ConnectPP---0.7.2.THM-Prf.s

%------------------------------------------------------------------------------
% File     : ConnectPP---0.7.2
% Problem  : SWW473+5 : 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 : n020.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Sep 24 09:07:59 AM UTC 2026

% Result   : Theorem 4.02s 4.36s
% Output   : Proof 4.09s
% 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_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_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_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_Groups_Ominus__class_Ominus_res,hypothesis,
    ti(fun(nat,fun(nat,nat)),minus_minus(nat)) = minus_minus(nat),
    file('theBenchmark.p',tsy_c_Groups_Ominus__class_Ominus_res) ).

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

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

fof(tsy_c_Orderings_Oord__class_Oless__eq_res,axiom,
    ! [X_a] :
      ( preorder(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_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_fNot_res,axiom,
    ti(fun(bool,bool),fNot) = fNot,
    file('theBenchmark.p',tsy_c_fNot_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] : hAPP(X_a,X_c,ti(fun(X_a,X_c),B_1_1),B_2) = hAPP(X_a,X_c,B_1_1,B_2),
    file('theBenchmark.p',tsy_c_hAPP_arg1) ).

fof(tsy_c_hAPP_arg2,axiom,
    ! [X_a,X_c,B_1_1,B_2] : hAPP(X_a,X_c,B_1_1,ti(X_a,B_2)) = hAPP(X_a,X_c,B_1_1,B_2),
    file('theBenchmark.p',tsy_c_hAPP_arg2) ).

fof(tsy_c_hAPP_res,axiom,
    ! [X_c,X_a,B_1_1,B_2] : ti(X_c,hAPP(X_a,X_c,B_1_1,B_2)) = hAPP(X_a,X_c,B_1_1,B_2),
    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__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(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_1] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1))
     => 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_1)))) ),
    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_1] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1))
     => 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_1))) ),
    file('theBenchmark.p',fact_3_finite_OinsertI) ).

fof(fact_4_card__image__le,axiom,
    ! [X_c,X_b,F,A_1] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1))
     => 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_1))),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_1))) ),
    file('theBenchmark.p',fact_4_card__image__le) ).

fof(fact_5_card__mono,axiom,
    ! [X_b,A_1,B] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_1),B))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_1)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B))) ) ),
    file('theBenchmark.p',fact_5_card__mono) ).

fof(fact_6_card__seteq,axiom,
    ! [X_b,A_1,B] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_1),B))
       => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),B)),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_1)))
         => ti(fun(X_b,bool),A_1) = ti(fun(X_b,bool),B) ) ) ),
    file('theBenchmark.p',fact_6_card__seteq) ).

fof(fact_7_card__insert__le,axiom,
    ! [X_b,X_2,A_1] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_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_1)),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_2),A_1)))) ),
    file('theBenchmark.p',fact_7_card__insert__le) ).

fof(fact_8_card__insert__if,axiom,
    ! [X_b,X_2,A_1] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1))
     => ( ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1))
         => 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_2),A_1)) = hAPP(nat,nat,suc,hAPP(fun(X_b,bool),nat,finite_card(X_b),A_1)) )
        & ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1))
         => 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_2),A_1)) = hAPP(fun(X_b,bool),nat,finite_card(X_b),A_1) ) ) ),
    file('theBenchmark.p',fact_8_card__insert__if) ).

fof(fact_9_card__insert__disjoint,axiom,
    ! [X_b,X_2,A_1] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1))
     => ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1))
       => 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_2),A_1)) = hAPP(nat,nat,suc,hAPP(fun(X_b,bool),nat,finite_card(X_b),A_1)) ) ),
    file('theBenchmark.p',fact_9_card__insert__disjoint) ).

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

fof(fact_11_Suc__diff__le,axiom,
    ! [N_1,M_2] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M_2))
     => hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M_2)),N_1) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_2),N_1)) ),
    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_1] : hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1)) ),
    file('theBenchmark.p',fact_14_finite__code) ).

fof(fact_15_finite,axiom,
    ! [X_b] :
      ( finite_finite_1(X_b)
     => ! [A_1] : hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1)) ),
    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_1,Nat] :
      ( hAPP(nat,nat,suc,Nat_1) = hAPP(nat,nat,suc,Nat)
    <=> Nat_1 = Nat ),
    file('theBenchmark.p',fact_17_nat_Oinject) ).

fof(fact_18_Suc__n__not__n,axiom,
    ! [N_1] : hAPP(nat,nat,suc,N_1) != N_1,
    file('theBenchmark.p',fact_18_Suc__n__not__n) ).

fof(fact_19_n__not__Suc__n,axiom,
    ! [N_1] : N_1 != hAPP(nat,nat,suc,N_1),
    file('theBenchmark.p',fact_19_n__not__Suc__n) ).

fof(fact_20_le__antisym,axiom,
    ! [M_2,N_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_1))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M_2))
       => M_2 = N_1 ) ),
    file('theBenchmark.p',fact_20_le__antisym) ).

fof(fact_21_le__trans,axiom,
    ! [K_1,I_1,J] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),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_1),K_1)) ) ),
    file('theBenchmark.p',fact_21_le__trans) ).

fof(fact_22_eq__imp__le,axiom,
    ! [M_2,N_1] :
      ( M_2 = N_1
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_1)) ),
    file('theBenchmark.p',fact_22_eq__imp__le) ).

fof(fact_23_nat__le__linear,axiom,
    ! [M_2,N_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M_2))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_1)) ),
    file('theBenchmark.p',fact_23_nat__le__linear) ).

fof(fact_24_le__refl,axiom,
    ! [N_1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),N_1)),
    file('theBenchmark.p',fact_24_le__refl) ).

fof(fact_25_diff__commute,axiom,
    ! [I_1,J,K_1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J)),K_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),K_1)),J),
    file('theBenchmark.p',fact_25_diff__commute) ).

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

fof(fact_27_finite__insert,axiom,
    ! [X_b,A_2,A_1] :
      ( 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_1)))
    <=> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1)) ),
    file('theBenchmark.p',fact_27_finite__insert) ).

fof(fact_28_finite__subset,axiom,
    ! [X_b,A_1,B] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_1),B))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B))
       => hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1)) ) ),
    file('theBenchmark.p',fact_28_finite__subset) ).

fof(fact_29_rev__finite__subset,axiom,
    ! [X_b,A_1,B] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_1),B))
       => hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1)) ) ),
    file('theBenchmark.p',fact_29_rev__finite__subset) ).

fof(fact_30_Suc__leD,axiom,
    ! [M_2,N_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M_2)),N_1))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_1)) ),
    file('theBenchmark.p',fact_30_Suc__leD) ).

fof(fact_31_le__SucE,axiom,
    ! [M_2,N_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),hAPP(nat,nat,suc,N_1)))
     => ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_1))
       => M_2 = hAPP(nat,nat,suc,N_1) ) ),
    file('theBenchmark.p',fact_31_le__SucE) ).

fof(fact_32_le__SucI,axiom,
    ! [M_2,N_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_1))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),hAPP(nat,nat,suc,N_1))) ),
    file('theBenchmark.p',fact_32_le__SucI) ).

fof(fact_33_Suc__le__mono,axiom,
    ! [Na,M_3] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Na)),hAPP(nat,nat,suc,M_3)))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Na),M_3)) ),
    file('theBenchmark.p',fact_33_Suc__le__mono) ).

fof(fact_34_le__Suc__eq,axiom,
    ! [M_3,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),hAPP(nat,nat,suc,Na)))
    <=> ( M_3 = hAPP(nat,nat,suc,Na)
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),Na)) ) ),
    file('theBenchmark.p',fact_34_le__Suc__eq) ).

fof(fact_35_not__less__eq__eq,axiom,
    ! [M_3,Na] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),Na))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Na)),M_3)) ),
    file('theBenchmark.p',fact_35_not__less__eq__eq) ).

fof(fact_36_Suc__n__not__le__n,axiom,
    ! [N_1] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N_1)),N_1)),
    file('theBenchmark.p',fact_36_Suc__n__not__le__n) ).

fof(fact_37_Suc__diff__diff,axiom,
    ! [M_2,N_1,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_2)),N_1)),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_2),N_1)),K_1),
    file('theBenchmark.p',fact_37_Suc__diff__diff) ).

fof(fact_38_diff__Suc__Suc,axiom,
    ! [M_2,N_1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M_2)),hAPP(nat,nat,suc,N_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_2),N_1),
    file('theBenchmark.p',fact_38_diff__Suc__Suc) ).

fof(fact_39_le__diff__iff,axiom,
    ! [Na,K,M_3] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),M_3))
     => ( 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_3),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_3),Na)) ) ) ),
    file('theBenchmark.p',fact_39_le__diff__iff) ).

fof(fact_40_Nat_Odiff__diff__eq,axiom,
    ! [N_1,K_1,M_2] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),M_2))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N_1))
       => hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_2),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),K_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_2),N_1) ) ),
    file('theBenchmark.p',fact_40_Nat_Odiff__diff__eq) ).

fof(fact_41_eq__diff__iff,axiom,
    ! [Na,K,M_3] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),M_3))
     => ( 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_3),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Na),K)
        <=> M_3 = Na ) ) ),
    file('theBenchmark.p',fact_41_eq__diff__iff) ).

fof(fact_42_diff__diff__cancel,axiom,
    ! [I_1,N_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),N_1))
     => hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),I_1)) = I_1 ),
    file('theBenchmark.p',fact_42_diff__diff__cancel) ).

fof(fact_43_diff__le__mono,axiom,
    ! [L,M_2,N_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_1))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_2),L)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),L))) ),
    file('theBenchmark.p',fact_43_diff__le__mono) ).

fof(fact_44_diff__le__mono2,axiom,
    ! [L,M_2,N_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_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),L),N_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L),M_2))) ),
    file('theBenchmark.p',fact_44_diff__le__mono2) ).

fof(fact_45_diff__le__self,axiom,
    ! [M_2,N_1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_2),N_1)),M_2)),
    file('theBenchmark.p',fact_45_diff__le__self) ).

fof(fact_46_finite__surj,axiom,
    ! [X_c,X_b,B,F,A_1] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_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),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_1)))
       => hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),B)) ) ),
    file('theBenchmark.p',fact_46_finite__surj) ).

fof(fact_47_finite__subset__image,axiom,
    ! [X_c,X_b,F,A_1,B] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_1)))
       => ? [C_2] :
            ( ti(fun(X_b,bool),B) = hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),C_2)
            & hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),C_2))
            & hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_eq(fun(X_c,bool)),C_2),A_1)) ) ) ),
    file('theBenchmark.p',fact_47_finite__subset__image) ).

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

fof(fact_49_pigeonhole__infinite,axiom,
    ! [X_c,X_b,F,A_1] :
      ( ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_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),F),A_1)))
       => ? [X_1] :
            ( ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),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_1))),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_1))))))
            & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_1)) ) ) ),
    file('theBenchmark.p',fact_49_pigeonhole__infinite) ).

fof(fact_50_image__eqI,axiom,
    ! [X_b,X_c,A_1,B_1,F,X_2] :
      ( ti(X_b,B_1) = hAPP(X_c,X_b,F,X_2)
     => ( hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_2),A_1))
       => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),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_1))) ) ),
    file('theBenchmark.p',fact_50_image__eqI) ).

fof(fact_51_equalityI,axiom,
    ! [X_b,A_1,B] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_1),B))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B),A_1))
       => ti(fun(X_b,bool),A_1) = ti(fun(X_b,bool),B) ) ),
    file('theBenchmark.p',fact_51_equalityI) ).

fof(fact_52_subsetD,axiom,
    ! [X_b,C_1,A_1,B] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_1),B))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_1))
       => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B)) ) ),
    file('theBenchmark.p',fact_52_subsetD) ).

fof(fact_53_insertCI,axiom,
    ! [X_b,B_1,A_2,B] :
      ( ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),B))
       => ti(X_b,A_2) = ti(X_b,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_1),B))) ),
    file('theBenchmark.p',fact_53_insertCI) ).

fof(fact_54_insertE,axiom,
    ! [X_b,A_2,B_1,A_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_1),A_1)))
     => ( ti(X_b,A_2) != ti(X_b,B_1)
       => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_1)) ) ),
    file('theBenchmark.p',fact_54_insertE) ).

fof(fact_55_insertI1,axiom,
    ! [X_b,A_2,B] : hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B))),
    file('theBenchmark.p',fact_55_insertI1) ).

fof(fact_56_insert__compr,axiom,
    ! [X_b,A_2,B] : hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),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),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))),
    file('theBenchmark.p',fact_56_insert__compr) ).

fof(fact_57_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_57_insert__Collect) ).

fof(fact_58_insert__absorb2,axiom,
    ! [X_b,X_2,A_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),X_2),A_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),A_1),
    file('theBenchmark.p',fact_58_insert__absorb2) ).

fof(fact_59_insert__commute,axiom,
    ! [X_b,X_2,Y_2,A_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_2),A_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),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),A_1)),
    file('theBenchmark.p',fact_59_insert__commute) ).

