[f_1150_1]) ).

cnf(f_1150_3,plain,
    preorder(nat),
    inference(clausify,[status(thm)],[f_1150_2]) ).

fof(f_1151_1,plain,
    linorder(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Orderings_Olinorder]) ).

fof(f_1151_2,plain,
    linorder(nat),
    inference(definitional_conversion,[status(esa)],[f_1151_1]) ).

cnf(f_1151_3,plain,
    linorder(nat),
    inference(clausify,[status(thm)],[f_1151_2]) ).

fof(f_1152_1,plain,
    monoid_mult(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Groups_Omonoid__mult]) ).

fof(f_1152_2,plain,
    monoid_mult(nat),
    inference(definitional_conversion,[status(esa)],[f_1152_1]) ).

cnf(f_1152_3,plain,
    monoid_mult(nat),
    inference(clausify,[status(thm)],[f_1152_2]) ).

fof(f_1153_1,plain,
    monoid_add(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Groups_Omonoid__add]) ).

fof(f_1153_2,plain,
    monoid_add(nat),
    inference(definitional_conversion,[status(esa)],[f_1153_1]) ).

cnf(f_1153_3,plain,
    monoid_add(nat),
    inference(clausify,[status(thm)],[f_1153_2]) ).

fof(f_1154_1,plain,
    semiring_1(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Rings_Osemiring__1]) ).

fof(f_1154_2,plain,
    semiring_1(nat),
    inference(definitional_conversion,[status(esa)],[f_1154_1]) ).

cnf(f_1154_3,plain,
    semiring_1(nat),
    inference(clausify,[status(thm)],[f_1154_2]) ).

fof(f_1155_1,plain,
    mult_zero(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Rings_Omult__zero]) ).

fof(f_1155_2,plain,
    mult_zero(nat),
    inference(definitional_conversion,[status(esa)],[f_1155_1]) ).

cnf(f_1155_3,plain,
    mult_zero(nat),
    inference(clausify,[status(thm)],[f_1155_2]) ).

fof(f_1156_1,plain,
    order(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Orderings_Oorder]) ).

fof(f_1156_2,plain,
    order(nat),
    inference(definitional_conversion,[status(esa)],[f_1156_1]) ).

cnf(f_1156_3,plain,
    order(nat),
    inference(clausify,[status(thm)],[f_1156_2]) ).

fof(f_1157_1,plain,
    semiring(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Rings_Osemiring]) ).

fof(f_1157_2,plain,
    semiring(nat),
    inference(definitional_conversion,[status(esa)],[f_1157_1]) ).

cnf(f_1157_3,plain,
    semiring(nat),
    inference(clausify,[status(thm)],[f_1157_2]) ).

fof(f_1158_1,plain,
    ord(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Orderings_Oord]) ).

fof(f_1158_2,plain,
    ord(nat),
    inference(definitional_conversion,[status(esa)],[f_1158_1]) ).

cnf(f_1158_3,plain,
    ord(nat),
    inference(clausify,[status(thm)],[f_1158_2]) ).

fof(f_1159_1,plain,
    bot(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Orderings_Obot]) ).

fof(f_1159_2,plain,
    bot(nat),
    inference(definitional_conversion,[status(esa)],[f_1159_1]) ).

cnf(f_1159_3,plain,
    bot(nat),
    inference(clausify,[status(thm)],[f_1159_2]) ).

fof(f_1160_1,plain,
    minus(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Groups_Ominus]) ).

fof(f_1160_2,plain,
    minus(nat),
    inference(definitional_conversion,[status(esa)],[f_1160_1]) ).

cnf(f_1160_3,plain,
    minus(nat),
    inference(clausify,[status(thm)],[f_1160_2]) ).

fof(f_1161_1,plain,
    zero(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Groups_Ozero]) ).

fof(f_1161_2,plain,
    zero(nat),
    inference(definitional_conversion,[status(esa)],[f_1161_1]) ).

cnf(f_1161_3,plain,
    zero(nat),
    inference(clausify,[status(thm)],[f_1161_2]) ).

fof(f_1162_1,plain,
    number(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Int_Onumber]) ).

fof(f_1162_2,plain,
    number(nat),
    inference(definitional_conversion,[status(esa)],[f_1162_1]) ).

cnf(f_1162_3,plain,
    number(nat),
    inference(clausify,[status(thm)],[f_1162_2]) ).

fof(f_1163_1,plain,
    one(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Groups_Oone]) ).

fof(f_1163_2,plain,
    one(nat),
    inference(definitional_conversion,[status(esa)],[f_1163_1]) ).

cnf(f_1163_3,plain,
    one(nat),
    inference(clausify,[status(thm)],[f_1163_2]) ).

fof(f_1164_1,plain,
    preorder(bool),
    inference(fof_nnf,[status(thm)],[arity_HOL_Obool___Orderings_Opreorder]) ).

fof(f_1164_2,plain,
    preorder(bool),
    inference(definitional_conversion,[status(esa)],[f_1164_1]) ).

cnf(f_1164_3,plain,
    preorder(bool),
    inference(clausify,[status(thm)],[f_1164_2]) ).

fof(f_1165_1,plain,
    finite_finite_1(bool),
    inference(fof_nnf,[status(thm)],[arity_HOL_Obool___Finite__Set_Ofinite]) ).

fof(f_1165_2,plain,
    finite_finite_1(bool),
    inference(definitional_conversion,[status(esa)],[f_1165_1]) ).

cnf(f_1165_3,plain,
    finite_finite_1(bool),
    inference(clausify,[status(thm)],[f_1165_2]) ).

fof(f_1166_1,plain,
    order(bool),
    inference(fof_nnf,[status(thm)],[arity_HOL_Obool___Orderings_Oorder]) ).

fof(f_1166_2,plain,
    order(bool),
    inference(definitional_conversion,[status(esa)],[f_1166_1]) ).

cnf(f_1166_3,plain,
    order(bool),
    inference(clausify,[status(thm)],[f_1166_2]) ).

fof(f_1167_1,plain,
    ord(bool),
    inference(fof_nnf,[status(thm)],[arity_HOL_Obool___Orderings_Oord]) ).

fof(f_1167_2,plain,
    ord(bool),
    inference(definitional_conversion,[status(esa)],[f_1167_1]) ).

cnf(f_1167_3,plain,
    ord(bool),
    inference(clausify,[status(thm)],[f_1167_2]) ).

fof(f_1168_1,plain,
    bot(bool),
    inference(fof_nnf,[status(thm)],[arity_HOL_Obool___Orderings_Obot]) ).

fof(f_1168_2,plain,
    bot(bool),
    inference(definitional_conversion,[status(esa)],[f_1168_1]) ).

cnf(f_1168_3,plain,
    bot(bool),
    inference(clausify,[status(thm)],[f_1168_2]) ).

fof(f_1169_1,plain,
    minus(bool),
    inference(fof_nnf,[status(thm)],[arity_HOL_Obool___Groups_Ominus]) ).

fof(f_1169_2,plain,
    minus(bool),
    inference(definitional_conversion,[status(esa)],[f_1169_1]) ).

cnf(f_1169_3,plain,
    minus(bool),
    inference(clausify,[status(thm)],[f_1169_2]) ).

fof(f_1170_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_1170_2,plain,
    ! [U_4018,U_4017] :
      ( finite_finite_1(sum_sum(U_4018,U_4017))
      | ~ finite_finite_1(U_4018)
      | ~ finite_finite_1(U_4017) ),
    inference(variable_rename,[status(thm)],[f_1170_1]) ).

fof(f_1170_3,plain,
    ! [U_4018,U_4017] :
      ( finite_finite_1(sum_sum(U_4018,U_4017))
      | ~ finite_finite_1(U_4018)
      | ~ finite_finite_1(U_4017) ),
    inference(definitional_conversion,[status(esa)],[f_1170_2]) ).

cnf(f_1170_4,plain,
    ( finite_finite_1(sum_sum(U_4018,U_4017))
    | ~ finite_finite_1(U_4018)
    | ~ finite_finite_1(U_4017) ),
    inference(clausify,[status(thm)],[f_1170_3]) ).

fof(f_1171_1,plain,
    ! [T,A] : ti(T,ti(T,A)) = ti(T,A),
    inference(fof_nnf,[status(thm)],[help_ti_idem]) ).

fof(f_1171_2,plain,
    ! [U_4020,U_4019] : ti(U_4020,ti(U_4020,U_4019)) = ti(U_4020,U_4019),
    inference(variable_rename,[status(thm)],[f_1171_1]) ).

fof(f_1171_3,plain,
    ! [U_4019,U_4020] : ti(U_4020,ti(U_4020,U_4019)) = ti(U_4020,U_4019),
    inference(definitional_conversion,[status(esa)],[f_1171_2]) ).

cnf(f_1171_4,plain,
    ti(U_4020,ti(U_4020,U_4019)) = ti(U_4020,U_4019),
    inference(clausify,[status(thm)],[f_1171_3]) ).