fof(fact_60_insert__iff,axiom,
    ! [X_b,A_2,B_1,A_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_1),A_1)))
    <=> ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_1))
        | ti(X_b,A_2) = ti(X_b,B_1) ) ),
    file('theBenchmark.p',fact_60_insert__iff) ).

fof(fact_61_insert__code,axiom,
    ! [X_b,Y_2,A_1,X_2] :
      ( 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_1),X_2))
    <=> ( hBOOL(hAPP(X_b,bool,A_1,X_2))
        | ti(X_b,Y_2) = ti(X_b,X_2) ) ),
    file('theBenchmark.p',fact_61_insert__code) ).

fof(fact_62_insert__ident,axiom,
    ! [X_b,B,X_2,A_1] :
      ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1))
     => ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B))
       => ( hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),A_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),B)
        <=> ti(fun(X_b,bool),A_1) = ti(fun(X_b,bool),B) ) ) ),
    file('theBenchmark.p',fact_62_insert__ident) ).

fof(fact_63_insertI2,axiom,
    ! [X_b,B_1,A_2,B] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),B))
     => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_1),B))) ),
    file('theBenchmark.p',fact_63_insertI2) ).

fof(fact_64_insert__absorb,axiom,
    ! [X_b,A_2,A_1] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_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),A_1) = ti(fun(X_b,bool),A_1) ),
    file('theBenchmark.p',fact_64_insert__absorb) ).

fof(fact_65_subset__refl,axiom,
    ! [X_b,A_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_1),A_1)),
    file('theBenchmark.p',fact_65_subset__refl) ).

fof(fact_66_set__eq__subset,axiom,
    ! [X_b,A_1,B] :
      ( ti(fun(X_b,bool),A_1) = ti(fun(X_b,bool),B)
    <=> ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B),A_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_1),B)) ) ),
    file('theBenchmark.p',fact_66_set__eq__subset) ).

fof(fact_67_equalityD1,axiom,
    ! [X_b,A_1,B] :
      ( ti(fun(X_b,bool),A_1) = ti(fun(X_b,bool),B)
     => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_1),B)) ),
    file('theBenchmark.p',fact_67_equalityD1) ).

fof(fact_68_equalityD2,axiom,
    ! [X_b,A_1,B] :
      ( ti(fun(X_b,bool),A_1) = ti(fun(X_b,bool),B)
     => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B),A_1)) ),
    file('theBenchmark.p',fact_68_equalityD2) ).

fof(fact_69_in__mono,axiom,
    ! [X_b,X_2,A_1,B] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_1),B))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1))
       => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B)) ) ),
    file('theBenchmark.p',fact_69_in__mono) ).

fof(fact_70_set__rev__mp,axiom,
    ! [X_b,B,X_2,A_1] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_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_1),B))
       => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B)) ) ),
    file('theBenchmark.p',fact_70_set__rev__mp) ).

fof(fact_71_set__mp,axiom,
    ! [X_b,X_2,A_1,B] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_1),B))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1))
       => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B)) ) ),
    file('theBenchmark.p',fact_71_set__mp) ).

fof(fact_72_subset__trans,axiom,
    ! [X_b,C,A_1,B] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_1),B))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B),C))
       => hBOOL(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_1),C)) ) ),
    file('theBenchmark.p',fact_72_subset__trans) ).

fof(fact_73_equalityE,axiom,
    ! [X_b,A_1,B] :
      ( ti(fun(X_b,bool),A_1) = ti(fun(X_b,bool),B)
     => ~ ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_1),B))
         => ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B),A_1)) ) ),
    file('theBenchmark.p',fact_73_equalityE) ).

fof(fact_74_ext,axiom,
    ! [X_b,X_c,F,G] :
      ( ! [X_1] : hAPP(X_b,X_c,F,X_1) = hAPP(X_b,X_c,G,X_1)
     => 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_2,A_1] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1))
    <=> hBOOL(hAPP(X_b,bool,A_1,X_2)) ),
    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_image__iff,axiom,
    ! [X_b,X_c,Z,F,A_1] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Z),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_1)))
    <=> ? [X_1] :
          ( ti(X_b,Z) = 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_1)) ) ),
    file('theBenchmark.p',fact_77_image__iff) ).

fof(fact_78_imageI,axiom,
    ! [X_c,X_b,F,X_2,A_1] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1))
     => 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)),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_1))) ),
    file('theBenchmark.p',fact_78_imageI) ).

fof(fact_79_rev__image__eqI,axiom,
    ! [X_c,X_b,B_1,F,X_2,A_1] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1))
     => ( ti(X_c,B_1) = hAPP(X_b,X_c,F,X_2)
       => hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),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_1))) ) ),
    file('theBenchmark.p',fact_79_rev__image__eqI) ).

fof(fact_80_insert__compr__raw,axiom,
    ! [X_b,X_1,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_1),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_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)),Xa))),
    file('theBenchmark.p',fact_80_insert__compr__raw) ).

fof(fact_81_image__image,axiom,
    ! [X_c,X_b,X_d,F,G,A_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_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_1)) = 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_1),
    file('theBenchmark.p',fact_81_image__image) ).

fof(fact_82_image__ident,axiom,
    ! [X_b,Y_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),combi(X_b)),Y_1) = ti(fun(X_b,bool),Y_1),
    file('theBenchmark.p',fact_82_image__ident) ).

fof(fact_83_subset__insertI,axiom,
    ! [X_b,B,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),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))),
    file('theBenchmark.p',fact_83_subset__insertI) ).

fof(fact_84_insert__subset,axiom,
    ! [X_b,X_2,A_1,B] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),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),A_1)),B))
    <=> ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_1),B))
        & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B)) ) ),
    file('theBenchmark.p',fact_84_insert__subset) ).

fof(fact_85_subset__insert,axiom,
    ! [X_b,B,X_2,A_1] :
      ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_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_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),B)))
      <=> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_1),B)) ) ),
    file('theBenchmark.p',fact_85_subset__insert) ).

fof(fact_86_subset__insertI2,axiom,
    ! [X_b,B_1,A_1,B] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_1),B))
     => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_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),B_1),B))) ),
    file('theBenchmark.p',fact_86_subset__insertI2) ).

fof(fact_87_insert__mono,axiom,
    ! [X_b,A_2,C,D] :
      ( hBOOL(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),D))
     => hBOOL(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)),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))) ),
    file('theBenchmark.p',fact_87_insert__mono) ).

fof(fact_88_image__insert,axiom,
    ! [X_c,X_b,F,A_2,B] : hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),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)) = 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)),
    file('theBenchmark.p',fact_88_image__insert) ).

fof(fact_89_insert__image,axiom,
    ! [X_c,X_b,F,X_2,A_1] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_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),hAPP(X_b,X_c,F,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),A_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_1) ),
    file('theBenchmark.p',fact_89_insert__image) ).

fof(fact_90_subset__image__iff,axiom,
    ! [X_b,X_c,B,F,A_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),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_1)))
    <=> ? [AA] :
          ( ti(fun(X_b,bool),B) = hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),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_1)) ) ),
    file('theBenchmark.p',fact_90_subset__image__iff) ).

fof(fact_91_image__mono,axiom,
    ! [X_c,X_b,F,A_1,B] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_1),B))
     => 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_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),B))) ),
    file('theBenchmark.p',fact_91_image__mono) ).

fof(fact_92_imageE,axiom,
    ! [X_b,X_c,B_1,F,A_1] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),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_1)))
     => ~ ! [X_1] :
            ( ti(X_b,B_1) = 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_1)) ) ),
    file('theBenchmark.p',fact_92_imageE) ).

fof(fact_93_subsetI,axiom,
    ! [X_b,B,A_1] :
      ( ! [X_1] :
          ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_1))
         => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B)) )
     => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_1),B)) ),
    file('theBenchmark.p',fact_93_subsetI) ).

fof(fact_94_zero__induct__lemma,axiom,
    ! [I,Pa,K] :
      ( hBOOL(hAPP(nat,bool,Pa,K))
     => ( ! [N_2] :
            ( hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,N_2)))
           => hBOOL(hAPP(nat,bool,Pa,N_2)) )
       => hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),K),I))) ) ),
    file('theBenchmark.p',fact_94_zero__induct__lemma) ).

fof(fact_95_Suc__le__D,axiom,
    ! [N_1,M_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N_1)),M_1))
     => ? [M] : M_1 = hAPP(nat,nat,suc,M) ),
    file('theBenchmark.p',fact_95_Suc__le__D) ).

fof(fact_96_image__subsetI,axiom,
    ! [X_c,X_b,F,B,A_1] :
      ( ! [X_1] :
          ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_1))
         => 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)),B)) )
     => 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_1)),B)) ),
    file('theBenchmark.p',fact_96_image__subsetI) ).

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

fof(fact_98_finite__nat__set__iff__bounded__le,axiom,
    ! [N] :
      ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),N))
    <=> ? [M] :
        ! [X_1] :
          ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_1),N))
         => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X_1),M)) ) ),
    file('theBenchmark.p',fact_98_finite__nat__set__iff__bounded__le) ).

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

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

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

fof(help_fNot_1_1_U,axiom,
    ! [P] :
      ( ~ hBOOL(P)
      | ~ hBOOL(hAPP(bool,bool,fNot,P)) ),
    file('theBenchmark.p',help_fNot_1_1_U) ).

fof(help_fNot_2_1_U,axiom,
    ! [P] :
      ( hBOOL(hAPP(bool,bool,fNot,P))
      | hBOOL(P) ),
    file('theBenchmark.p',help_fNot_2_1_U) ).

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

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

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

fof(help_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_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]) ).

cnf(f_1_3,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_2]) ).

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]) ).

cnf(f_2_3,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_2]) ).

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]) ).

cnf(f_3_3,plain,
    ti(fun(U_6,U_6),combi(U_6)) = combi(U_6),
    inference(clausify,[status(thm)],[f_3_2]) ).

fof(f_4_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_4_2,plain,
    ! [U_9,U_8,U_7] : ti(fun(fun(U_9,fun(U_8,U_7)),fun(fun(U_9,U_8),fun(U_9,U_7))),combs(U_9,U_8,U_7)) = combs(U_9,U_8,U_7),
    inference(variable_rename,[status(thm)],[f_4_1]) ).

cnf(f_4_3,plain,
    ti(fun(fun(U_9,fun(U_8,U_7)),fun(fun(U_9,U_8),fun(U_9,U_7))),combs(U_9,U_8,U_7)) = combs(U_9,U_8,U_7),
    inference(clausify,[status(thm)],[f_4_2]) ).

fof(f_5_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_5_2,plain,
    ! [U_10] : ti(fun(fun(U_10,bool),nat),finite_card(U_10)) = finite_card(U_10),
    inference(variable_rename,[status(thm)],[f_5_1]) ).

cnf(f_5_3,plain,
    ti(fun(fun(U_10,bool),nat),finite_card(U_10)) = finite_card(U_10),
    inference(clausify,[status(thm)],[f_5_2]) ).

fof(f_6_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_6_2,plain,
    ! [U_11] : ti(fun(fun(U_11,bool),bool),finite_finite(U_11)) = finite_finite(U_11),
    inference(variable_rename,[status(thm)],[f_6_1]) ).

cnf(f_6_3,plain,
    ti(fun(fun(U_11,bool),bool),finite_finite(U_11)) = finite_finite(U_11),
    inference(clausify,[status(thm)],[f_6_2]) ).

fof(f_7_1,plain,
    ti(fun(nat,fun(nat,nat)),minus_minus(nat)) = minus_minus(nat),
    inference(fof_nnf,[status(thm)],[tsy_c_Groups_Ominus__class_Ominus_res]) ).

cnf(f_7_2,plain,
    ti(fun(nat,fun(nat,nat)),minus_minus(nat)) = minus_minus(nat),
    inference(clausify,[status(thm)],[f_7_1]) ).

fof(f_8_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_8_2,plain,
    ! [U_12] : ti(U_12,undefined(U_12)) = undefined(U_12),
    inference(variable_rename,[status(thm)],[f_8_1]) ).

cnf(f_8_3,plain,
    ti(U_12,undefined(U_12)) = undefined(U_12),
    inference(clausify,[status(thm)],[f_8_2]) ).

fof(f_9_1,plain,
    ti(fun(nat,nat),suc) = suc,
    inference(fof_nnf,[status(thm)],[tsy_c_Nat_OSuc_res]) ).

cnf(f_9_2,plain,
    ti(fun(nat,nat),suc) = suc,
    inference(clausify,[status(thm)],[f_9_1]) ).

fof(f_10_1,plain,
    ! [X_a] :
      ( ti(fun(X_a,fun(X_a,bool)),ord_less_eq(X_a)) = ord_less_eq(X_a)
      | ~ preorder(X_a) ),
    inference(fof_nnf,[status(thm)],[tsy_c_Orderings_Oord__class_Oless__eq_res]) ).

fof(f_10_2,plain,
    ! [U_13] :
      ( ti(fun(U_13,fun(U_13,bool)),ord_less_eq(U_13)) = ord_less_eq(U_13)
      | ~ preorder(U_13) ),
    inference(variable_rename,[status(thm)],[f_10_1]) ).