fof(f_1172_1,plain,
    ! [X_a,X,Y] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),hAPP(bool,fun(X_a,fun(X_a,X_a)),if(X_a),fTrue),X),Y) = ti(X_a,X),
    inference(fof_nnf,[status(thm)],[help_If_1_1_T]) ).

fof(f_1172_2,plain,
    ! [U_4023,U_4022,U_4021] : hAPP(U_4023,U_4023,hAPP(U_4023,fun(U_4023,U_4023),hAPP(bool,fun(U_4023,fun(U_4023,U_4023)),if(U_4023),fTrue),U_4022),U_4021) = ti(U_4023,U_4022),
    inference(variable_rename,[status(thm)],[f_1172_1]) ).

fof(f_1172_3,plain,
    ! [U_4021,U_4022,U_4023] : hAPP(U_4023,U_4023,hAPP(U_4023,fun(U_4023,U_4023),hAPP(bool,fun(U_4023,fun(U_4023,U_4023)),if(U_4023),fTrue),U_4022),U_4021) = ti(U_4023,U_4022),
    inference(definitional_conversion,[status(esa)],[f_1172_2]) ).

cnf(f_1172_4,plain,
    hAPP(U_4023,U_4023,hAPP(U_4023,fun(U_4023,U_4023),hAPP(bool,fun(U_4023,fun(U_4023,U_4023)),if(U_4023),fTrue),U_4022),U_4021) = ti(U_4023,U_4022),
    inference(clausify,[status(thm)],[f_1172_3]) ).

fof(f_1173_1,plain,
    ! [X_a,X,Y] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),hAPP(bool,fun(X_a,fun(X_a,X_a)),if(X_a),fFalse),X),Y) = ti(X_a,Y),
    inference(fof_nnf,[status(thm)],[help_If_2_1_T]) ).

fof(f_1173_2,plain,
    ! [U_4026,U_4025,U_4024] : hAPP(U_4026,U_4026,hAPP(U_4026,fun(U_4026,U_4026),hAPP(bool,fun(U_4026,fun(U_4026,U_4026)),if(U_4026),fFalse),U_4025),U_4024) = ti(U_4026,U_4024),
    inference(variable_rename,[status(thm)],[f_1173_1]) ).

fof(f_1173_3,plain,
    ! [U_4024,U_4026,U_4025] : hAPP(U_4026,U_4026,hAPP(U_4026,fun(U_4026,U_4026),hAPP(bool,fun(U_4026,fun(U_4026,U_4026)),if(U_4026),fFalse),U_4025),U_4024) = ti(U_4026,U_4024),
    inference(definitional_conversion,[status(esa)],[f_1173_2]) ).

cnf(f_1173_4,plain,
    hAPP(U_4026,U_4026,hAPP(U_4026,fun(U_4026,U_4026),hAPP(bool,fun(U_4026,fun(U_4026,U_4026)),if(U_4026),fFalse),U_4025),U_4024) = ti(U_4026,U_4024),
    inference(clausify,[status(thm)],[f_1173_3]) ).

fof(f_1174_1,plain,
    ! [P] :
      ( ti(bool,P) = fFalse
      | ti(bool,P) = fTrue ),
    inference(fof_nnf,[status(thm)],[help_If_3_1_T]) ).

fof(f_1174_2,plain,
    ! [U_4027] :
      ( ti(bool,U_4027) = fFalse
      | ti(bool,U_4027) = fTrue ),
    inference(variable_rename,[status(thm)],[f_1174_1]) ).

fof(f_1174_3,plain,
    ! [U_4027] :
      ( ti(bool,U_4027) = fFalse
      | ti(bool,U_4027) = fTrue ),
    inference(definitional_conversion,[status(esa)],[f_1174_2]) ).

cnf(f_1174_4,plain,
    ( ti(bool,U_4027) = fFalse
    | ti(bool,U_4027) = fTrue ),
    inference(clausify,[status(thm)],[f_1174_3]) ).

fof(f_1175_1,plain,
    ! [P] :
      ( ~ hBOOL(P)
      | ~ hBOOL(hAPP(bool,bool,fNot,P)) ),
    inference(fof_nnf,[status(thm)],[help_fNot_1_1_U]) ).

fof(f_1175_2,plain,
    ! [U_4028] :
      ( ~ hBOOL(U_4028)
      | ~ hBOOL(hAPP(bool,bool,fNot,U_4028)) ),
    inference(variable_rename,[status(thm)],[f_1175_1]) ).

fof(f_1175_3,plain,
    ! [U_4028] :
      ( ~ hBOOL(U_4028)
      | ~ hBOOL(hAPP(bool,bool,fNot,U_4028)) ),
    inference(definitional_conversion,[status(esa)],[f_1175_2]) ).

cnf(f_1175_4,plain,
    ( ~ hBOOL(U_4028)
    | ~ hBOOL(hAPP(bool,bool,fNot,U_4028)) ),
    inference(clausify,[status(thm)],[f_1175_3]) ).

fof(f_1176_1,plain,
    ! [P] :
      ( hBOOL(hAPP(bool,bool,fNot,P))
      | hBOOL(P) ),
    inference(fof_nnf,[status(thm)],[help_fNot_2_1_U]) ).

fof(f_1176_2,plain,
    ! [U_4029] :
      ( hBOOL(hAPP(bool,bool,fNot,U_4029))
      | hBOOL(U_4029) ),
    inference(variable_rename,[status(thm)],[f_1176_1]) ).

fof(f_1176_3,plain,
    ! [U_4029] :
      ( hBOOL(hAPP(bool,bool,fNot,U_4029))
      | hBOOL(U_4029) ),
    inference(definitional_conversion,[status(esa)],[f_1176_2]) ).

cnf(f_1176_4,plain,
    ( hBOOL(hAPP(bool,bool,fNot,U_4029))
    | hBOOL(U_4029) ),
    inference(clausify,[status(thm)],[f_1176_3]) ).

fof(f_1177_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_1177_2,plain,
    ! [U_4035,U_4034,U_4033,U_4032,U_4031,U_4030] : hAPP(U_4035,U_4034,hAPP(fun(U_4035,U_4033),fun(U_4035,U_4034),hAPP(fun(U_4033,U_4034),fun(fun(U_4035,U_4033),fun(U_4035,U_4034)),combb(U_4033,U_4034,U_4035),U_4032),U_4031),U_4030) = hAPP(U_4033,U_4034,U_4032,hAPP(U_4035,U_4033,U_4031,U_4030)),
    inference(variable_rename,[status(thm)],[f_1177_1]) ).

fof(f_1177_3,plain,
    ! [U_4033,U_4030,U_4031,U_4032,U_4034,U_4035] : hAPP(U_4035,U_4034,hAPP(fun(U_4035,U_4033),fun(U_4035,U_4034),hAPP(fun(U_4033,U_4034),fun(fun(U_4035,U_4033),fun(U_4035,U_4034)),combb(U_4033,U_4034,U_4035),U_4032),U_4031),U_4030) = hAPP(U_4033,U_4034,U_4032,hAPP(U_4035,U_4033,U_4031,U_4030)),
    inference(definitional_conversion,[status(esa)],[f_1177_2]) ).

cnf(f_1177_4,plain,
    hAPP(U_4035,U_4034,hAPP(fun(U_4035,U_4033),fun(U_4035,U_4034),hAPP(fun(U_4033,U_4034),fun(fun(U_4035,U_4033),fun(U_4035,U_4034)),combb(U_4033,U_4034,U_4035),U_4032),U_4031),U_4030) = hAPP(U_4033,U_4034,U_4032,hAPP(U_4035,U_4033,U_4031,U_4030)),
    inference(clausify,[status(thm)],[f_1177_3]) ).

fof(f_1178_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_1178_2,plain,
    ! [U_4041,U_4040,U_4039,U_4038,U_4037,U_4036] : hAPP(U_4041,U_4040,hAPP(U_4039,fun(U_4041,U_4040),hAPP(fun(U_4041,fun(U_4039,U_4040)),fun(U_4039,fun(U_4041,U_4040)),combc(U_4041,U_4039,U_4040),U_4038),U_4037),U_4036) = hAPP(U_4039,U_4040,hAPP(U_4041,fun(U_4039,U_4040),U_4038,U_4036),U_4037),
    inference(variable_rename,[status(thm)],[f_1178_1]) ).

fof(f_1178_3,plain,
    ! [U_4036,U_4037,U_4039,U_4038,U_4040,U_4041] : hAPP(U_4041,U_4040,hAPP(U_4039,fun(U_4041,U_4040),hAPP(fun(U_4041,fun(U_4039,U_4040)),fun(U_4039,fun(U_4041,U_4040)),combc(U_4041,U_4039,U_4040),U_4038),U_4037),U_4036) = hAPP(U_4039,U_4040,hAPP(U_4041,fun(U_4039,U_4040),U_4038,U_4036),U_4037),
    inference(definitional_conversion,[status(esa)],[f_1178_2]) ).

cnf(f_1178_4,plain,
    hAPP(U_4041,U_4040,hAPP(U_4039,fun(U_4041,U_4040),hAPP(fun(U_4041,fun(U_4039,U_4040)),fun(U_4039,fun(U_4041,U_4040)),combc(U_4041,U_4039,U_4040),U_4038),U_4037),U_4036) = hAPP(U_4039,U_4040,hAPP(U_4041,fun(U_4039,U_4040),U_4038,U_4036),U_4037),
    inference(clausify,[status(thm)],[f_1178_3]) ).

fof(f_1179_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_1179_2,plain,
    ! [U_4043,U_4042] : hAPP(U_4043,U_4043,combi(U_4043),U_4042) = ti(U_4043,U_4042),
    inference(variable_rename,[status(thm)],[f_1179_1]) ).

fof(f_1179_3,plain,
    ! [U_4043,U_4042] : hAPP(U_4043,U_4043,combi(U_4043),U_4042) = ti(U_4043,U_4042),
    inference(definitional_conversion,[status(esa)],[f_1179_2]) ).

cnf(f_1179_4,plain,
    hAPP(U_4043,U_4043,combi(U_4043),U_4042) = ti(U_4043,U_4042),
    inference(clausify,[status(thm)],[f_1179_3]) ).

fof(f_1180_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_1180_2,plain,
    ! [U_4047,U_4046,U_4045,U_4044] : hAPP(U_4047,U_4046,hAPP(U_4046,fun(U_4047,U_4046),combk(U_4046,U_4047),U_4045),U_4044) = ti(U_4046,U_4045),
    inference(variable_rename,[status(thm)],[f_1180_1]) ).

fof(f_1180_3,plain,
    ! [U_4044,U_4045,U_4046,U_4047] : hAPP(U_4047,U_4046,hAPP(U_4046,fun(U_4047,U_4046),combk(U_4046,U_4047),U_4045),U_4044) = ti(U_4046,U_4045),
    inference(definitional_conversion,[status(esa)],[f_1180_2]) ).

cnf(f_1180_4,plain,
    hAPP(U_4047,U_4046,hAPP(U_4046,fun(U_4047,U_4046),combk(U_4046,U_4047),U_4045),U_4044) = ti(U_4046,U_4045),
    inference(clausify,[status(thm)],[f_1180_3]) ).

fof(f_1181_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_1181_2,plain,
    ! [U_4053,U_4052,U_4051,U_4050,U_4049,U_4048] : hAPP(U_4053,U_4052,hAPP(fun(U_4053,U_4051),fun(U_4053,U_4052),hAPP(fun(U_4053,fun(U_4051,U_4052)),fun(fun(U_4053,U_4051),fun(U_4053,U_4052)),combs(U_4053,U_4051,U_4052),U_4050),U_4049),U_4048) = hAPP(U_4051,U_4052,hAPP(U_4053,fun(U_4051,U_4052),U_4050,U_4048),hAPP(U_4053,U_4051,U_4049,U_4048)),
    inference(variable_rename,[status(thm)],[f_1181_1]) ).

fof(f_1181_3,plain,
    ! [U_4051,U_4048,U_4049,U_4050,U_4052,U_4053] : hAPP(U_4053,U_4052,hAPP(fun(U_4053,U_4051),fun(U_4053,U_4052),hAPP(fun(U_4053,fun(U_4051,U_4052)),fun(fun(U_4053,U_4051),fun(U_4053,U_4052)),combs(U_4053,U_4051,U_4052),U_4050),U_4049),U_4048) = hAPP(U_4051,U_4052,hAPP(U_4053,fun(U_4051,U_4052),U_4050,U_4048),hAPP(U_4053,U_4051,U_4049,U_4048)),
    inference(definitional_conversion,[status(esa)],[f_1181_2]) ).

cnf(f_1181_4,plain,
    hAPP(U_4053,U_4052,hAPP(fun(U_4053,U_4051),fun(U_4053,U_4052),hAPP(fun(U_4053,fun(U_4051,U_4052)),fun(fun(U_4053,U_4051),fun(U_4053,U_4052)),combs(U_4053,U_4051,U_4052),U_4050),U_4049),U_4048) = hAPP(U_4051,U_4052,hAPP(U_4053,fun(U_4051,U_4052),U_4050,U_4048),hAPP(U_4053,U_4051,U_4049,U_4048)),
    inference(clausify,[status(thm)],[f_1181_3]) ).

fof(f_1182_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_1182_2,plain,
    ! [U_4055,U_4054] :
      ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,U_4054),U_4055))
      | ~ hBOOL(U_4055)
      | ~ hBOOL(U_4054) ),
    inference(variable_rename,[status(thm)],[f_1182_1]) ).

fof(f_1182_3,plain,
    ! [U_4055] :
      ( ! [U_4054] :
          ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,U_4054),U_4055))
          | ~ hBOOL(U_4054) )
      | ~ hBOOL(U_4055) ),
    inference(miniscope,[status(thm)],[f_1182_2]) ).

fof(f_1182_4,plain,
    ! [U_4055,U_4054] :
      ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,U_4054),U_4055))
      | ~ hBOOL(U_4054)
      | ~ hBOOL(U_4055) ),
    inference(definitional_conversion,[status(esa)],[f_1182_3]) ).

cnf(f_1182_5,plain,
    ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,U_4054),U_4055))
    | ~ hBOOL(U_4054)
    | ~ hBOOL(U_4055) ),
    inference(clausify,[status(thm)],[f_1182_4]) ).

fof(f_1183_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_1183_2,plain,
    ! [U_4057,U_4056] :
      ( hBOOL(U_4057)
      | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,U_4057),U_4056)) ),
    inference(variable_rename,[status(thm)],[f_1183_1]) ).

fof(f_1183_3,plain,
    ! [U_4057] :
      ( ! [U_4056] : ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,U_4057),U_4056))
      | hBOOL(U_4057) ),
    inference(miniscope,[status(thm)],[f_1183_2]) ).

fof(f_1183_4,plain,
    ! [U_4057,U_4056] :
      ( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,U_4057),U_4056))
      | hBOOL(U_4057) ),
    inference(definitional_conversion,[status(esa)],[f_1183_3]) ).

cnf(f_1183_5,plain,
    ( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,U_4057),U_4056))
    | hBOOL(U_4057) ),
    inference(clausify,[status(thm)],[f_1183_4]) ).

fof(f_1184_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_1184_2,plain,
    ! [U_4059,U_4058] :
      ( hBOOL(U_4058)
      | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,U_4059),U_4058)) ),
    inference(variable_rename,[status(thm)],[f_1184_1]) ).

fof(f_1184_3,plain,
    ! [U_4058,U_4059] :
      ( hBOOL(U_4058)
      | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,U_4059),U_4058)) ),
    inference(definitional_conversion,[status(esa)],[f_1184_2]) ).

cnf(f_1184_4,plain,
    ( hBOOL(U_4058)
    | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,U_4059),U_4058)) ),
    inference(clausify,[status(thm)],[f_1184_3]) ).

fof(f_1185_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_1185_2,plain,
    ! [U_4061,U_4060] :
      ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,U_4060),U_4061))
      | ~ hBOOL(U_4060) ),
    inference(variable_rename,[status(thm)],[f_1185_1]) ).

fof(f_1185_3,plain,
    ! [U_4060,U_4061] :
      ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,U_4060),U_4061))
      | ~ hBOOL(U_4060) ),
    inference(definitional_conversion,[status(esa)],[f_1185_2]) ).

cnf(f_1185_4,plain,
    ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,U_4060),U_4061))
    | ~ hBOOL(U_4060) ),
    inference(clausify,[status(thm)],[f_1185_3]) ).

fof(f_1186_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_1186_2,plain,
    ! [U_4063,U_4062] :
      ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,U_4063),U_4062))
      | ~ hBOOL(U_4062) ),
    inference(variable_rename,[status(thm)],[f_1186_1]) ).

fof(f_1186_3,plain,
    ! [U_4062,U_4063] :
      ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,U_4063),U_4062))
      | ~ hBOOL(U_4062) ),
    inference(definitional_conversion,[status(esa)],[f_1186_2]) ).

cnf(f_1186_4,plain,
    ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,U_4063),U_4062))
    | ~ hBOOL(U_4062) ),
    inference(clausify,[status(thm)],[f_1186_3]) ).

fof(f_1187_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_1187_2,plain,
    ! [U_4065,U_4064] :
      ( hBOOL(U_4064)
      | hBOOL(U_4065)
      | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,U_4065),U_4064)) ),
    inference(variable_rename,[status(thm)],[f_1187_1]) ).

fof(f_1187_3,plain,
    ! [U_4065] :
      ( ! [U_4064] :
          ( hBOOL(U_4064)
          | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,U_4065),U_4064)) )
      | hBOOL(U_4065) ),
    inference(miniscope,[status(thm)],[f_1187_2]) ).

fof(f_1187_4,plain,
    ! [U_4064,U_4065] :
      ( hBOOL(U_4064)
      | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,U_4065),U_4064))
      | hBOOL(U_4065) ),
    inference(definitional_conversion,[status(esa)],[f_1187_3]) ).