cnf(f_10_3,plain,
    ( ti(fun(U_13,fun(U_13,bool)),ord_less_eq(U_13)) = ord_less_eq(U_13)
    | ~ preorder(U_13) ),
    inference(clausify,[status(thm)],[f_10_2]) ).

fof(f_11_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_11_2,plain,
    ! [U_14] : ti(fun(fun(U_14,bool),fun(U_14,bool)),collect(U_14)) = collect(U_14),
    inference(variable_rename,[status(thm)],[f_11_1]) ).

cnf(f_11_3,plain,
    ti(fun(fun(U_14,bool),fun(U_14,bool)),collect(U_14)) = collect(U_14),
    inference(clausify,[status(thm)],[f_11_2]) ).

fof(f_12_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_12_2,plain,
    ! [U_16,U_15] : ti(fun(fun(U_16,U_15),fun(fun(U_16,bool),fun(U_15,bool))),image(U_16,U_15)) = image(U_16,U_15),
    inference(variable_rename,[status(thm)],[f_12_1]) ).

cnf(f_12_3,plain,
    ti(fun(fun(U_16,U_15),fun(fun(U_16,bool),fun(U_15,bool))),image(U_16,U_15)) = image(U_16,U_15),
    inference(clausify,[status(thm)],[f_12_2]) ).

fof(f_13_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_13_2,plain,
    ! [U_17] : ti(fun(U_17,fun(fun(U_17,bool),fun(U_17,bool))),insert(U_17)) = insert(U_17),
    inference(variable_rename,[status(thm)],[f_13_1]) ).

cnf(f_13_3,plain,
    ti(fun(U_17,fun(fun(U_17,bool),fun(U_17,bool))),insert(U_17)) = insert(U_17),
    inference(clausify,[status(thm)],[f_13_2]) ).

fof(f_14_1,plain,
    ti(fun(bool,bool),fNot) = fNot,
    inference(fof_nnf,[status(thm)],[tsy_c_fNot_res]) ).

cnf(f_14_2,plain,
    ti(fun(bool,bool),fNot) = fNot,
    inference(clausify,[status(thm)],[f_14_1]) ).

fof(f_15_1,plain,
    ti(fun(bool,fun(bool,bool)),fconj) = fconj,
    inference(fof_nnf,[status(thm)],[tsy_c_fconj_res]) ).

cnf(f_15_2,plain,
    ti(fun(bool,fun(bool,bool)),fconj) = fconj,
    inference(clausify,[status(thm)],[f_15_1]) ).

fof(f_16_1,plain,
    ti(fun(bool,fun(bool,bool)),fdisj) = fdisj,
    inference(fof_nnf,[status(thm)],[tsy_c_fdisj_res]) ).

cnf(f_16_2,plain,
    ti(fun(bool,fun(bool,bool)),fdisj) = fdisj,
    inference(clausify,[status(thm)],[f_16_1]) ).

fof(f_17_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_17_2,plain,
    ! [U_18] : ti(fun(U_18,fun(U_18,bool)),fequal(U_18)) = fequal(U_18),
    inference(variable_rename,[status(thm)],[f_17_1]) ).

cnf(f_17_3,plain,
    ti(fun(U_18,fun(U_18,bool)),fequal(U_18)) = fequal(U_18),
    inference(clausify,[status(thm)],[f_17_2]) ).

fof(f_18_1,plain,
    ti(fun(bool,fun(bool,bool)),fimplies) = fimplies,
    inference(fof_nnf,[status(thm)],[tsy_c_fimplies_res]) ).

cnf(f_18_2,plain,
    ti(fun(bool,fun(bool,bool)),fimplies) = fimplies,
    inference(clausify,[status(thm)],[f_18_1]) ).

fof(f_19_1,plain,
    ! [X_a,X_c,B_1_1,B_2] : hAPP(X_a,X_c,ti(fun(X_a,X_c),B_1_1),B_2) = hAPP(X_a,X_c,B_1_1,B_2),
    inference(fof_nnf,[status(thm)],[tsy_c_hAPP_arg1]) ).

fof(f_19_2,plain,
    ! [U_22,U_21,U_20,U_19] : hAPP(U_22,U_21,ti(fun(U_22,U_21),U_20),U_19) = hAPP(U_22,U_21,U_20,U_19),
    inference(variable_rename,[status(thm)],[f_19_1]) ).

cnf(f_19_3,plain,
    hAPP(U_22,U_21,ti(fun(U_22,U_21),U_20),U_19) = hAPP(U_22,U_21,U_20,U_19),
    inference(clausify,[status(thm)],[f_19_2]) ).

fof(f_20_1,plain,
    ! [X_a,X_c,B_1_1,B_2] : hAPP(X_a,X_c,B_1_1,ti(X_a,B_2)) = hAPP(X_a,X_c,B_1_1,B_2),
    inference(fof_nnf,[status(thm)],[tsy_c_hAPP_arg2]) ).

fof(f_20_2,plain,
    ! [U_26,U_25,U_24,U_23] : hAPP(U_26,U_25,U_24,ti(U_26,U_23)) = hAPP(U_26,U_25,U_24,U_23),
    inference(variable_rename,[status(thm)],[f_20_1]) ).

cnf(f_20_3,plain,
    hAPP(U_26,U_25,U_24,ti(U_26,U_23)) = hAPP(U_26,U_25,U_24,U_23),
    inference(clausify,[status(thm)],[f_20_2]) ).

fof(f_21_1,plain,
    ! [X_c,X_a,B_1_1,B_2] : ti(X_c,hAPP(X_a,X_c,B_1_1,B_2)) = hAPP(X_a,X_c,B_1_1,B_2),
    inference(fof_nnf,[status(thm)],[tsy_c_hAPP_res]) ).

fof(f_21_2,plain,
    ! [U_30,U_29,U_28,U_27] : ti(U_30,hAPP(U_29,U_30,U_28,U_27)) = hAPP(U_29,U_30,U_28,U_27),
    inference(variable_rename,[status(thm)],[f_21_1]) ).

cnf(f_21_3,plain,
    ti(U_30,hAPP(U_29,U_30,U_28,U_27)) = hAPP(U_29,U_30,U_28,U_27),
    inference(clausify,[status(thm)],[f_21_2]) ).

fof(f_22_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_22_2,plain,
    ! [U_31] :
      ( ( hBOOL(ti(bool,U_31))
        | ~ hBOOL(U_31) )
      & ( hBOOL(U_31)
        | ~ hBOOL(ti(bool,U_31)) ) ),
    inference(variable_rename,[status(thm)],[f_22_1]) ).

fof(f_22_3,plain,
    ( ! [U_33] :
        ( hBOOL(ti(bool,U_33))
        | ~ hBOOL(U_33) )
    & ! [U_32] :
        ( hBOOL(U_32)
        | ~ hBOOL(ti(bool,U_32)) ) ),
    inference(miniscope,[status(thm)],[f_22_2]) ).

cnf(f_22_4,plain,
    ( hBOOL(U_32)
    | ~ hBOOL(ti(bool,U_32)) ),
    inference(clausify,[status(thm)],[f_22_3]) ).

cnf(f_22_5,plain,
    ( hBOOL(ti(bool,U_33))
    | ~ hBOOL(U_33) ),
    inference(clausify,[status(thm)],[f_22_3]) ).

fof(f_23_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_23_2,plain,
    ! [U_34] : ti(fun(U_34,fun(fun(U_34,bool),bool)),member(U_34)) = member(U_34),
    inference(variable_rename,[status(thm)],[f_23_1]) ).

cnf(f_23_3,plain,
    ti(fun(U_34,fun(fun(U_34,bool),bool)),member(U_34)) = member(U_34),
    inference(clausify,[status(thm)],[f_23_2]) ).

fof(f_24_1,plain,
    ti(fun(x_a,bool),g) = g,
    inference(fof_nnf,[status(thm)],[tsy_v_G_res]) ).

cnf(f_24_2,plain,
    ti(fun(x_a,bool),g) = g,
    inference(clausify,[status(thm)],[f_24_1]) ).

fof(f_25_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]) ).

cnf(f_25_2,plain,
    ti(fun(fun(x_a,bool),fun(fun(x_a,bool),bool)),p) = p,
    inference(clausify,[status(thm)],[f_25_1]) ).

fof(f_26_1,plain,
    ti(fun(pname,bool),u) = u,
    inference(fof_nnf,[status(thm)],[tsy_v_U_res]) ).

cnf(f_26_2,plain,
    ti(fun(pname,bool),u) = u,
    inference(clausify,[status(thm)],[f_26_1]) ).

fof(f_27_1,plain,
    ti(fun(pname,x_a),mgt_call) = mgt_call,
    inference(fof_nnf,[status(thm)],[tsy_v_mgt__call_res]) ).

cnf(f_27_2,plain,
    ti(fun(pname,x_a),mgt_call) = mgt_call,
    inference(clausify,[status(thm)],[f_27_1]) ).

fof(f_28_1,plain,
    ti(nat,na) = na,
    inference(fof_nnf,[status(thm)],[tsy_v_na_res]) ).

cnf(f_28_2,plain,
    ti(nat,na) = na,
    inference(clausify,[status(thm)],[f_28_1]) ).

fof(f_29_1,plain,
    ti(pname,pn) = pn,
    inference(fof_nnf,[status(thm)],[tsy_v_pn_res]) ).

cnf(f_29_2,plain,
    ti(pname,pn) = pn,
    inference(clausify,[status(thm)],[f_29_1]) ).

fof(f_30_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_30_2,plain,
    ! [U_36,U_35] :
      ( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,U_35),U_36))
      | ~ 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_36),U_35)) ),
    inference(variable_rename,[status(thm)],[f_30_1]) ).

cnf(f_30_3,plain,
    ( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,U_35),U_36))
    | ~ 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_36),U_35)) ),
    inference(clausify,[status(thm)],[f_30_2]) ).

fof(f_31_1,plain,
    ! [X_b,A_1] :
      ( 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_1))))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_1_finite__Collect__subsets]) ).

fof(f_31_2,plain,
    ! [U_38,U_37] :
      ( hBOOL(hAPP(fun(fun(U_38,bool),bool),bool,finite_finite(fun(U_38,bool)),hAPP(fun(fun(U_38,bool),bool),fun(fun(U_38,bool),bool),collect(fun(U_38,bool)),hAPP(fun(U_38,bool),fun(fun(U_38,bool),bool),hAPP(fun(fun(U_38,bool),fun(fun(U_38,bool),bool)),fun(fun(U_38,bool),fun(fun(U_38,bool),bool)),combc(fun(U_38,bool),fun(U_38,bool),bool),ord_less_eq(fun(U_38,bool))),U_37))))
      | ~ hBOOL(hAPP(fun(U_38,bool),bool,finite_finite(U_38),U_37)) ),
    inference(variable_rename,[status(thm)],[f_31_1]) ).

cnf(f_31_3,plain,
    ( hBOOL(hAPP(fun(fun(U_38,bool),bool),bool,finite_finite(fun(U_38,bool)),hAPP(fun(fun(U_38,bool),bool),fun(fun(U_38,bool),bool),collect(fun(U_38,bool)),hAPP(fun(U_38,bool),fun(fun(U_38,bool),bool),hAPP(fun(fun(U_38,bool),fun(fun(U_38,bool),bool)),fun(fun(U_38,bool),fun(fun(U_38,bool),bool)),combc(fun(U_38,bool),fun(U_38,bool),bool),ord_less_eq(fun(U_38,bool))),U_37))))
    | ~ hBOOL(hAPP(fun(U_38,bool),bool,finite_finite(U_38),U_37)) ),
    inference(clausify,[status(thm)],[f_31_2]) ).

fof(f_32_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_32_2,plain,
    ! [U_42,U_41,U_40,U_39] :
      ( hBOOL(hAPP(fun(U_42,bool),bool,finite_finite(U_42),hAPP(fun(U_41,bool),fun(U_42,bool),hAPP(fun(U_41,U_42),fun(fun(U_41,bool),fun(U_42,bool)),image(U_41,U_42),U_40),U_39)))
      | ~ hBOOL(hAPP(fun(U_41,bool),bool,finite_finite(U_41),U_39)) ),
    inference(variable_rename,[status(thm)],[f_32_1]) ).

cnf(f_32_3,plain,
    ( hBOOL(hAPP(fun(U_42,bool),bool,finite_finite(U_42),hAPP(fun(U_41,bool),fun(U_42,bool),hAPP(fun(U_41,U_42),fun(fun(U_41,bool),fun(U_42,bool)),image(U_41,U_42),U_40),U_39)))
    | ~ hBOOL(hAPP(fun(U_41,bool),bool,finite_finite(U_41),U_39)) ),
    inference(clausify,[status(thm)],[f_32_2]) ).

fof(f_33_1,plain,
    ! [X_b,A_2,A_1] :
      ( 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_1)))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_3_finite_OinsertI]) ).