cnf(f_1187_5,plain,
    ( hBOOL(U_4064)
    | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,U_4065),U_4064))
    | hBOOL(U_4065) ),
    inference(clausify,[status(thm)],[f_1187_4]) ).

fof(f_1188_1,plain,
    ~ hBOOL(fFalse),
    inference(fof_nnf,[status(thm)],[help_fFalse_1_1_U]) ).

fof(f_1188_2,plain,
    ~ hBOOL(fFalse),
    inference(definitional_conversion,[status(esa)],[f_1188_1]) ).

cnf(f_1188_3,plain,
    ~ hBOOL(fFalse),
    inference(clausify,[status(thm)],[f_1188_2]) ).

fof(f_1189_1,plain,
    ! [P] :
      ( ti(bool,P) = fFalse
      | ti(bool,P) = fTrue ),
    inference(fof_nnf,[status(thm)],[help_fFalse_1_1_T]) ).

fof(f_1189_2,plain,
    ! [U_4066] :
      ( ti(bool,U_4066) = fFalse
      | ti(bool,U_4066) = fTrue ),
    inference(variable_rename,[status(thm)],[f_1189_1]) ).

fof(f_1189_3,plain,
    ! [U_4066] :
      ( ti(bool,U_4066) = fFalse
      | ti(bool,U_4066) = fTrue ),
    inference(definitional_conversion,[status(esa)],[f_1189_2]) ).

cnf(f_1189_4,plain,
    ( ti(bool,U_4066) = fFalse
    | ti(bool,U_4066) = fTrue ),
    inference(clausify,[status(thm)],[f_1189_3]) ).

fof(f_1190_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_1190_2,plain,
    ! [U_4069,U_4068,U_4067] :
      ( ti(U_4069,U_4068) = ti(U_4069,U_4067)
      | ~ hBOOL(hAPP(U_4069,bool,hAPP(U_4069,fun(U_4069,bool),fequal(U_4069),U_4068),U_4067)) ),
    inference(variable_rename,[status(thm)],[f_1190_1]) ).

fof(f_1190_3,plain,
    ! [U_4067,U_4068,U_4069] :
      ( ti(U_4069,U_4068) = ti(U_4069,U_4067)
      | ~ hBOOL(hAPP(U_4069,bool,hAPP(U_4069,fun(U_4069,bool),fequal(U_4069),U_4068),U_4067)) ),
    inference(definitional_conversion,[status(esa)],[f_1190_2]) ).

cnf(f_1190_4,plain,
    ( ti(U_4069,U_4068) = ti(U_4069,U_4067)
    | ~ hBOOL(hAPP(U_4069,bool,hAPP(U_4069,fun(U_4069,bool),fequal(U_4069),U_4068),U_4067)) ),
    inference(clausify,[status(thm)],[f_1190_3]) ).

fof(f_1191_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_1191_2,plain,
    ! [U_4072,U_4071,U_4070] :
      ( hBOOL(hAPP(U_4072,bool,hAPP(U_4072,fun(U_4072,bool),fequal(U_4072),U_4071),U_4070))
      | ti(U_4072,U_4071) != ti(U_4072,U_4070) ),
    inference(variable_rename,[status(thm)],[f_1191_1]) ).

fof(f_1191_3,plain,
    ! [U_4070,U_4071,U_4072] :
      ( hBOOL(hAPP(U_4072,bool,hAPP(U_4072,fun(U_4072,bool),fequal(U_4072),U_4071),U_4070))
      | ti(U_4072,U_4071) != ti(U_4072,U_4070) ),
    inference(definitional_conversion,[status(esa)],[f_1191_2]) ).

cnf(f_1191_4,plain,
    ( hBOOL(hAPP(U_4072,bool,hAPP(U_4072,fun(U_4072,bool),fequal(U_4072),U_4071),U_4070))
    | ti(U_4072,U_4071) != ti(U_4072,U_4070) ),
    inference(clausify,[status(thm)],[f_1191_3]) ).

fof(f_1192_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_1192_2,plain,
    ! [U_4074,U_4073] :
      ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,U_4073),U_4074))
      | hBOOL(U_4073) ),
    inference(variable_rename,[status(thm)],[f_1192_1]) ).

fof(f_1192_3,plain,
    ! [U_4073,U_4074] :
      ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,U_4073),U_4074))
      | hBOOL(U_4073) ),
    inference(definitional_conversion,[status(esa)],[f_1192_2]) ).

cnf(f_1192_4,plain,
    ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,U_4073),U_4074))
    | hBOOL(U_4073) ),
    inference(clausify,[status(thm)],[f_1192_3]) ).

fof(f_1193_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_1193_2,plain,
    ! [U_4076,U_4075] :
      ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,U_4076),U_4075))
      | ~ hBOOL(U_4075) ),
    inference(variable_rename,[status(thm)],[f_1193_1]) ).

fof(f_1193_3,plain,
    ! [U_4075,U_4076] :
      ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,U_4076),U_4075))
      | ~ hBOOL(U_4075) ),
    inference(definitional_conversion,[status(esa)],[f_1193_2]) ).

cnf(f_1193_4,plain,
    ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,U_4076),U_4075))
    | ~ hBOOL(U_4075) ),
    inference(clausify,[status(thm)],[f_1193_3]) ).

fof(f_1194_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_1194_2,plain,
    ! [U_4078,U_4077] :
      ( hBOOL(U_4077)
      | ~ hBOOL(U_4078)
      | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,U_4078),U_4077)) ),
    inference(variable_rename,[status(thm)],[f_1194_1]) ).

fof(f_1194_3,plain,
    ! [U_4078] :
      ( ! [U_4077] :
          ( hBOOL(U_4077)
          | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,U_4078),U_4077)) )
      | ~ hBOOL(U_4078) ),
    inference(miniscope,[status(thm)],[f_1194_2]) ).

fof(f_1194_4,plain,
    ! [U_4077,U_4078] :
      ( hBOOL(U_4077)
      | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,U_4078),U_4077))
      | ~ hBOOL(U_4078) ),
    inference(definitional_conversion,[status(esa)],[f_1194_3]) ).

cnf(f_1194_5,plain,
    ( hBOOL(U_4077)
    | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,U_4078),U_4077))
    | ~ hBOOL(U_4078) ),
    inference(clausify,[status(thm)],[f_1194_4]) ).

fof(f_1195_1,plain,
    hBOOL(hAPP(fun(pname,bool),bool,finite_finite(pname),u)),
    inference(fof_nnf,[status(thm)],[conj_0]) ).

fof(f_1195_2,plain,
    hBOOL(hAPP(fun(pname,bool),bool,finite_finite(pname),u)),
    inference(definitional_conversion,[status(esa)],[f_1195_1]) ).

cnf(f_1195_3,plain,
    hBOOL(hAPP(fun(pname,bool),bool,finite_finite(pname),u)),
    inference(clausify,[status(thm)],[f_1195_2]) ).

fof(f_1196_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_1196_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_1196_1]) ).

cnf(f_1196_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_1196_2]) ).

fof(f_1197_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_1197_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_1197_1]) ).

cnf(f_1197_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_1197_2]) ).

fof(f_1198_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_1198_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_1198_1]) ).

cnf(f_1198_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_1198_2]) ).

fof(f_1199_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_1199_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_1199_1]) ).

cnf(f_1199_3,plain,
    hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u)),
    inference(clausify,[status(thm)],[f_1199_2]) ).

fof(f_1200_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_1200_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_1200_1]) ).

cnf(f_1200_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_1200_2]) ).

fof(f_1201_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_1201_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_1201_1]) ).

cnf(f_1201_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_1201_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,
    ( finite_fold_image(Eq_x_0,Eq_x_1) = finite_fold_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_16,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_17,axiom,
    ( finite908156982e_idem(Eq_x_0,Eq_x_1) = finite908156982e_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_18,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_19,axiom,
    ( finite2073411215e_idem(Eq_x_0) = finite2073411215e_idem(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_20,axiom,
    ( abs_abs(Eq_x_0) = abs_abs(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_21,axiom,
    ( minus_minus(Eq_x_0) = minus_minus(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_22,axiom,
    ( one_one(Eq_x_0) = one_one(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_23,axiom,
    ( plus_plus(Eq_x_0) = plus_plus(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_24,axiom,
    ( times_times(Eq_x_0) = times_times(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_25,axiom,
    ( zero_zero(Eq_x_0) = zero_zero(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_26,axiom,
    ( the(Eq_x_0) = the(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_27,axiom,
    ( undefined(Eq_x_0) = undefined(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_28,axiom,
    ( if(Eq_x_0) = if(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_29,axiom,
    ( number_number_of(Eq_x_0) = number_number_of(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_30,axiom,
    ( ring_1_Ints(Eq_x_0) = ring_1_Ints(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_31,axiom,
    ( nat_case(Eq_x_0) = nat_case(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_32,axiom,
    ( semiring_1_of_nat(Eq_x_0) = semiring_1_of_nat(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_33,axiom,
    ( semiri532925092at_aux(Eq_x_0) = semiri532925092at_aux(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_34,axiom,
    ( the_1(Eq_x_0) = the_1(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_35,axiom,
    ( bot_bot(Eq_x_0) = bot_bot(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_36,axiom,
    ( ord_less(Eq_x_0) = ord_less(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_37,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_38,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_39,axiom,
    ( collect(Eq_x_0) = collect(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_40,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_41,axiom,
    ( insert(Eq_x_0) = insert(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_42,axiom,
    ( the_elem(Eq_x_0) = the_elem(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_43,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_44,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_45,axiom,
    ( fequal(Eq_x_0) = fequal(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_46,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_47,axiom,
    ( member(Eq_x_0) = member(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_48,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_49,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_50,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_51,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_52,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_53,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_54,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_55,axiom,
    ( sK8(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK8(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_56,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_57,axiom,
    ( sK10(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK10(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_58,axiom,
    ( sK11(Eq_x_0,Eq_x_1,Eq_x_2) = sK11(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_59,axiom,
    ( sK12(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK12(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_60,axiom,
    ( sK13(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK13(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_61,axiom,
    ( sK14(Eq_x_0) = sK14(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_62,axiom,
    ( sK15(Eq_x_0,Eq_x_1) = sK15(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,
    ( 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_64,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_65,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_66,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_67,axiom,
    ( sK20(Eq_x_0,Eq_x_1) = sK20(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_68,axiom,
    ( 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_69,axiom,
    ( sK22(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK22(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_70,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_71,axiom,
    ( sK24(Eq_x_0,Eq_x_1,Eq_x_2) = sK24(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_72,axiom,
    ( sK25(Eq_x_0,Eq_x_1,Eq_x_2) = sK25(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_73,axiom,
    ( sK26(Eq_x_0,Eq_x_1,Eq_x_2) = sK26(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_74,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_75,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_76,axiom,
    ( sK29(Eq_x_0,Eq_x_1) = sK29(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_77,axiom,
    ( sK30(Eq_x_0,Eq_x_1) = sK30(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_78,axiom,
    ( sK31(Eq_x_0,Eq_x_1) = sK31(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_79,axiom,
    ( sK32(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK32(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_80,axiom,
    ( sK33(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK33(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_81,axiom,
    ( sK34(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK34(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_82,axiom,
    ( sK35(Eq_x_0,Eq_x_1,Eq_x_2) = sK35(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_83,axiom,
    ( sK36(Eq_x_0,Eq_x_1,Eq_x_2) = sK36(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_84,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_85,axiom,
    ( sK38(Eq_x_0,Eq_x_1) = sK38(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_86,axiom,
    ( sK39(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK39(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_87,axiom,
    ( sK40(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK40(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_88,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_89,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_90,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_91,axiom,
    ( sK44(Eq_x_0,Eq_x_1,Eq_x_2) = sK44(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_92,axiom,
    ( sK45(Eq_x_0) = sK45(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_93,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_94,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_95,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_96,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_97,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_98,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_99,axiom,
    ( sK52(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK52(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_100,axiom,
    ( sK53(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK53(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_101,axiom,
    ( sK54(Eq_x_0,Eq_x_1) = sK54(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_102,axiom,
    ( sK55(Eq_x_0,Eq_x_1) = sK55(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_103,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_104,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_105,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_106,axiom,
    ( sK59(Eq_x_0,Eq_x_1) = sK59(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_107,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_108,axiom,
    ( sK61(Eq_x_0,Eq_x_1,Eq_x_2) = sK61(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_109,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_110,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_111,axiom,
    ( sK64(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK64(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,
    ( sK65(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK65(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,
    ( 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_114,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_115,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_116,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_117,axiom,
    ( sK70(Eq_x_0,Eq_x_1,Eq_x_2) = sK70(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_118,axiom,
    ( sK71(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK71(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_119,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_120,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_121,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_122,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_123,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_124,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_125,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_126,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_127,axiom,
    ( sK80(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK80(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_128,axiom,
    ( sK81(Eq_x_0,Eq_x_1,Eq_x_2) = sK81(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_129,axiom,
    ( sK82(Eq_x_0) = sK82(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_130,axiom,
    ( sK83(Eq_x_0,Eq_x_1) = sK83(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_131,axiom,
    ( sK84(Eq_x_0,Eq_x_1,Eq_x_2) = sK84(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_132,axiom,
    ( sK85(Eq_x_0,Eq_x_1,Eq_x_2) = sK85(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_133,axiom,
    ( sK86(Eq_x_0,Eq_x_1) = sK86(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_134,axiom,
    ( sK87(Eq_x_0,Eq_x_1,Eq_x_2) = sK87(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_135,axiom,
    ( sK88(Eq_x_0,Eq_x_1,Eq_x_2) = sK88(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_136,axiom,
    ( sK89(Eq_x_0,Eq_x_1) = sK89(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_137,axiom,
    ( sK90(Eq_x_0,Eq_x_1) = sK90(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_138,axiom,
    ( sK91(Eq_x_0,Eq_x_1) = sK91(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_139,axiom,
    ( sK92(Eq_x_0) = sK92(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_140,axiom,
    ( sK93(Eq_x_0,Eq_x_1,Eq_x_2) = sK93(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_141,axiom,
    ( sK94(Eq_x_0,Eq_x_1,Eq_x_2) = sK94(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_142,axiom,
    ( sK95(Eq_x_0) = sK95(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_143,axiom,
    ( sK96(Eq_x_0) = sK96(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_144,axiom,
    ( sK97(Eq_x_0) = sK97(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_145,axiom,
    ( sK98(Eq_x_0,Eq_x_1) = sK98(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_146,axiom,
    ( sK99(Eq_x_0,Eq_x_1,Eq_x_2) = sK99(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_147,axiom,
    ( sK100(Eq_x_0,Eq_x_1,Eq_x_2) = sK100(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_148,axiom,
    ( sK101(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK101(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_149,axiom,
    ( sK102(Eq_x_0,Eq_x_1,Eq_x_2) = sK102(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_150,axiom,
    ( sK103(Eq_x_0,Eq_x_1,Eq_x_2) = sK103(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_151,axiom,
    ( sK104(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK104(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_152,axiom,
    ( sK105(Eq_x_0,Eq_x_1,Eq_x_2) = sK105(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_153,axiom,
    ( sK106(Eq_x_0,Eq_x_1,Eq_x_2) = sK106(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_154,axiom,
    ( sK107(Eq_x_0,Eq_x_1) = sK107(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_155,axiom,
    ( sK108(Eq_x_0,Eq_x_1,Eq_x_2) = sK108(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_156,axiom,
    ( sK109(Eq_x_0,Eq_x_1,Eq_x_2) = sK109(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_157,axiom,
    ( sK110(Eq_x_0,Eq_x_1) = sK110(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_158,axiom,
    ( sK111(Eq_x_0,Eq_x_1) = sK111(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_159,axiom,
    ( sK112(Eq_x_0,Eq_x_1) = sK112(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_160,axiom,
    ( sK113(Eq_x_0,Eq_x_1) = sK113(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_161,axiom,
    ( sK114(Eq_x_0,Eq_x_1,Eq_x_2) = sK114(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_162,axiom,
    ( sK115(Eq_x_0,Eq_x_1,Eq_x_2) = sK115(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_163,axiom,
    ( sK116(Eq_x_0,Eq_x_1,Eq_x_2) = sK116(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_164,axiom,
    ( sK117(Eq_x_0,Eq_x_1,Eq_x_2) = sK117(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_165,axiom,
    ( sK118(Eq_x_0,Eq_x_1,Eq_x_2) = sK118(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_166,axiom,
    ( sK119(Eq_x_0,Eq_x_1,Eq_x_2) = sK119(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_167,axiom,
    ( sK120(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK120(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_168,axiom,
    ( sK121(Eq_x_0,Eq_x_1,Eq_x_2) = sK121(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_169,axiom,
    ( sK122(Eq_x_0,Eq_x_1,Eq_x_2) = sK122(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_170,axiom,
    ( sK123(Eq_x_0,Eq_x_1,Eq_x_2) = sK123(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_171,axiom,
    ( sK124(Eq_x_0,Eq_x_1,Eq_x_2) = sK124(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_172,axiom,
    ( sK125(Eq_x_0,Eq_x_1,Eq_x_2) = sK125(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_173,axiom,
    ( sK126(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK126(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_174,axiom,
    ( sK127(Eq_x_0,Eq_x_1,Eq_x_2) = sK127(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_175,axiom,
    ( sK128(Eq_x_0,Eq_x_1) = sK128(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_176,axiom,
    ( sK129(Eq_x_0) = sK129(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_177,axiom,
    ( sK130(Eq_x_0) = sK130(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_178,axiom,
    ( sK131(Eq_x_0) = sK131(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_179,axiom,
    ( sK132(Eq_x_0) = sK132(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_180,axiom,
    ( sK133(Eq_x_0,Eq_x_1) = sK133(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_181,axiom,
    ( sK134(Eq_x_0) = sK134(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_182,axiom,
    ( sK135(Eq_x_0) = sK135(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_183,axiom,
    ( sK136(Eq_x_0) = sK136(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_184,axiom,
    ( sK137(Eq_x_0) = sK137(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_185,axiom,
    ( sK138(Eq_x_0) = sK138(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_186,axiom,
    ( sK139(Eq_x_0) = sK139(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_187,axiom,