fof(f_33_2,plain,
    ! [U_45,U_44,U_43] :
      ( hBOOL(hAPP(fun(U_45,bool),bool,finite_finite(U_45),hAPP(fun(U_45,bool),fun(U_45,bool),hAPP(U_45,fun(fun(U_45,bool),fun(U_45,bool)),insert(U_45),U_44),U_43)))
      | ~ hBOOL(hAPP(fun(U_45,bool),bool,finite_finite(U_45),U_43)) ),
    inference(variable_rename,[status(thm)],[f_33_1]) ).

cnf(f_33_3,plain,
    ( hBOOL(hAPP(fun(U_45,bool),bool,finite_finite(U_45),hAPP(fun(U_45,bool),fun(U_45,bool),hAPP(U_45,fun(fun(U_45,bool),fun(U_45,bool)),insert(U_45),U_44),U_43)))
    | ~ hBOOL(hAPP(fun(U_45,bool),bool,finite_finite(U_45),U_43)) ),
    inference(clausify,[status(thm)],[f_33_2]) ).

fof(f_34_1,plain,
    ! [X_c,X_b,F,A_1] :
      ( 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_1))),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_1)))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_4_card__image__le]) ).

fof(f_34_2,plain,
    ! [U_49,U_48,U_47,U_46] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(U_49,bool),nat,finite_card(U_49),hAPP(fun(U_48,bool),fun(U_49,bool),hAPP(fun(U_48,U_49),fun(fun(U_48,bool),fun(U_49,bool)),image(U_48,U_49),U_47),U_46))),hAPP(fun(U_48,bool),nat,finite_card(U_48),U_46)))
      | ~ hBOOL(hAPP(fun(U_48,bool),bool,finite_finite(U_48),U_46)) ),
    inference(variable_rename,[status(thm)],[f_34_1]) ).

cnf(f_34_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(U_49,bool),nat,finite_card(U_49),hAPP(fun(U_48,bool),fun(U_49,bool),hAPP(fun(U_48,U_49),fun(fun(U_48,bool),fun(U_49,bool)),image(U_48,U_49),U_47),U_46))),hAPP(fun(U_48,bool),nat,finite_card(U_48),U_46)))
    | ~ hBOOL(hAPP(fun(U_48,bool),bool,finite_finite(U_48),U_46)) ),
    inference(clausify,[status(thm)],[f_34_2]) ).

fof(f_35_1,plain,
    ! [X_b,A_1,B] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_1)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B)))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_1),B))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B)) ),
    inference(fof_nnf,[status(thm)],[fact_5_card__mono]) ).

fof(f_35_2,plain,
    ! [U_52,U_51,U_50] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(U_52,bool),nat,finite_card(U_52),U_51)),hAPP(fun(U_52,bool),nat,finite_card(U_52),U_50)))
      | ~ hBOOL(hAPP(fun(U_52,bool),bool,hAPP(fun(U_52,bool),fun(fun(U_52,bool),bool),ord_less_eq(fun(U_52,bool)),U_51),U_50))
      | ~ hBOOL(hAPP(fun(U_52,bool),bool,finite_finite(U_52),U_50)) ),
    inference(variable_rename,[status(thm)],[f_35_1]) ).

cnf(f_35_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(U_52,bool),nat,finite_card(U_52),U_51)),hAPP(fun(U_52,bool),nat,finite_card(U_52),U_50)))
    | ~ hBOOL(hAPP(fun(U_52,bool),bool,hAPP(fun(U_52,bool),fun(fun(U_52,bool),bool),ord_less_eq(fun(U_52,bool)),U_51),U_50))
    | ~ hBOOL(hAPP(fun(U_52,bool),bool,finite_finite(U_52),U_50)) ),
    inference(clausify,[status(thm)],[f_35_2]) ).

fof(f_36_1,plain,
    ! [X_b,A_1,B] :
      ( ti(fun(X_b,bool),A_1) = ti(fun(X_b,bool),B)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),B)),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_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_1),B))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B)) ),
    inference(fof_nnf,[status(thm)],[fact_6_card__seteq]) ).

fof(f_36_2,plain,
    ! [U_55,U_54,U_53] :
      ( ti(fun(U_55,bool),U_54) = ti(fun(U_55,bool),U_53)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(U_55,bool),nat,finite_card(U_55),U_53)),hAPP(fun(U_55,bool),nat,finite_card(U_55),U_54)))
      | ~ hBOOL(hAPP(fun(U_55,bool),bool,hAPP(fun(U_55,bool),fun(fun(U_55,bool),bool),ord_less_eq(fun(U_55,bool)),U_54),U_53))
      | ~ hBOOL(hAPP(fun(U_55,bool),bool,finite_finite(U_55),U_53)) ),
    inference(variable_rename,[status(thm)],[f_36_1]) ).

cnf(f_36_3,plain,
    ( ti(fun(U_55,bool),U_54) = ti(fun(U_55,bool),U_53)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(U_55,bool),nat,finite_card(U_55),U_53)),hAPP(fun(U_55,bool),nat,finite_card(U_55),U_54)))
    | ~ hBOOL(hAPP(fun(U_55,bool),bool,hAPP(fun(U_55,bool),fun(fun(U_55,bool),bool),ord_less_eq(fun(U_55,bool)),U_54),U_53))
    | ~ hBOOL(hAPP(fun(U_55,bool),bool,finite_finite(U_55),U_53)) ),
    inference(clausify,[status(thm)],[f_36_2]) ).

fof(f_37_1,plain,
    ! [X_b,X_2,A_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_1)),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_2),A_1))))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_7_card__insert__le]) ).

fof(f_37_2,plain,
    ! [U_58,U_57,U_56] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(U_58,bool),nat,finite_card(U_58),U_56)),hAPP(fun(U_58,bool),nat,finite_card(U_58),hAPP(fun(U_58,bool),fun(U_58,bool),hAPP(U_58,fun(fun(U_58,bool),fun(U_58,bool)),insert(U_58),U_57),U_56))))
      | ~ hBOOL(hAPP(fun(U_58,bool),bool,finite_finite(U_58),U_56)) ),
    inference(variable_rename,[status(thm)],[f_37_1]) ).

cnf(f_37_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(U_58,bool),nat,finite_card(U_58),U_56)),hAPP(fun(U_58,bool),nat,finite_card(U_58),hAPP(fun(U_58,bool),fun(U_58,bool),hAPP(U_58,fun(fun(U_58,bool),fun(U_58,bool)),insert(U_58),U_57),U_56))))
    | ~ hBOOL(hAPP(fun(U_58,bool),bool,finite_finite(U_58),U_56)) ),
    inference(clausify,[status(thm)],[f_37_2]) ).

fof(f_38_1,plain,
    ! [X_b,X_2,A_1] :
      ( ( ( 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_2),A_1)) = hAPP(nat,nat,suc,hAPP(fun(X_b,bool),nat,finite_card(X_b),A_1))
          | hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1)) )
        & ( 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_2),A_1)) = hAPP(fun(X_b,bool),nat,finite_card(X_b),A_1)
          | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1)) ) )
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_8_card__insert__if]) ).

fof(f_38_2,plain,
    ! [U_61,U_60,U_59] :
      ( ( ( hAPP(fun(U_61,bool),nat,finite_card(U_61),hAPP(fun(U_61,bool),fun(U_61,bool),hAPP(U_61,fun(fun(U_61,bool),fun(U_61,bool)),insert(U_61),U_60),U_59)) = hAPP(nat,nat,suc,hAPP(fun(U_61,bool),nat,finite_card(U_61),U_59))
          | hBOOL(hAPP(fun(U_61,bool),bool,hAPP(U_61,fun(fun(U_61,bool),bool),member(U_61),U_60),U_59)) )
        & ( hAPP(fun(U_61,bool),nat,finite_card(U_61),hAPP(fun(U_61,bool),fun(U_61,bool),hAPP(U_61,fun(fun(U_61,bool),fun(U_61,bool)),insert(U_61),U_60),U_59)) = hAPP(fun(U_61,bool),nat,finite_card(U_61),U_59)
          | ~ hBOOL(hAPP(fun(U_61,bool),bool,hAPP(U_61,fun(fun(U_61,bool),bool),member(U_61),U_60),U_59)) ) )
      | ~ hBOOL(hAPP(fun(U_61,bool),bool,finite_finite(U_61),U_59)) ),
    inference(variable_rename,[status(thm)],[f_38_1]) ).

cnf(f_38_3,plain,
    ( hAPP(fun(U_61,bool),nat,finite_card(U_61),hAPP(fun(U_61,bool),fun(U_61,bool),hAPP(U_61,fun(fun(U_61,bool),fun(U_61,bool)),insert(U_61),U_60),U_59)) = hAPP(fun(U_61,bool),nat,finite_card(U_61),U_59)
    | ~ hBOOL(hAPP(fun(U_61,bool),bool,hAPP(U_61,fun(fun(U_61,bool),bool),member(U_61),U_60),U_59))
    | ~ hBOOL(hAPP(fun(U_61,bool),bool,finite_finite(U_61),U_59)) ),
    inference(clausify,[status(thm)],[f_38_2]) ).

cnf(f_38_4,plain,
    ( hAPP(fun(U_61,bool),nat,finite_card(U_61),hAPP(fun(U_61,bool),fun(U_61,bool),hAPP(U_61,fun(fun(U_61,bool),fun(U_61,bool)),insert(U_61),U_60),U_59)) = hAPP(nat,nat,suc,hAPP(fun(U_61,bool),nat,finite_card(U_61),U_59))
    | hBOOL(hAPP(fun(U_61,bool),bool,hAPP(U_61,fun(fun(U_61,bool),bool),member(U_61),U_60),U_59))
    | ~ hBOOL(hAPP(fun(U_61,bool),bool,finite_finite(U_61),U_59)) ),
    inference(clausify,[status(thm)],[f_38_2]) ).

fof(f_39_1,plain,
    ! [X_b,X_2,A_1] :
      ( 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_2),A_1)) = hAPP(nat,nat,suc,hAPP(fun(X_b,bool),nat,finite_card(X_b),A_1))
      | hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_9_card__insert__disjoint]) ).

fof(f_39_2,plain,
    ! [U_64,U_63,U_62] :
      ( hAPP(fun(U_64,bool),nat,finite_card(U_64),hAPP(fun(U_64,bool),fun(U_64,bool),hAPP(U_64,fun(fun(U_64,bool),fun(U_64,bool)),insert(U_64),U_63),U_62)) = hAPP(nat,nat,suc,hAPP(fun(U_64,bool),nat,finite_card(U_64),U_62))
      | hBOOL(hAPP(fun(U_64,bool),bool,hAPP(U_64,fun(fun(U_64,bool),bool),member(U_64),U_63),U_62))
      | ~ hBOOL(hAPP(fun(U_64,bool),bool,finite_finite(U_64),U_62)) ),
    inference(variable_rename,[status(thm)],[f_39_1]) ).

cnf(f_39_3,plain,
    ( hAPP(fun(U_64,bool),nat,finite_card(U_64),hAPP(fun(U_64,bool),fun(U_64,bool),hAPP(U_64,fun(fun(U_64,bool),fun(U_64,bool)),insert(U_64),U_63),U_62)) = hAPP(nat,nat,suc,hAPP(fun(U_64,bool),nat,finite_card(U_64),U_62))
    | hBOOL(hAPP(fun(U_64,bool),bool,hAPP(U_64,fun(fun(U_64,bool),bool),member(U_64),U_63),U_62))
    | ~ hBOOL(hAPP(fun(U_64,bool),bool,finite_finite(U_64),U_62)) ),
    inference(clausify,[status(thm)],[f_39_2]) ).

fof(f_40_1,plain,
    ! [X_b,Q_1,Pa] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),Pa)),Q_1))))
      | ( ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Q_1)))
        & ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa))) ) ),
    inference(fof_nnf,[status(thm)],[fact_10_finite__Collect__conjI]) ).

fof(f_40_2,plain,
    ! [U_67,U_66,U_65] :
      ( hBOOL(hAPP(fun(U_67,bool),bool,finite_finite(U_67),hAPP(fun(U_67,bool),fun(U_67,bool),collect(U_67),hAPP(fun(U_67,bool),fun(U_67,bool),hAPP(fun(U_67,fun(bool,bool)),fun(fun(U_67,bool),fun(U_67,bool)),combs(U_67,bool,bool),hAPP(fun(U_67,bool),fun(U_67,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_67,bool),fun(U_67,fun(bool,bool))),combb(bool,fun(bool,bool),U_67),fconj),U_65)),U_66))))
      | ( ~ hBOOL(hAPP(fun(U_67,bool),bool,finite_finite(U_67),hAPP(fun(U_67,bool),fun(U_67,bool),collect(U_67),U_66)))
        & ~ hBOOL(hAPP(fun(U_67,bool),bool,finite_finite(U_67),hAPP(fun(U_67,bool),fun(U_67,bool),collect(U_67),U_65))) ) ),
    inference(variable_rename,[status(thm)],[f_40_1]) ).