    ( sK140(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK140(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_188,axiom,
    ( sK141(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK141(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_189,axiom,
    ( sK142(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK142(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_190,axiom,
    ( sK143(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK143(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_191,axiom,
    ( sK144(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK144(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_192,axiom,
    ( sK145(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7,Eq_x_8,Eq_x_9) = sK145(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7,Eq_y_8,Eq_y_9)
    | Eq_x_9 != Eq_y_9
    | Eq_x_8 != Eq_y_8
    | Eq_x_7 != Eq_y_7
    | 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_193,axiom,
    ( sK146(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7,Eq_x_8,Eq_x_9) = sK146(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7,Eq_y_8,Eq_y_9)
    | Eq_x_9 != Eq_y_9
    | Eq_x_8 != Eq_y_8
    | Eq_x_7 != Eq_y_7
    | 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_194,axiom,
    ( sK147(Eq_x_0,Eq_x_1,Eq_x_2) = sK147(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_195,axiom,
    ( sK148(Eq_x_0,Eq_x_1,Eq_x_2) = sK148(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_196,axiom,
    ( sK149(Eq_x_0,Eq_x_1,Eq_x_2) = sK149(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_197,axiom,
    ( sK150(Eq_x_0,Eq_x_1,Eq_x_2) = sK150(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_198,axiom,
    ( sK151(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK151(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_199,axiom,
    ( sK152(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK152(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_200,axiom,
    ( ordere142940540dd_abs(Eq_y_0)
    | ~ ordere142940540dd_abs(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_201,axiom,
    ( minus(Eq_y_0)
    | ~ minus(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_202,axiom,
    ( one(Eq_y_0)
    | ~ one(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_203,axiom,
    ( monoid_add(Eq_y_0)
    | ~ monoid_add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_204,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_205,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_206,axiom,
    ( ab_semigroup_mult(Eq_y_0)
    | ~ ab_semigroup_mult(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_207,axiom,
    ( monoid_mult(Eq_y_0)
    | ~ monoid_mult(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_208,axiom,
    ( semiring(Eq_y_0)
    | ~ semiring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_209,axiom,
    ( no_zero_divisors(Eq_y_0)
    | ~ no_zero_divisors(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_210,axiom,
    ( mult_zero(Eq_y_0)
    | ~ mult_zero(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_211,axiom,
    ( zero(Eq_y_0)
    | ~ zero(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_212,axiom,
    ( number(Eq_y_0)
    | ~ number(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_213,axiom,
    ( ring_1(Eq_y_0)
    | ~ ring_1(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_214,axiom,
    ( semiring_1(Eq_y_0)
    | ~ semiring_1(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_215,axiom,
    ( bot(Eq_y_0)
    | ~ bot(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_216,axiom,
    ( ord(Eq_y_0)
    | ~ ord(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_217,axiom,
    ( hBOOL(Eq_y_0)
    | ~ hBOOL(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_218,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_219,axiom,
    ( order(Eq_y_0)
    | ~ order(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_220,axiom,
    ( preorder(Eq_y_0)
    | ~ preorder(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_221,axiom,
    ( linorder(Eq_y_0)
    | ~ linorder(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_222,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_223,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_224,axiom,
    ( cancel146912293up_add(Eq_y_0)
    | ~ cancel146912293up_add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_225,axiom,
    ( ordere236663937imp_le(Eq_y_0)
    | ~ ordere236663937imp_le(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_226,axiom,
    ( ordere779506340up_add(Eq_y_0)
    | ~ ordere779506340up_add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_227,axiom,
    ( group_add(Eq_y_0)
    | ~ group_add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_228,axiom,
    ( ordere223160158up_add(Eq_y_0)
    | ~ ordere223160158up_add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_229,axiom,
    ( linordered_semidom(Eq_y_0)
    | ~ linordered_semidom(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_230,axiom,
    ( linordered_idom(Eq_y_0)
    | ~ linordered_idom(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_231,axiom,
    ( dense_linorder(Eq_y_0)
    | ~ dense_linorder(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_232,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_233,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_234,axiom,
    ( linord219039673up_add(Eq_y_0)
    | ~ linord219039673up_add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_235,axiom,
    ( ordere216010020id_add(Eq_y_0)
    | ~ ordere216010020id_add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_236,axiom,
    ( comm_semiring_1(Eq_y_0)
    | ~ comm_semiring_1(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_237,axiom,
    ( semiri456707255roduct(Eq_y_0)
    | ~ semiri456707255roduct(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_238,axiom,
    ( linordered_field(Eq_y_0)
    | ~ linordered_field(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_239,axiom,
    ( linord626643107strict(Eq_y_0)
    | ~ linord626643107strict(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_240,axiom,
    ( ring_n68954251visors(Eq_y_0)
    | ~ ring_n68954251visors(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_241,axiom,
    ( ab_sem1668676832m_mult(Eq_y_0)
    | ~ ab_sem1668676832m_mult(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_242,axiom,
    ( comm_semiring(Eq_y_0)
    | ~ comm_semiring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_243,axiom,
    ( comm_monoid_mult(Eq_y_0)
    | ~ comm_monoid_mult(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_244,axiom,
    ( number_ring(Eq_y_0)
    | ~ number_ring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_245,axiom,
    ( ring_char_0(Eq_y_0)
    | ~ ring_char_0(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_246,axiom,
    ( ring(Eq_y_0)
    | ~ ring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_247,axiom,
    ( ordere453448008miring(Eq_y_0)
    | ~ ordere453448008miring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_248,axiom,
    ( ordered_ring(Eq_y_0)
    | ~ ordered_ring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_249,axiom,
    ( ordered_semiring(Eq_y_0)
    | ~ ordered_semiring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_250,axiom,
    ( ordere1490568538miring(Eq_y_0)
    | ~ ordere1490568538miring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_251,axiom,
    ( linord581940658strict(Eq_y_0)
    | ~ linord581940658strict(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_252,axiom,
    ( linordered_ring(Eq_y_0)
    | ~ linordered_ring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_253,axiom,
    ( linord20386208strict(Eq_y_0)
    | ~ linord20386208strict(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_254,axiom,
    ( linord893533164strict(Eq_y_0)
    | ~ linord893533164strict(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_255,axiom,
    ( linordered_semiring(Eq_y_0)
    | ~ linordered_semiring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_256,axiom,
    ( linord1278240602ring_1(Eq_y_0)
    | ~ linord1278240602ring_1(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_257,axiom,
    ( linord1117847801e_zero(Eq_y_0)
    | ~ linord1117847801e_zero(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_258,axiom,
    ( number_semiring(Eq_y_0)
    | ~ number_semiring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_259,axiom,
    ( semiring_char_0(Eq_y_0)
    | ~ semiring_char_0(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_260,axiom,
    ( ordered_ring_abs(Eq_y_0)
    | ~ ordered_ring_abs(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_261,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_262,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_263,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_264,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_265,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_266,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_267,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_268,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_269,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_270,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_271,axiom,
    ( sP10(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP10(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP11(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP11(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_273,axiom,
    ( sP12(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP12(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP13(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP13(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_275,axiom,
    ( sP14(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP14(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_276,axiom,
    ( sP15(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP15(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_277,axiom,
    ( sP16(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP16(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_278,axiom,
    ( sP17(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP17(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_279,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_280,axiom,
    ( sP19(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP19(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_281,axiom,
    ( sP20(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP20(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_282,axiom,
    ( sP21(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP21(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_283,axiom,
    ( sP22(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP22(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_284,axiom,
    ( sP23(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP23(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_285,axiom,
    ( sP24(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP24(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_286,axiom,
    ( sP25(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP25(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_287,axiom,
    ( sP26(Eq_y_0,Eq_y_1)
    | ~ sP26(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_288,axiom,
    ( sP27(Eq_y_0,Eq_y_1)
    | ~ sP27(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_289,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_290,axiom,
    ( sP29(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP29(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_291,axiom,
    ( sP30(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP30(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_292,axiom,
    ( sP31(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP31(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_293,axiom,
    ( sP32(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP32(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_294,axiom,
    ( sP33(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP33(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_295,axiom,
    ( sP34(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP34(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_296,axiom,
    ( sP35(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP35(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_297,axiom,
    ( sP36(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP36(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_298,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_299,axiom,
    ( sP38(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP38(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_300,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_301,axiom,
    ( sP40(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP40(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_302,axiom,
    ( sP41(Eq_y_0,Eq_y_1)
    | ~ sP41(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_303,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_304,axiom,
    ( sP43(Eq_y_0,Eq_y_1)
    | ~ sP43(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_305,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_306,axiom,
    ( sP45(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP45(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_307,axiom,
    ( sP46(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP46(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_308,axiom,
    ( sP47(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP47(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_309,axiom,
    ( sP48(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP48(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_310,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_311,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_312,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_313,axiom,
    ( sP52(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP52(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_314,axiom,
    ( sP53(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP53(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_315,axiom,
    ( sP54(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP54(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_316,axiom,
    ( sP55(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP55(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_317,axiom,
    ( sP56(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP56(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_318,axiom,
    ( sP57(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP57(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_319,axiom,
    ( sP58(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP58(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_320,axiom,
    ( sP59(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP59(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_321,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_322,axiom,
    ( sP61(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP61(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_323,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_324,axiom,
    ( sP63(Eq_y_0,Eq_y_1)
    | ~ sP63(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_325,axiom,
    ( sP64(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP64(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_326,axiom,
    ( sP65(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP65(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_327,axiom,
    ( sP66(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP66(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_328,axiom,