cnf(f_40_3,plain,
    ( ~ hBOOL(hAPP(fun(U_67,bool),bool,finite_finite(U_67),hAPP(fun(U_67,bool),fun(U_67,bool),collect(U_67),U_65)))
    | hBOOL(hAPP(fun(U_67,bool),bool,finite_finite(U_67),hAPP(fun(U_67,bool),fun(U_67,bool),collect(U_67),hAPP(fun(U_67,bool),fun(U_67,bool),hAPP(fun(U_67,fun(bool,bool)),fun(fun(U_67,bool),fun(U_67,bool)),combs(U_67,bool,bool),hAPP(fun(U_67,bool),fun(U_67,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_67,bool),fun(U_67,fun(bool,bool))),combb(bool,fun(bool,bool),U_67),fconj),U_65)),U_66)))) ),
    inference(clausify,[status(thm)],[f_40_2]) ).

cnf(f_40_4,plain,
    ( ~ hBOOL(hAPP(fun(U_67,bool),bool,finite_finite(U_67),hAPP(fun(U_67,bool),fun(U_67,bool),collect(U_67),U_66)))
    | hBOOL(hAPP(fun(U_67,bool),bool,finite_finite(U_67),hAPP(fun(U_67,bool),fun(U_67,bool),collect(U_67),hAPP(fun(U_67,bool),fun(U_67,bool),hAPP(fun(U_67,fun(bool,bool)),fun(fun(U_67,bool),fun(U_67,bool)),combs(U_67,bool,bool),hAPP(fun(U_67,bool),fun(U_67,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_67,bool),fun(U_67,fun(bool,bool))),combb(bool,fun(bool,bool),U_67),fconj),U_65)),U_66)))) ),
    inference(clausify,[status(thm)],[f_40_2]) ).

fof(f_41_1,plain,
    ! [N_1,M_2] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M_2)),N_1) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_2),N_1))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M_2)) ),
    inference(fof_nnf,[status(thm)],[fact_11_Suc__diff__le]) ).

fof(f_41_2,plain,
    ! [U_69,U_68] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,U_68)),U_69) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_68),U_69))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_69),U_68)) ),
    inference(variable_rename,[status(thm)],[f_41_1]) ).

cnf(f_41_3,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,U_68)),U_69) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_68),U_69))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_69),U_68)) ),
    inference(clausify,[status(thm)],[f_41_2]) ).

fof(f_42_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_42_2,plain,
    ! [U_70] : 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_70)))),
    inference(variable_rename,[status(thm)],[f_42_1]) ).

cnf(f_42_3,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_70)))),
    inference(clausify,[status(thm)],[f_42_2]) ).

fof(f_43_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_43_2,plain,
    ! [U_71] : 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_71))) = hAPP(nat,nat,suc,U_71),
    inference(variable_rename,[status(thm)],[f_43_1]) ).

cnf(f_43_3,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_71))) = hAPP(nat,nat,suc,U_71),
    inference(clausify,[status(thm)],[f_43_2]) ).

fof(f_44_1,plain,
    ! [X_b] :
      ( ! [A_1] : hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1))
      | ~ finite_finite_1(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_14_finite__code]) ).

fof(f_44_2,plain,
    ! [U_73] :
      ( ! [U_72] : hBOOL(hAPP(fun(U_73,bool),bool,finite_finite(U_73),U_72))
      | ~ finite_finite_1(U_73) ),
    inference(variable_rename,[status(thm)],[f_44_1]) ).

cnf(f_44_3,plain,
    ( hBOOL(hAPP(fun(U_73,bool),bool,finite_finite(U_73),U_72))
    | ~ finite_finite_1(U_73) ),
    inference(clausify,[status(thm)],[f_44_2]) ).

fof(f_45_1,plain,
    ! [X_b] :
      ( ! [A_1] : hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1))
      | ~ finite_finite_1(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_15_finite]) ).

fof(f_45_2,plain,
    ! [U_75] :
      ( ! [U_74] : hBOOL(hAPP(fun(U_75,bool),bool,finite_finite(U_75),U_74))
      | ~ finite_finite_1(U_75) ),
    inference(variable_rename,[status(thm)],[f_45_1]) ).

cnf(f_45_3,plain,
    ( hBOOL(hAPP(fun(U_75,bool),bool,finite_finite(U_75),U_74))
    | ~ finite_finite_1(U_75) ),
    inference(clausify,[status(thm)],[f_45_2]) ).

fof(f_46_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_46_2,plain,
    ! [U_77,U_76] :
      ( U_77 = U_76
      | hAPP(nat,nat,suc,U_77) != hAPP(nat,nat,suc,U_76) ),
    inference(variable_rename,[status(thm)],[f_46_1]) ).

cnf(f_46_3,plain,
    ( U_77 = U_76
    | hAPP(nat,nat,suc,U_77) != hAPP(nat,nat,suc,U_76) ),
    inference(clausify,[status(thm)],[f_46_2]) ).

fof(f_47_1,plain,
    ! [Nat_1,Nat] :
      ( ( hAPP(nat,nat,suc,Nat_1) = hAPP(nat,nat,suc,Nat)
        | Nat_1 != Nat )
      & ( Nat_1 = Nat
        | hAPP(nat,nat,suc,Nat_1) != hAPP(nat,nat,suc,Nat) ) ),
    inference(fof_nnf,[status(thm)],[fact_17_nat_Oinject]) ).

fof(f_47_2,plain,
    ! [U_79,U_78] :
      ( ( hAPP(nat,nat,suc,U_79) = hAPP(nat,nat,suc,U_78)
        | U_79 != U_78 )
      & ( U_79 = U_78
        | hAPP(nat,nat,suc,U_79) != hAPP(nat,nat,suc,U_78) ) ),
    inference(variable_rename,[status(thm)],[f_47_1]) ).

fof(f_47_3,plain,
    ( ! [U_83,U_81] :
        ( hAPP(nat,nat,suc,U_83) = hAPP(nat,nat,suc,U_81)
        | U_83 != U_81 )
    & ! [U_82,U_80] :
        ( U_82 = U_80
        | hAPP(nat,nat,suc,U_82) != hAPP(nat,nat,suc,U_80) ) ),
    inference(miniscope,[status(thm)],[f_47_2]) ).

cnf(f_47_4,plain,
    ( U_82 = U_80
    | hAPP(nat,nat,suc,U_82) != hAPP(nat,nat,suc,U_80) ),
    inference(clausify,[status(thm)],[f_47_3]) ).

cnf(f_47_5,plain,
    ( hAPP(nat,nat,suc,U_83) = hAPP(nat,nat,suc,U_81)
    | U_83 != U_81 ),
    inference(clausify,[status(thm)],[f_47_3]) ).

fof(f_48_1,plain,
    ! [N_1] : hAPP(nat,nat,suc,N_1) != N_1,
    inference(fof_nnf,[status(thm)],[fact_18_Suc__n__not__n]) ).

fof(f_48_2,plain,
    ! [U_84] : hAPP(nat,nat,suc,U_84) != U_84,
    inference(variable_rename,[status(thm)],[f_48_1]) ).

cnf(f_48_3,plain,
    hAPP(nat,nat,suc,U_84) != U_84,
    inference(clausify,[status(thm)],[f_48_2]) ).

fof(f_49_1,plain,
    ! [N_1] : N_1 != hAPP(nat,nat,suc,N_1),
    inference(fof_nnf,[status(thm)],[fact_19_n__not__Suc__n]) ).

fof(f_49_2,plain,
    ! [U_85] : U_85 != hAPP(nat,nat,suc,U_85),
    inference(variable_rename,[status(thm)],[f_49_1]) ).

cnf(f_49_3,plain,
    U_85 != hAPP(nat,nat,suc,U_85),
    inference(clausify,[status(thm)],[f_49_2]) ).

fof(f_50_1,plain,
    ! [M_2,N_1] :
      ( M_2 = N_1
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M_2))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_1)) ),
    inference(fof_nnf,[status(thm)],[fact_20_le__antisym]) ).

fof(f_50_2,plain,
    ! [U_87,U_86] :
      ( U_87 = U_86
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_86),U_87))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_87),U_86)) ),
    inference(variable_rename,[status(thm)],[f_50_1]) ).

cnf(f_50_3,plain,
    ( U_87 = U_86
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_86),U_87))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_87),U_86)) ),
    inference(clausify,[status(thm)],[f_50_2]) ).

fof(f_51_1,plain,
    ! [K_1,I_1,J] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),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_1),J)) ),
    inference(fof_nnf,[status(thm)],[fact_21_le__trans]) ).

fof(f_51_2,plain,
    ! [U_90,U_89,U_88] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_89),U_90))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_88),U_90))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_89),U_88)) ),
    inference(variable_rename,[status(thm)],[f_51_1]) ).

cnf(f_51_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_89),U_90))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_88),U_90))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_89),U_88)) ),
    inference(clausify,[status(thm)],[f_51_2]) ).

fof(f_52_1,plain,
    ! [M_2,N_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_1))
      | M_2 != N_1 ),
    inference(fof_nnf,[status(thm)],[fact_22_eq__imp__le]) ).

fof(f_52_2,plain,
    ! [U_92,U_91] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_92),U_91))
      | U_92 != U_91 ),
    inference(variable_rename,[status(thm)],[f_52_1]) ).

cnf(f_52_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_92),U_91))
    | U_92 != U_91 ),
    inference(clausify,[status(thm)],[f_52_2]) ).

fof(f_53_1,plain,
    ! [M_2,N_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M_2))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_1)) ),
    inference(fof_nnf,[status(thm)],[fact_23_nat__le__linear]) ).

fof(f_53_2,plain,
    ! [U_94,U_93] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_93),U_94))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_94),U_93)) ),
    inference(variable_rename,[status(thm)],[f_53_1]) ).

cnf(f_53_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_93),U_94))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_94),U_93)) ),
    inference(clausify,[status(thm)],[f_53_2]) ).

fof(f_54_1,plain,
    ! [N_1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),N_1)),
    inference(fof_nnf,[status(thm)],[fact_24_le__refl]) ).

fof(f_54_2,plain,
    ! [U_95] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_95),U_95)),
    inference(variable_rename,[status(thm)],[f_54_1]) ).

cnf(f_54_3,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_95),U_95)),
    inference(clausify,[status(thm)],[f_54_2]) ).

fof(f_55_1,plain,
    ! [I_1,J,K_1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J)),K_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),K_1)),J),
    inference(fof_nnf,[status(thm)],[fact_25_diff__commute]) ).

fof(f_55_2,plain,
    ! [U_98,U_97,U_96] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_98),U_97)),U_96) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_98),U_96)),U_97),
    inference(variable_rename,[status(thm)],[f_55_1]) ).

cnf(f_55_3,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_98),U_97)),U_96) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_98),U_96)),U_97),
    inference(clausify,[status(thm)],[f_55_2]) ).

fof(f_56_1,plain,
    ! [X_b,Pa,Q_1] :
      ( ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fdisj),Pa)),Q_1))))
        | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Q_1)))
        | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa))) )
      & ( ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Q_1)))
          & hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa))) )
        | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fdisj),Pa)),Q_1)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_26_finite__Collect__disjI]) ).

fof(f_56_2,plain,
    ! [U_101,U_100,U_99] :
      ( ( hBOOL(hAPP(fun(U_101,bool),bool,finite_finite(U_101),hAPP(fun(U_101,bool),fun(U_101,bool),collect(U_101),hAPP(fun(U_101,bool),fun(U_101,bool),hAPP(fun(U_101,fun(bool,bool)),fun(fun(U_101,bool),fun(U_101,bool)),combs(U_101,bool,bool),hAPP(fun(U_101,bool),fun(U_101,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_101,bool),fun(U_101,fun(bool,bool))),combb(bool,fun(bool,bool),U_101),fdisj),U_100)),U_99))))
        | ~ hBOOL(hAPP(fun(U_101,bool),bool,finite_finite(U_101),hAPP(fun(U_101,bool),fun(U_101,bool),collect(U_101),U_99)))
        | ~ hBOOL(hAPP(fun(U_101,bool),bool,finite_finite(U_101),hAPP(fun(U_101,bool),fun(U_101,bool),collect(U_101),U_100))) )
      & ( ( hBOOL(hAPP(fun(U_101,bool),bool,finite_finite(U_101),hAPP(fun(U_101,bool),fun(U_101,bool),collect(U_101),U_99)))
          & hBOOL(hAPP(fun(U_101,bool),bool,finite_finite(U_101),hAPP(fun(U_101,bool),fun(U_101,bool),collect(U_101),U_100))) )
        | ~ hBOOL(hAPP(fun(U_101,bool),bool,finite_finite(U_101),hAPP(fun(U_101,bool),fun(U_101,bool),collect(U_101),hAPP(fun(U_101,bool),fun(U_101,bool),hAPP(fun(U_101,fun(bool,bool)),fun(fun(U_101,bool),fun(U_101,bool)),combs(U_101,bool,bool),hAPP(fun(U_101,bool),fun(U_101,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_101,bool),fun(U_101,fun(bool,bool))),combb(bool,fun(bool,bool),U_101),fdisj),U_100)),U_99)))) ) ),
    inference(variable_rename,[status(thm)],[f_56_1]) ).

fof(f_56_3,plain,
    ( ! [U_107,U_105,U_103] :
        ( hBOOL(hAPP(fun(U_107,bool),bool,finite_finite(U_107),hAPP(fun(U_107,bool),fun(U_107,bool),collect(U_107),hAPP(fun(U_107,bool),fun(U_107,bool),hAPP(fun(U_107,fun(bool,bool)),fun(fun(U_107,bool),fun(U_107,bool)),combs(U_107,bool,bool),hAPP(fun(U_107,bool),fun(U_107,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_107,bool),fun(U_107,fun(bool,bool))),combb(bool,fun(bool,bool),U_107),fdisj),U_105)),U_103))))
        | ~ hBOOL(hAPP(fun(U_107,bool),bool,finite_finite(U_107),hAPP(fun(U_107,bool),fun(U_107,bool),collect(U_107),U_103)))
        | ~ hBOOL(hAPP(fun(U_107,bool),bool,finite_finite(U_107),hAPP(fun(U_107,bool),fun(U_107,bool),collect(U_107),U_105))) )
    & ! [U_106,U_104,U_102] :
        ( ( hBOOL(hAPP(fun(U_106,bool),bool,finite_finite(U_106),hAPP(fun(U_106,bool),fun(U_106,bool),collect(U_106),U_102)))
          & hBOOL(hAPP(fun(U_106,bool),bool,finite_finite(U_106),hAPP(fun(U_106,bool),fun(U_106,bool),collect(U_106),U_104))) )
        | ~ hBOOL(hAPP(fun(U_106,bool),bool,finite_finite(U_106),hAPP(fun(U_106,bool),fun(U_106,bool),collect(U_106),hAPP(fun(U_106,bool),fun(U_106,bool),hAPP(fun(U_106,fun(bool,bool)),fun(fun(U_106,bool),fun(U_106,bool)),combs(U_106,bool,bool),hAPP(fun(U_106,bool),fun(U_106,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_106,bool),fun(U_106,fun(bool,bool))),combb(bool,fun(bool,bool),U_106),fdisj),U_104)),U_102)))) ) ),
    inference(miniscope,[status(thm)],[f_56_2]) ).

cnf(f_56_4,plain,
    ( hBOOL(hAPP(fun(U_106,bool),bool,finite_finite(U_106),hAPP(fun(U_106,bool),fun(U_106,bool),collect(U_106),U_104)))
    | ~ hBOOL(hAPP(fun(U_106,bool),bool,finite_finite(U_106),hAPP(fun(U_106,bool),fun(U_106,bool),collect(U_106),hAPP(fun(U_106,bool),fun(U_106,bool),hAPP(fun(U_106,fun(bool,bool)),fun(fun(U_106,bool),fun(U_106,bool)),combs(U_106,bool,bool),hAPP(fun(U_106,bool),fun(U_106,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_106,bool),fun(U_106,fun(bool,bool))),combb(bool,fun(bool,bool),U_106),fdisj),U_104)),U_102)))) ),
    inference(clausify,[status(thm)],[f_56_3]) ).

cnf(f_56_5,plain,
    ( hBOOL(hAPP(fun(U_106,bool),bool,finite_finite(U_106),hAPP(fun(U_106,bool),fun(U_106,bool),collect(U_106),U_102)))
    | ~ hBOOL(hAPP(fun(U_106,bool),bool,finite_finite(U_106),hAPP(fun(U_106,bool),fun(U_106,bool),collect(U_106),hAPP(fun(U_106,bool),fun(U_106,bool),hAPP(fun(U_106,fun(bool,bool)),fun(fun(U_106,bool),fun(U_106,bool)),combs(U_106,bool,bool),hAPP(fun(U_106,bool),fun(U_106,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_106,bool),fun(U_106,fun(bool,bool))),combb(bool,fun(bool,bool),U_106),fdisj),U_104)),U_102)))) ),
    inference(clausify,[status(thm)],[f_56_3]) ).

cnf(f_56_6,plain,
    ( hBOOL(hAPP(fun(U_107,bool),bool,finite_finite(U_107),hAPP(fun(U_107,bool),fun(U_107,bool),collect(U_107),hAPP(fun(U_107,bool),fun(U_107,bool),hAPP(fun(U_107,fun(bool,bool)),fun(fun(U_107,bool),fun(U_107,bool)),combs(U_107,bool,bool),hAPP(fun(U_107,bool),fun(U_107,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_107,bool),fun(U_107,fun(bool,bool))),combb(bool,fun(bool,bool),U_107),fdisj),U_105)),U_103))))
    | ~ hBOOL(hAPP(fun(U_107,bool),bool,finite_finite(U_107),hAPP(fun(U_107,bool),fun(U_107,bool),collect(U_107),U_103)))
    | ~ hBOOL(hAPP(fun(U_107,bool),bool,finite_finite(U_107),hAPP(fun(U_107,bool),fun(U_107,bool),collect(U_107),U_105))) ),
    inference(clausify,[status(thm)],[f_56_3]) ).

fof(f_57_1,plain,
    ! [X_b,A_2,A_1] :
      ( ( 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_1)))
        | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1)) )
      & ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1))
        | ~ 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_1))) ) ),
    inference(fof_nnf,[status(thm)],[fact_27_finite__insert]) ).

fof(f_57_2,plain,
    ! [U_110,U_109,U_108] :
      ( ( hBOOL(hAPP(fun(U_110,bool),bool,finite_finite(U_110),hAPP(fun(U_110,bool),fun(U_110,bool),hAPP(U_110,fun(fun(U_110,bool),fun(U_110,bool)),insert(U_110),U_109),U_108)))
        | ~ hBOOL(hAPP(fun(U_110,bool),bool,finite_finite(U_110),U_108)) )
      & ( hBOOL(hAPP(fun(U_110,bool),bool,finite_finite(U_110),U_108))
        | ~ hBOOL(hAPP(fun(U_110,bool),bool,finite_finite(U_110),hAPP(fun(U_110,bool),fun(U_110,bool),hAPP(U_110,fun(fun(U_110,bool),fun(U_110,bool)),insert(U_110),U_109),U_108))) ) ),
    inference(variable_rename,[status(thm)],[f_57_1]) ).

fof(f_57_3,plain,
    ( ! [U_116,U_114,U_112] :
        ( hBOOL(hAPP(fun(U_116,bool),bool,finite_finite(U_116),hAPP(fun(U_116,bool),fun(U_116,bool),hAPP(U_116,fun(fun(U_116,bool),fun(U_116,bool)),insert(U_116),U_114),U_112)))
        | ~ hBOOL(hAPP(fun(U_116,bool),bool,finite_finite(U_116),U_112)) )
    & ! [U_115,U_113,U_111] :
        ( hBOOL(hAPP(fun(U_115,bool),bool,finite_finite(U_115),U_111))
        | ~ hBOOL(hAPP(fun(U_115,bool),bool,finite_finite(U_115),hAPP(fun(U_115,bool),fun(U_115,bool),hAPP(U_115,fun(fun(U_115,bool),fun(U_115,bool)),insert(U_115),U_113),U_111))) ) ),
    inference(miniscope,[status(thm)],[f_57_2]) ).

cnf(f_57_4,plain,
    ( hBOOL(hAPP(fun(U_115,bool),bool,finite_finite(U_115),U_111))
    | ~ hBOOL(hAPP(fun(U_115,bool),bool,finite_finite(U_115),hAPP(fun(U_115,bool),fun(U_115,bool),hAPP(U_115,fun(fun(U_115,bool),fun(U_115,bool)),insert(U_115),U_113),U_111))) ),
    inference(clausify,[status(thm)],[f_57_3]) ).

cnf(f_57_5,plain,
    ( hBOOL(hAPP(fun(U_116,bool),bool,finite_finite(U_116),hAPP(fun(U_116,bool),fun(U_116,bool),hAPP(U_116,fun(fun(U_116,bool),fun(U_116,bool)),insert(U_116),U_114),U_112)))
    | ~ hBOOL(hAPP(fun(U_116,bool),bool,finite_finite(U_116),U_112)) ),
    inference(clausify,[status(thm)],[f_57_3]) ).

fof(f_58_1,plain,
    ! [X_b,A_1,B] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_1),B)) ),
    inference(fof_nnf,[status(thm)],[fact_28_finite__subset]) ).

fof(f_58_2,plain,
    ! [U_119,U_118,U_117] :
      ( hBOOL(hAPP(fun(U_119,bool),bool,finite_finite(U_119),U_118))
      | ~ hBOOL(hAPP(fun(U_119,bool),bool,finite_finite(U_119),U_117))
      | ~ hBOOL(hAPP(fun(U_119,bool),bool,hAPP(fun(U_119,bool),fun(fun(U_119,bool),bool),ord_less_eq(fun(U_119,bool)),U_118),U_117)) ),
    inference(variable_rename,[status(thm)],[f_58_1]) ).

cnf(f_58_3,plain,
    ( hBOOL(hAPP(fun(U_119,bool),bool,finite_finite(U_119),U_118))
    | ~ hBOOL(hAPP(fun(U_119,bool),bool,finite_finite(U_119),U_117))
    | ~ hBOOL(hAPP(fun(U_119,bool),bool,hAPP(fun(U_119,bool),fun(fun(U_119,bool),bool),ord_less_eq(fun(U_119,bool)),U_118),U_117)) ),
    inference(clausify,[status(thm)],[f_58_2]) ).

fof(f_59_1,plain,
    ! [X_b,A_1,B] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_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_1),B))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B)) ),
    inference(fof_nnf,[status(thm)],[fact_29_rev__finite__subset]) ).

fof(f_59_2,plain,
    ! [U_122,U_121,U_120] :
      ( hBOOL(hAPP(fun(U_122,bool),bool,finite_finite(U_122),U_121))
      | ~ hBOOL(hAPP(fun(U_122,bool),bool,hAPP(fun(U_122,bool),fun(fun(U_122,bool),bool),ord_less_eq(fun(U_122,bool)),U_121),U_120))
      | ~ hBOOL(hAPP(fun(U_122,bool),bool,finite_finite(U_122),U_120)) ),
    inference(variable_rename,[status(thm)],[f_59_1]) ).

cnf(f_59_3,plain,
    ( hBOOL(hAPP(fun(U_122,bool),bool,finite_finite(U_122),U_121))
    | ~ hBOOL(hAPP(fun(U_122,bool),bool,hAPP(fun(U_122,bool),fun(fun(U_122,bool),bool),ord_less_eq(fun(U_122,bool)),U_121),U_120))
    | ~ hBOOL(hAPP(fun(U_122,bool),bool,finite_finite(U_122),U_120)) ),
    inference(clausify,[status(thm)],[f_59_2]) ).

fof(f_60_1,plain,
    ! [M_2,N_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_1))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M_2)),N_1)) ),
    inference(fof_nnf,[status(thm)],[fact_30_Suc__leD]) ).

fof(f_60_2,plain,
    ! [U_124,U_123] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_124),U_123))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_124)),U_123)) ),
    inference(variable_rename,[status(thm)],[f_60_1]) ).

cnf(f_60_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_124),U_123))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_124)),U_123)) ),
    inference(clausify,[status(thm)],[f_60_2]) ).

fof(f_61_1,plain,
    ! [M_2,N_1] :
      ( M_2 = hAPP(nat,nat,suc,N_1)
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_1))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),hAPP(nat,nat,suc,N_1))) ),
    inference(fof_nnf,[status(thm)],[fact_31_le__SucE]) ).

fof(f_61_2,plain,
    ! [U_126,U_125] :
      ( U_126 = hAPP(nat,nat,suc,U_125)
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_126),U_125))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_126),hAPP(nat,nat,suc,U_125))) ),
    inference(variable_rename,[status(thm)],[f_61_1]) ).

cnf(f_61_3,plain,
    ( U_126 = hAPP(nat,nat,suc,U_125)
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_126),U_125))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_126),hAPP(nat,nat,suc,U_125))) ),
    inference(clausify,[status(thm)],[f_61_2]) ).

fof(f_62_1,plain,
    ! [M_2,N_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),hAPP(nat,nat,suc,N_1)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_1)) ),
    inference(fof_nnf,[status(thm)],[fact_32_le__SucI]) ).

fof(f_62_2,plain,
    ! [U_128,U_127] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_128),hAPP(nat,nat,suc,U_127)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_128),U_127)) ),
    inference(variable_rename,[status(thm)],[f_62_1]) ).

cnf(f_62_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_128),hAPP(nat,nat,suc,U_127)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_128),U_127)) ),
    inference(clausify,[status(thm)],[f_62_2]) ).

fof(f_63_1,plain,
    ! [Na,M_3] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Na)),hAPP(nat,nat,suc,M_3)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Na),M_3)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Na),M_3))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Na)),hAPP(nat,nat,suc,M_3))) ) ),
    inference(fof_nnf,[status(thm)],[fact_33_Suc__le__mono]) ).

fof(f_63_2,plain,
    ! [U_130,U_129] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_130)),hAPP(nat,nat,suc,U_129)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_130),U_129)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_130),U_129))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_130)),hAPP(nat,nat,suc,U_129))) ) ),
    inference(variable_rename,[status(thm)],[f_63_1]) ).

fof(f_63_3,plain,
    ( ! [U_134,U_132] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_134)),hAPP(nat,nat,suc,U_132)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_134),U_132)) )
    & ! [U_133,U_131] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_133),U_131))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_133)),hAPP(nat,nat,suc,U_131))) ) ),
    inference(miniscope,[status(thm)],[f_63_2]) ).