    ( sP67(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP67(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_329,axiom,
    ( sP68(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP68(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_330,axiom,
    ( sP69(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP69(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_331,axiom,
    ( sP70(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP70(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_332,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_333,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_334,axiom,
    ( sP73(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP73(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_335,axiom,
    ( sP74(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP74(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_336,axiom,
    ( sP75(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP75(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_337,axiom,
    ( sP76(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP76(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_338,axiom,
    ( sP77(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP77(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_339,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_340,axiom,
    ( sP79(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP79(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_341,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_342,axiom,
    ( sP81(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP81(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_343,axiom,
    ( sP82(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP82(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_344,axiom,
    ( sP83(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP83(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_345,axiom,
    ( sP84(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP84(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_346,axiom,
    ( sP85(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP85(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_347,axiom,
    ( sP86(Eq_y_0,Eq_y_1)
    | ~ sP86(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_348,axiom,
    ( sP87(Eq_y_0,Eq_y_1)
    | ~ sP87(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_349,axiom,
    ( sP88(Eq_y_0,Eq_y_1)
    | ~ sP88(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_350,axiom,
    ( sP89(Eq_y_0,Eq_y_1)
    | ~ sP89(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_351,axiom,
    ( sP90(Eq_y_0,Eq_y_1)
    | ~ sP90(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_352,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_353,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_354,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_355,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_356,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_357,axiom,
    ( sP96(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP96(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_358,axiom,
    ( sP97(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP97(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_359,axiom,
    ( sP98(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP98(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_360,axiom,
    ( sP99(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP99(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_361,axiom,
    ( sP100(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP100(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_362,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_363,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_364,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_365,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_366,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_367,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_368,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_369,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_370,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_371,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_372,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_373,axiom,
    ( sP112(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP112(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_374,axiom,
    ( sP113(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP113(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_375,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_376,axiom,
    ( sP115(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP115(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_377,axiom,
    ( sP116(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP116(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_378,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_379,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_380,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_381,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_382,axiom,
    ( sP121(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP121(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_383,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_384,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_385,axiom,
    ( sP124(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP124(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_386,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_387,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_388,axiom,
    ( sP127(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP127(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_389,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_390,axiom,
    ( sP129(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP129(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_391,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_392,axiom,
    ( sP131(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP131(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_393,axiom,
    ( sP132(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP132(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_394,axiom,
    ( sP133(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP133(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_395,axiom,
    ( sP134(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP134(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_396,axiom,
    ( sP135(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP135(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_397,axiom,
    ( sP136(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP136(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_398,axiom,
    ( sP137(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP137(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_399,axiom,
    ( sP138(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP138(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_400,axiom,
    ( sP139(Eq_y_0,Eq_y_1)
    | ~ sP139(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_401,axiom,
    ( sP140(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP140(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_402,axiom,
    ( sP141(Eq_y_0,Eq_y_1)
    | ~ sP141(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_403,axiom,
    ( sP142(Eq_y_0,Eq_y_1)
    | ~ sP142(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_404,axiom,
    ( sP143(Eq_y_0,Eq_y_1)
    | ~ sP143(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_405,axiom,
    ( sP144(Eq_y_0,Eq_y_1)
    | ~ sP144(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_406,axiom,
    ( sP145(Eq_y_0,Eq_y_1)
    | ~ sP145(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_407,axiom,
    ( sP146(Eq_y_0,Eq_y_1)
    | ~ sP146(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_408,axiom,
    ( sP147(Eq_y_0,Eq_y_1)
    | ~ sP147(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_409,axiom,
    ( sP148(Eq_y_0,Eq_y_1)
    | ~ sP148(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_410,axiom,
    ( sP149(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP149(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_411,axiom,
    ( sP150(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP150(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_412,axiom,
    ( sP151(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP151(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_413,axiom,
    ( sP152(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP152(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_414,axiom,
    ( sP153(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP153(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_415,axiom,
    ( sP154(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP154(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_416,axiom,
    ( sP155(Eq_y_0,Eq_y_1)
    | ~ sP155(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_417,axiom,
    ( sP156(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP156(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_418,axiom,
    ( sP157(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP157(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_419,axiom,
    ( sP158(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP158(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_420,axiom,
    ( sP159(Eq_y_0,Eq_y_1)
    | ~ sP159(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_421,axiom,
    ( sP160(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP160(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_422,axiom,
    ( sP161(Eq_y_0,Eq_y_1)
    | ~ sP161(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_423,axiom,
    ( sP162(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP162(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_424,axiom,
    ( sP163(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP163(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_425,axiom,
    ( sP164(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP164(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_426,axiom,
    ( sP165(Eq_y_0)
    | ~ sP165(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_427,axiom,
    ( sP166(Eq_y_0,Eq_y_1)
    | ~ sP166(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_428,axiom,
    ( sP167(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP167(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_429,axiom,
    ( sP168(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP168(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_430,axiom,
    ( sP169(Eq_y_0,Eq_y_1)
    | ~ sP169(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_431,axiom,
    ( sP170(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP170(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_432,axiom,
    ( sP171(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP171(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_433,axiom,
    ( sP172(Eq_y_0,Eq_y_1)
    | ~ sP172(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_434,axiom,
    ( sP173(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP173(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_435,axiom,
    ( sP174(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP174(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_436,axiom,
    ( sP175(Eq_y_0,Eq_y_1)
    | ~ sP175(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_437,axiom,
    ( sP176(Eq_y_0,Eq_y_1)
    | ~ sP176(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_438,axiom,
    ( sP177(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP177(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_439,axiom,
    ( sP178(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP178(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_440,axiom,
    ( sP179(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP179(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_441,axiom,
    ( sP180(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP180(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_442,axiom,
    ( sP181(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP181(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_443,axiom,
    ( sP182(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7,Eq_y_8)
    | ~ sP182(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7,Eq_x_8)
    | Eq_x_8 != Eq_y_8
    | Eq_x_7 != Eq_y_7
    | 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_444,axiom,
    ( sP183(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP183(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_445,axiom,
    ( sP184(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7,Eq_y_8)
    | ~ sP184(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7,Eq_x_8)
    | Eq_x_8 != Eq_y_8
    | Eq_x_7 != Eq_y_7
    | 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_446,axiom,
    ( sP185(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP185(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_447,axiom,
    ( sP186(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP186(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_448,axiom,
    ( sP187(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP187(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_449,axiom,
    ( sP188(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP188(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_450,axiom,
    ( sP189(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP189(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_451,axiom,
    ( sP190(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP190(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_452,axiom,
    ( sP191(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP191(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_453,axiom,
    ( sP192(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP192(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_454,axiom,
    ( sP193(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP193(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_455,axiom,
    ( sP194(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP194(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_456,axiom,
    ( sP195(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP195(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_457,axiom,
    ( sP196(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP196(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_458,axiom,
    ( sP197(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP197(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_459,axiom,
    ( sP198(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP198(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_460,axiom,
    ( sP199(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP199(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_461,axiom,
    ( sP200(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP200(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_462,axiom,
    ( sP201(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP201(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_463,axiom,
    ( sP202(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP202(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_464,axiom,
    ( sP203(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP203(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_465,axiom,
    ( sP204(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP204(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_466,axiom,
    ( sP205(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP205(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_467,axiom,
    ( sP206(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP206(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_468,axiom,
    ( sP207(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP207(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_469,axiom,
    ( sP208(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7,Eq_y_8,Eq_y_9,Eq_y_10)
    | ~ sP208(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7,Eq_x_8,Eq_x_9,Eq_x_10)
    | Eq_x_10 != Eq_y_10
    | Eq_x_9 != Eq_y_9
    | Eq_x_8 != Eq_y_8
    | Eq_x_7 != Eq_y_7
    | 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_470,axiom,
    ( sP209(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7,Eq_y_8,Eq_y_9,Eq_y_10)
    | ~ sP209(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7,Eq_x_8,Eq_x_9,Eq_x_10)
    | Eq_x_10 != Eq_y_10
    | Eq_x_9 != Eq_y_9
    | Eq_x_8 != Eq_y_8
    | Eq_x_7 != Eq_y_7
    | 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_471,axiom,
    ( sP210(Eq_y_0,Eq_y_1)
    | ~ sP210(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_472,axiom,
    ( sP211(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP211(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_473,axiom,
    ( sP212(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP212(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_474,axiom,
    ( sP213(Eq_y_0,Eq_y_1)
    | ~ sP213(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_475,axiom,
    ( sP214(Eq_y_0,Eq_y_1)
    | ~ sP214(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_476,axiom,
    ( sP215(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP215(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_477,axiom,
    ( sP216(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP216(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_478,axiom,
    ( sP217(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP217(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_479,axiom,
    ( sP218(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP218(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_480,axiom,
    ( sP219(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP219(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_481,axiom,
    ( sP220(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP220(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_482,axiom,
    ( sP221(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7,Eq_y_8,Eq_y_9,Eq_y_10)
    | ~ sP221(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7,Eq_x_8,Eq_x_9,Eq_x_10)
    | Eq_x_10 != Eq_y_10
    | Eq_x_9 != Eq_y_9
    | Eq_x_8 != Eq_y_8
    | Eq_x_7 != Eq_y_7
    | 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_483,axiom,
    ( sP222(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7,Eq_y_8,Eq_y_9,Eq_y_10)
    | ~ sP222(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7,Eq_x_8,Eq_x_9,Eq_x_10)
    | Eq_x_10 != Eq_y_10
    | Eq_x_9 != Eq_y_9
    | Eq_x_8 != Eq_y_8
    | Eq_x_7 != Eq_y_7
    | 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_484,axiom,
    ( sP223(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7,Eq_y_8,Eq_y_9,Eq_y_10)
    | ~ sP223(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7,Eq_x_8,Eq_x_9,Eq_x_10)
    | Eq_x_10 != Eq_y_10
    | Eq_x_9 != Eq_y_9
    | Eq_x_8 != Eq_y_8
    | Eq_x_7 != Eq_y_7
    | 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_485,axiom,
    ( sP224(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7,Eq_y_8,Eq_y_9,Eq_y_10)
    | ~ sP224(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7,Eq_x_8,Eq_x_9,Eq_x_10)
    | Eq_x_10 != Eq_y_10
    | Eq_x_9 != Eq_y_9
    | Eq_x_8 != Eq_y_8
    | Eq_x_7 != Eq_y_7
    | 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_486,axiom,
    ( sP225(Eq_y_0,Eq_y_1)
    | ~ sP225(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_487,axiom,
    ( sP226(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP226(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_488,axiom,
    ( sP227(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP227(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_489,axiom,
    ( sP228(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP228(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_490,axiom,
    ( sP229(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP229(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_491,axiom,
    ( sP230(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP230(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_492,axiom,
    ( sP231(Eq_y_0,Eq_y_1)
    | ~ sP231(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_493,axiom,
    ( sP232(Eq_y_0,Eq_y_1)
    | ~ sP232(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_494,axiom,
    ( sP233(Eq_y_0,Eq_y_1)
    | ~ sP233(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_495,axiom,
    ( sP234(Eq_y_0,Eq_y_1)
    | ~ sP234(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_496,axiom,
    ( sP235(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP235(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_497,axiom,
    ( sP236(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP236(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_498,axiom,
    ( sP237(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP237(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_499,axiom,
    ( sP238(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP238(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_500,axiom,
    ( sP239(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP239(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_501,axiom,
    ( sP240(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP240(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_502,axiom,
    ( sP241(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP241(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_503,axiom,
    ( sP242(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP242(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_504,axiom,
    ( sP243(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP243(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_505,axiom,
    ( sP244(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP244(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_506,axiom,
    ( sP245(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP245(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_507,axiom,
    ( sP246(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP246(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_508,axiom,
    ( sP247(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP247(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_509,axiom,
    ( sP248(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP248(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_510,axiom,
    ( sP249(Eq_y_0,Eq_y_1)
    | ~ sP249(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_511,axiom,
    ( sP250(Eq_y_0,Eq_y_1)
    | ~ sP250(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_512,axiom,
    ( sP251(Eq_y_0,Eq_y_1)
    | ~ sP251(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_513,axiom,
    ( sP252(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP252(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_514,axiom,
    ( sP253(Eq_y_0,Eq_y_1)
    | ~ sP253(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_515,axiom,
    ( sP254(Eq_y_0,Eq_y_1)
    | ~ sP254(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_516,axiom,
    ( sP255(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP255(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_517,axiom,
    ( sP256(Eq_y_0,Eq_y_1)
    | ~ sP256(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_518,axiom,
    ( sP257(Eq_y_0,Eq_y_1)
    | ~ sP257(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_519,axiom,
    ( sP258(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP258(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_520,axiom,
    ( sP259(Eq_y_0,Eq_y_1)
    | ~ sP259(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_521,axiom,
    ( sP260(Eq_y_0,Eq_y_1)
    | ~ sP260(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_522,axiom,
    ( sP261(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP261(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_523,axiom,
    ( sP262(Eq_y_0,Eq_y_1)
    | ~ sP262(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_524,axiom,
    ( sP263(Eq_y_0,Eq_y_1)
    | ~ sP263(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_525,axiom,
    ( sP264(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP264(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_526,axiom,
    ( sP265(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP265(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_527,axiom,
    ( sP266(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP266(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_528,axiom,
    ( sP267(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP267(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_529,axiom,
    ( sP268(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP268(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_530,axiom,
    ( sP269(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP269(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_531,axiom,
    ( sP270(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP270(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_532,axiom,
    ( sP271(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP271(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_533,axiom,
    ( sP272(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP272(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_534,axiom,
    ( sP273(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP273(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_535,axiom,
    ( sP274(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP274(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_536,axiom,
    ( sP275(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP275(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_537,axiom,
    ( sP276(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP276(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_538,axiom,
    ( sP277(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP277(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_539,axiom,
    ( sP278(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP278(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_540,axiom,
    ( sP279(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP279(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_541,axiom,
    ( sP280(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP280(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_542,axiom,
    ( sP281(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP281(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_543,axiom,
    ( sP282(Eq_y_0)
    | ~ sP282(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_544,axiom,
    ( sP283(Eq_y_0)
    | ~ sP283(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_545,axiom,
    ( sP284(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP284(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_546,axiom,
    ( sP285(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP285(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_547,axiom,
    ( sP286(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP286(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_548,axiom,
    ( sP287(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP287(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_549,axiom,
    ( sP288(Eq_y_0)
    | ~ sP288(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_550,axiom,
    ( sP289(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP289(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_551,axiom,
    ( sP290(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP290(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_552,axiom,
    ( sP291(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7,Eq_y_8,Eq_y_9)
    | ~ sP291(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7,Eq_x_8,Eq_x_9)
    | Eq_x_9 != Eq_y_9
    | Eq_x_8 != Eq_y_8
    | Eq_x_7 != Eq_y_7
    | 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_553,axiom,
    ( sP292(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7,Eq_y_8,Eq_y_9)
    | ~ sP292(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7,Eq_x_8,Eq_x_9)
    | Eq_x_9 != Eq_y_9
    | Eq_x_8 != Eq_y_8
    | Eq_x_7 != Eq_y_7
    | 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_554,axiom,
    ( sP293(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP293(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_555,axiom,
    ( sP294(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP294(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_556,axiom,
    ( sP295(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP295(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_557,axiom,
    ( sP296(Eq_y_0,Eq_y_1)
    | ~ sP296(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_558,axiom,
    ( sP297(Eq_y_0,Eq_y_1)
    | ~ sP297(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_559,axiom,
    ( sP298(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP298(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_560,axiom,
    ( sP299(Eq_y_0,Eq_y_1)
    | ~ sP299(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_561,axiom,
    ( sP300(Eq_y_0,Eq_y_1)
    | ~ sP300(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_562,axiom,
    ( sP301(Eq_y_0,Eq_y_1)
    | ~ sP301(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_563,axiom,
    ( sP302(Eq_y_0,Eq_y_1)
    | ~ sP302(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_564,axiom,
    ( sP303(Eq_y_0,Eq_y_1)
    | ~ sP303(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_565,axiom,
    ( sP304(Eq_y_0,Eq_y_1)
    | ~ sP304(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_566,axiom,
    ( sP305(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP305(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_567,axiom,
    ( sP306(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP306(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_568,axiom,
    ( sP307(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP307(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_569,axiom,
    ( sP308(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP308(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_570,axiom,
    ( sP309(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP309(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_571,axiom,
    ( sP310(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP310(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_572,axiom,
    ( sP311(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP311(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(sat_proved,plain,
    $false,
    inference(cadical,[status(thm)],[]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SWW473+7 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.03  This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04  % Command  : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37  % Computer : n026.cluster.edu
% 0.10/0.37  % Model    : x86_64 x86_64
% 0.10/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37  % Memory   : 8046.5625MB
% 0.10/0.37  % OS       : Linux 6.8.0-71-generic
% 0.10/0.37  % CPULimit : 300
% 0.10/0.37  % WCLimit  : 300
% 0.10/0.37  % DateTime : Sun Sep 20 05:44:22 UTC 2026
% 0.10/0.37  % CPUTime  : 
% 273.54/273.86  % SZS status Theorem for theBenchmark
% 273.54/273.86  % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------