cnf(f_63_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_133),U_131))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_133)),hAPP(nat,nat,suc,U_131))) ),
    inference(clausify,[status(thm)],[f_63_3]) ).

cnf(f_63_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_134)),hAPP(nat,nat,suc,U_132)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_134),U_132)) ),
    inference(clausify,[status(thm)],[f_63_3]) ).

fof(f_64_1,plain,
    ! [M_3,Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),hAPP(nat,nat,suc,Na)))
        | ( M_3 != hAPP(nat,nat,suc,Na)
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),Na)) ) )
      & ( M_3 = hAPP(nat,nat,suc,Na)
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),Na))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),hAPP(nat,nat,suc,Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_34_le__Suc__eq]) ).

fof(f_64_2,plain,
    ! [U_136,U_135] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_136),hAPP(nat,nat,suc,U_135)))
        | ( U_136 != hAPP(nat,nat,suc,U_135)
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_136),U_135)) ) )
      & ( U_136 = hAPP(nat,nat,suc,U_135)
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_136),U_135))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_136),hAPP(nat,nat,suc,U_135))) ) ),
    inference(variable_rename,[status(thm)],[f_64_1]) ).

fof(f_64_3,plain,
    ( ! [U_140,U_138] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_140),hAPP(nat,nat,suc,U_138)))
        | ( U_140 != hAPP(nat,nat,suc,U_138)
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_140),U_138)) ) )
    & ! [U_139,U_137] :
        ( U_139 = hAPP(nat,nat,suc,U_137)
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_139),U_137))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_139),hAPP(nat,nat,suc,U_137))) ) ),
    inference(miniscope,[status(thm)],[f_64_2]) ).

cnf(f_64_4,plain,
    ( U_139 = hAPP(nat,nat,suc,U_137)
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_139),U_137))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_139),hAPP(nat,nat,suc,U_137))) ),
    inference(clausify,[status(thm)],[f_64_3]) ).

cnf(f_64_5,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_140),U_138))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_140),hAPP(nat,nat,suc,U_138))) ),
    inference(clausify,[status(thm)],[f_64_3]) ).

cnf(f_64_6,plain,
    ( U_140 != hAPP(nat,nat,suc,U_138)
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_140),hAPP(nat,nat,suc,U_138))) ),
    inference(clausify,[status(thm)],[f_64_3]) ).

fof(f_65_1,plain,
    ! [M_3,Na] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),Na))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Na)),M_3)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Na)),M_3))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_35_not__less__eq__eq]) ).

fof(f_65_2,plain,
    ! [U_142,U_141] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_142),U_141))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_141)),U_142)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_141)),U_142))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_142),U_141)) ) ),
    inference(variable_rename,[status(thm)],[f_65_1]) ).

fof(f_65_3,plain,
    ( ! [U_146,U_144] :
        ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_146),U_144))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_144)),U_146)) )
    & ! [U_145,U_143] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_143)),U_145))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_145),U_143)) ) ),
    inference(miniscope,[status(thm)],[f_65_2]) ).

cnf(f_65_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_143)),U_145))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_145),U_143)) ),
    inference(clausify,[status(thm)],[f_65_3]) ).

cnf(f_65_5,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_146),U_144))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_144)),U_146)) ),
    inference(clausify,[status(thm)],[f_65_3]) ).

fof(f_66_1,plain,
    ! [N_1] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N_1)),N_1)),
    inference(fof_nnf,[status(thm)],[fact_36_Suc__n__not__le__n]) ).

fof(f_66_2,plain,
    ! [U_147] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_147)),U_147)),
    inference(variable_rename,[status(thm)],[f_66_1]) ).

cnf(f_66_3,plain,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_147)),U_147)),
    inference(clausify,[status(thm)],[f_66_2]) ).

fof(f_67_1,plain,
    ! [M_2,N_1,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_2)),N_1)),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_2),N_1)),K_1),
    inference(fof_nnf,[status(thm)],[fact_37_Suc__diff__diff]) ).

fof(f_67_2,plain,
    ! [U_150,U_149,U_148] : 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_150)),U_149)),hAPP(nat,nat,suc,U_148)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_150),U_149)),U_148),
    inference(variable_rename,[status(thm)],[f_67_1]) ).

cnf(f_67_3,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_150)),U_149)),hAPP(nat,nat,suc,U_148)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_150),U_149)),U_148),
    inference(clausify,[status(thm)],[f_67_2]) ).

fof(f_68_1,plain,
    ! [M_2,N_1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M_2)),hAPP(nat,nat,suc,N_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_2),N_1),
    inference(fof_nnf,[status(thm)],[fact_38_diff__Suc__Suc]) ).

fof(f_68_2,plain,
    ! [U_152,U_151] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,U_152)),hAPP(nat,nat,suc,U_151)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_152),U_151),
    inference(variable_rename,[status(thm)],[f_68_1]) ).

cnf(f_68_3,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,U_152)),hAPP(nat,nat,suc,U_151)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_152),U_151),
    inference(clausify,[status(thm)],[f_68_2]) ).

fof(f_69_1,plain,
    ! [Na,K,M_3] :
      ( ( ( 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_3),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_3),Na)) )
        & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),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_3),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_3)) ),
    inference(fof_nnf,[status(thm)],[fact_39_le__diff__iff]) ).

fof(f_69_2,plain,
    ! [U_155,U_154,U_153] :
      ( ( ( 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_153),U_154)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_155),U_154)))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_153),U_155)) )
        & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_153),U_155))
          | ~ 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_153),U_154)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_155),U_154))) ) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_154),U_155))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_154),U_153)) ),
    inference(variable_rename,[status(thm)],[f_69_1]) ).

cnf(f_69_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_153),U_155))
    | ~ 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_153),U_154)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_155),U_154)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_154),U_155))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_154),U_153)) ),
    inference(clausify,[status(thm)],[f_69_2]) ).

cnf(f_69_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_153),U_154)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_155),U_154)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_153),U_155))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_154),U_155))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_154),U_153)) ),
    inference(clausify,[status(thm)],[f_69_2]) ).

fof(f_70_1,plain,
    ! [N_1,K_1,M_2] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_2),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),K_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_2),N_1)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N_1))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),M_2)) ),
    inference(fof_nnf,[status(thm)],[fact_40_Nat_Odiff__diff__eq]) ).

fof(f_70_2,plain,
    ! [U_158,U_157,U_156] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_156),U_157)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_158),U_157)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_156),U_158)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_157),U_158))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_157),U_156)) ),
    inference(variable_rename,[status(thm)],[f_70_1]) ).

cnf(f_70_3,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_156),U_157)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_158),U_157)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_156),U_158)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_157),U_158))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_157),U_156)) ),
    inference(clausify,[status(thm)],[f_70_2]) ).

fof(f_71_1,plain,
    ! [Na,K,M_3] :
      ( ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_3),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Na),K)
          | M_3 != Na )
        & ( M_3 = Na
          | hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_3),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_3)) ),
    inference(fof_nnf,[status(thm)],[fact_41_eq__diff__iff]) ).

fof(f_71_2,plain,
    ! [U_161,U_160,U_159] :
      ( ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_159),U_160) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_161),U_160)
          | U_159 != U_161 )
        & ( U_159 = U_161
          | hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_159),U_160) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_161),U_160) ) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_160),U_161))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_160),U_159)) ),
    inference(variable_rename,[status(thm)],[f_71_1]) ).

cnf(f_71_3,plain,
    ( U_159 = U_161
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_159),U_160) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_161),U_160)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_160),U_161))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_160),U_159)) ),
    inference(clausify,[status(thm)],[f_71_2]) ).

cnf(f_71_4,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_159),U_160) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_161),U_160)
    | U_159 != U_161
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_160),U_161))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_160),U_159)) ),
    inference(clausify,[status(thm)],[f_71_2]) ).

fof(f_72_1,plain,
    ! [I_1,N_1] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),I_1)) = I_1
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),N_1)) ),
    inference(fof_nnf,[status(thm)],[fact_42_diff__diff__cancel]) ).

fof(f_72_2,plain,
    ! [U_163,U_162] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_162),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_162),U_163)) = U_163
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_163),U_162)) ),
    inference(variable_rename,[status(thm)],[f_72_1]) ).

cnf(f_72_3,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_162),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_162),U_163)) = U_163
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_163),U_162)) ),
    inference(clausify,[status(thm)],[f_72_2]) ).

fof(f_73_1,plain,
    ! [L,M_2,N_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_2),L)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),L)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_1)) ),
    inference(fof_nnf,[status(thm)],[fact_43_diff__le__mono]) ).

fof(f_73_2,plain,
    ! [U_166,U_165,U_164] :
      ( 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_165),U_166)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_164),U_166)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_165),U_164)) ),
    inference(variable_rename,[status(thm)],[f_73_1]) ).

cnf(f_73_3,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_165),U_166)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_164),U_166)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_165),U_164)) ),
    inference(clausify,[status(thm)],[f_73_2]) ).

fof(f_74_1,plain,
    ! [L,M_2,N_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),L),N_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L),M_2)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_1)) ),
    inference(fof_nnf,[status(thm)],[fact_44_diff__le__mono2]) ).

fof(f_74_2,plain,
    ! [U_169,U_168,U_167] :
      ( 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_169),U_167)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_169),U_168)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_168),U_167)) ),
    inference(variable_rename,[status(thm)],[f_74_1]) ).

cnf(f_74_3,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_169),U_167)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_169),U_168)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_168),U_167)) ),
    inference(clausify,[status(thm)],[f_74_2]) ).

fof(f_75_1,plain,
    ! [M_2,N_1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_2),N_1)),M_2)),
    inference(fof_nnf,[status(thm)],[fact_45_diff__le__self]) ).

fof(f_75_2,plain,
    ! [U_171,U_170] : 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_171),U_170)),U_171)),
    inference(variable_rename,[status(thm)],[f_75_1]) ).

cnf(f_75_3,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_171),U_170)),U_171)),
    inference(clausify,[status(thm)],[f_75_2]) ).

fof(f_76_1,plain,
    ! [X_c,X_b,B,F,A_1] :
      ( hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),B))
      | ~ 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),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_1)))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_46_finite__surj]) ).

fof(f_76_2,plain,
    ! [U_176,U_175,U_174,U_173,U_172] :
      ( hBOOL(hAPP(fun(U_176,bool),bool,finite_finite(U_176),U_174))
      | ~ hBOOL(hAPP(fun(U_176,bool),bool,hAPP(fun(U_176,bool),fun(fun(U_176,bool),bool),ord_less_eq(fun(U_176,bool)),U_174),hAPP(fun(U_175,bool),fun(U_176,bool),hAPP(fun(U_175,U_176),fun(fun(U_175,bool),fun(U_176,bool)),image(U_175,U_176),U_173),U_172)))
      | ~ hBOOL(hAPP(fun(U_175,bool),bool,finite_finite(U_175),U_172)) ),
    inference(variable_rename,[status(thm)],[f_76_1]) ).

cnf(f_76_3,plain,
    ( hBOOL(hAPP(fun(U_176,bool),bool,finite_finite(U_176),U_174))
    | ~ hBOOL(hAPP(fun(U_176,bool),bool,hAPP(fun(U_176,bool),fun(fun(U_176,bool),bool),ord_less_eq(fun(U_176,bool)),U_174),hAPP(fun(U_175,bool),fun(U_176,bool),hAPP(fun(U_175,U_176),fun(fun(U_175,bool),fun(U_176,bool)),image(U_175,U_176),U_173),U_172)))
    | ~ hBOOL(hAPP(fun(U_175,bool),bool,finite_finite(U_175),U_172)) ),
    inference(clausify,[status(thm)],[f_76_2]) ).

fof(f_77_1,plain,
    ! [X_c,X_b,F,A_1,B] :
      ( ? [C_2] :
          ( ti(fun(X_b,bool),B) = hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),C_2)
          & hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),C_2))
          & hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_eq(fun(X_c,bool)),C_2),A_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),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_1)))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B)) ),
    inference(fof_nnf,[status(thm)],[fact_47_finite__subset__image]) ).

fof(f_77_2,plain,
    ! [U_182,U_181,U_180,U_179,U_178] :
      ( ? [U_177] :
          ( ti(fun(U_181,bool),U_178) = hAPP(fun(U_182,bool),fun(U_181,bool),hAPP(fun(U_182,U_181),fun(fun(U_182,bool),fun(U_181,bool)),image(U_182,U_181),U_180),U_177)
          & hBOOL(hAPP(fun(U_182,bool),bool,finite_finite(U_182),U_177))
          & hBOOL(hAPP(fun(U_182,bool),bool,hAPP(fun(U_182,bool),fun(fun(U_182,bool),bool),ord_less_eq(fun(U_182,bool)),U_177),U_179)) )
      | ~ hBOOL(hAPP(fun(U_181,bool),bool,hAPP(fun(U_181,bool),fun(fun(U_181,bool),bool),ord_less_eq(fun(U_181,bool)),U_178),hAPP(fun(U_182,bool),fun(U_181,bool),hAPP(fun(U_182,U_181),fun(fun(U_182,bool),fun(U_181,bool)),image(U_182,U_181),U_180),U_179)))
      | ~ hBOOL(hAPP(fun(U_181,bool),bool,finite_finite(U_181),U_178)) ),
    inference(variable_rename,[status(thm)],[f_77_1]) ).

fof(f_77_3,plain,
    ! [U_182,U_181,U_180,U_179,U_178] :
      ( ( ti(fun(U_181,bool),U_178) = hAPP(fun(U_182,bool),fun(U_181,bool),hAPP(fun(U_182,U_181),fun(fun(U_182,bool),fun(U_181,bool)),image(U_182,U_181),U_180),sK1(U_182,U_181,U_180,U_179,U_178))
        & hBOOL(hAPP(fun(U_182,bool),bool,finite_finite(U_182),sK1(U_182,U_181,U_180,U_179,U_178)))
        & hBOOL(hAPP(fun(U_182,bool),bool,hAPP(fun(U_182,bool),fun(fun(U_182,bool),bool),ord_less_eq(fun(U_182,bool)),sK1(U_182,U_181,U_180,U_179,U_178)),U_179)) )
      | ~ hBOOL(hAPP(fun(U_181,bool),bool,hAPP(fun(U_181,bool),fun(fun(U_181,bool),bool),ord_less_eq(fun(U_181,bool)),U_178),hAPP(fun(U_182,bool),fun(U_181,bool),hAPP(fun(U_182,U_181),fun(fun(U_182,bool),fun(U_181,bool)),image(U_182,U_181),U_180),U_179)))
      | ~ hBOOL(hAPP(fun(U_181,bool),bool,finite_finite(U_181),U_178)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_177,sK1(U_182,U_181,U_180,U_179,U_178))],[f_77_2]) ).

cnf(f_77_4,plain,
    ( hBOOL(hAPP(fun(U_182,bool),bool,hAPP(fun(U_182,bool),fun(fun(U_182,bool),bool),ord_less_eq(fun(U_182,bool)),sK1(U_182,U_181,U_180,U_179,U_178)),U_179))
    | ~ hBOOL(hAPP(fun(U_181,bool),bool,hAPP(fun(U_181,bool),fun(fun(U_181,bool),bool),ord_less_eq(fun(U_181,bool)),U_178),hAPP(fun(U_182,bool),fun(U_181,bool),hAPP(fun(U_182,U_181),fun(fun(U_182,bool),fun(U_181,bool)),image(U_182,U_181),U_180),U_179)))
    | ~ hBOOL(hAPP(fun(U_181,bool),bool,finite_finite(U_181),U_178)) ),
    inference(clausify,[status(thm)],[f_77_3]) ).

cnf(f_77_5,plain,
    ( hBOOL(hAPP(fun(U_182,bool),bool,finite_finite(U_182),sK1(U_182,U_181,U_180,U_179,U_178)))
    | ~ hBOOL(hAPP(fun(U_181,bool),bool,hAPP(fun(U_181,bool),fun(fun(U_181,bool),bool),ord_less_eq(fun(U_181,bool)),U_178),hAPP(fun(U_182,bool),fun(U_181,bool),hAPP(fun(U_182,U_181),fun(fun(U_182,bool),fun(U_181,bool)),image(U_182,U_181),U_180),U_179)))
    | ~ hBOOL(hAPP(fun(U_181,bool),bool,finite_finite(U_181),U_178)) ),
    inference(clausify,[status(thm)],[f_77_3]) ).

cnf(f_77_6,plain,
    ( ti(fun(U_181,bool),U_178) = hAPP(fun(U_182,bool),fun(U_181,bool),hAPP(fun(U_182,U_181),fun(fun(U_182,bool),fun(U_181,bool)),image(U_182,U_181),U_180),sK1(U_182,U_181,U_180,U_179,U_178))
    | ~ hBOOL(hAPP(fun(U_181,bool),bool,hAPP(fun(U_181,bool),fun(fun(U_181,bool),bool),ord_less_eq(fun(U_181,bool)),U_178),hAPP(fun(U_182,bool),fun(U_181,bool),hAPP(fun(U_182,U_181),fun(fun(U_182,bool),fun(U_181,bool)),image(U_182,U_181),U_180),U_179)))
    | ~ hBOOL(hAPP(fun(U_181,bool),bool,finite_finite(U_181),U_178)) ),
    inference(clausify,[status(thm)],[f_77_3]) ).

fof(f_78_1,plain,
    ! [X_b] :
      ( ! [Na,N_3,F] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(nat,X_b,F,Na)),hAPP(nat,X_b,F,N_3)))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Na),N_3))
          | ? [N_2] : ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(nat,X_b,F,N_2)),hAPP(nat,X_b,F,hAPP(nat,nat,suc,N_2)))) )
      | ~ order(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_48_lift__Suc__mono__le]) ).

fof(f_78_2,plain,
    ! [U_187] :
      ( ! [U_186,U_185,U_184] :
          ( hBOOL(hAPP(U_187,bool,hAPP(U_187,fun(U_187,bool),ord_less_eq(U_187),hAPP(nat,U_187,U_184,U_186)),hAPP(nat,U_187,U_184,U_185)))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_186),U_185))
          | ? [U_183] : ~ hBOOL(hAPP(U_187,bool,hAPP(U_187,fun(U_187,bool),ord_less_eq(U_187),hAPP(nat,U_187,U_184,U_183)),hAPP(nat,U_187,U_184,hAPP(nat,nat,suc,U_183)))) )
      | ~ order(U_187) ),
    inference(variable_rename,[status(thm)],[f_78_1]) ).

fof(f_78_3,plain,
    ! [U_187] :
      ( ! [U_186,U_185,U_184] :
          ( hBOOL(hAPP(U_187,bool,hAPP(U_187,fun(U_187,bool),ord_less_eq(U_187),hAPP(nat,U_187,U_184,U_186)),hAPP(nat,U_187,U_184,U_185)))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_186),U_185))
          | ~ hBOOL(hAPP(U_187,bool,hAPP(U_187,fun(U_187,bool),ord_less_eq(U_187),hAPP(nat,U_187,U_184,sK2(U_187,U_186,U_185,U_184))),hAPP(nat,U_187,U_184,hAPP(nat,nat,suc,sK2(U_187,U_186,U_185,U_184))))) )
      | ~ order(U_187) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_183,sK2(U_187,U_186,U_185,U_184))],[f_78_2]) ).

cnf(f_78_4,plain,
    ( hBOOL(hAPP(U_187,bool,hAPP(U_187,fun(U_187,bool),ord_less_eq(U_187),hAPP(nat,U_187,U_184,U_186)),hAPP(nat,U_187,U_184,U_185)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_186),U_185))
    | ~ hBOOL(hAPP(U_187,bool,hAPP(U_187,fun(U_187,bool),ord_less_eq(U_187),hAPP(nat,U_187,U_184,sK2(U_187,U_186,U_185,U_184))),hAPP(nat,U_187,U_184,hAPP(nat,nat,suc,sK2(U_187,U_186,U_185,U_184)))))
    | ~ order(U_187) ),
    inference(clausify,[status(thm)],[f_78_3]) ).

fof(f_79_1,plain,
    ! [X_c,X_b,F,A_1] :
      ( ? [X_1] :
          ( ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),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_1))),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_1))))))
          & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_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),F),A_1)))
      | hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_49_pigeonhole__infinite]) ).

fof(f_79_2,plain,
    ! [U_192,U_191,U_190,U_189] :
      ( ? [U_188] :
          ( ~ hBOOL(hAPP(fun(U_191,bool),bool,finite_finite(U_191),hAPP(fun(U_191,bool),fun(U_191,bool),collect(U_191),hAPP(fun(U_191,bool),fun(U_191,bool),hAPP(fun(U_191,fun(bool,bool)),fun(fun(U_191,bool),fun(U_191,bool)),combs(U_191,bool,bool),hAPP(fun(U_191,bool),fun(U_191,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_191,bool),fun(U_191,fun(bool,bool))),combb(bool,fun(bool,bool),U_191),fconj),hAPP(fun(U_191,bool),fun(U_191,bool),hAPP(fun(U_191,fun(fun(U_191,bool),bool)),fun(fun(U_191,bool),fun(U_191,bool)),combc(U_191,fun(U_191,bool),bool),member(U_191)),U_189))),hAPP(U_192,fun(U_191,bool),hAPP(fun(U_191,fun(U_192,bool)),fun(U_192,fun(U_191,bool)),combc(U_191,U_192,bool),hAPP(fun(U_191,U_192),fun(U_191,fun(U_192,bool)),hAPP(fun(U_192,fun(U_192,bool)),fun(fun(U_191,U_192),fun(U_191,fun(U_192,bool))),combb(U_192,fun(U_192,bool),U_191),fequal(U_192)),U_190)),hAPP(U_191,U_192,U_190,U_188))))))
          & hBOOL(hAPP(fun(U_191,bool),bool,hAPP(U_191,fun(fun(U_191,bool),bool),member(U_191),U_188),U_189)) )
      | ~ hBOOL(hAPP(fun(U_192,bool),bool,finite_finite(U_192),hAPP(fun(U_191,bool),fun(U_192,bool),hAPP(fun(U_191,U_192),fun(fun(U_191,bool),fun(U_192,bool)),image(U_191,U_192),U_190),U_189)))
      | hBOOL(hAPP(fun(U_191,bool),bool,finite_finite(U_191),U_189)) ),
    inference(variable_rename,[status(thm)],[f_79_1]) ).

fof(f_79_3,plain,
    ! [U_192,U_191,U_190,U_189] :
      ( ( ~ hBOOL(hAPP(fun(U_191,bool),bool,finite_finite(U_191),hAPP(fun(U_191,bool),fun(U_191,bool),collect(U_191),hAPP(fun(U_191,bool),fun(U_191,bool),hAPP(fun(U_191,fun(bool,bool)),fun(fun(U_191,bool),fun(U_191,bool)),combs(U_191,bool,bool),hAPP(fun(U_191,bool),fun(U_191,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_191,bool),fun(U_191,fun(bool,bool))),combb(bool,fun(bool,bool),U_191),fconj),hAPP(fun(U_191,bool),fun(U_191,bool),hAPP(fun(U_191,fun(fun(U_191,bool),bool)),fun(fun(U_191,bool),fun(U_191,bool)),combc(U_191,fun(U_191,bool),bool),member(U_191)),U_189))),hAPP(U_192,fun(U_191,bool),hAPP(fun(U_191,fun(U_192,bool)),fun(U_192,fun(U_191,bool)),combc(U_191,U_192,bool),hAPP(fun(U_191,U_192),fun(U_191,fun(U_192,bool)),hAPP(fun(U_192,fun(U_192,bool)),fun(fun(U_191,U_192),fun(U_191,fun(U_192,bool))),combb(U_192,fun(U_192,bool),U_191),fequal(U_192)),U_190)),hAPP(U_191,U_192,U_190,sK3(U_192,U_191,U_190,U_189)))))))
        & hBOOL(hAPP(fun(U_191,bool),bool,hAPP(U_191,fun(fun(U_191,bool),bool),member(U_191),sK3(U_192,U_191,U_190,U_189)),U_189)) )
      | ~ hBOOL(hAPP(fun(U_192,bool),bool,finite_finite(U_192),hAPP(fun(U_191,bool),fun(U_192,bool),hAPP(fun(U_191,U_192),fun(fun(U_191,bool),fun(U_192,bool)),image(U_191,U_192),U_190),U_189)))
      | hBOOL(hAPP(fun(U_191,bool),bool,finite_finite(U_191),U_189)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_188,sK3(U_192,U_191,U_190,U_189))],[f_79_2]) ).

cnf(f_79_4,plain,
    ( hBOOL(hAPP(fun(U_191,bool),bool,hAPP(U_191,fun(fun(U_191,bool),bool),member(U_191),sK3(U_192,U_191,U_190,U_189)),U_189))
    | ~ hBOOL(hAPP(fun(U_192,bool),bool,finite_finite(U_192),hAPP(fun(U_191,bool),fun(U_192,bool),hAPP(fun(U_191,U_192),fun(fun(U_191,bool),fun(U_192,bool)),image(U_191,U_192),U_190),U_189)))
    | hBOOL(hAPP(fun(U_191,bool),bool,finite_finite(U_191),U_189)) ),
    inference(clausify,[status(thm)],[f_79_3]) ).

cnf(f_79_5,plain,
    ( ~ hBOOL(hAPP(fun(U_191,bool),bool,finite_finite(U_191),hAPP(fun(U_191,bool),fun(U_191,bool),collect(U_191),hAPP(fun(U_191,bool),fun(U_191,bool),hAPP(fun(U_191,fun(bool,bool)),fun(fun(U_191,bool),fun(U_191,bool)),combs(U_191,bool,bool),hAPP(fun(U_191,bool),fun(U_191,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_191,bool),fun(U_191,fun(bool,bool))),combb(bool,fun(bool,bool),U_191),fconj),hAPP(fun(U_191,bool),fun(U_191,bool),hAPP(fun(U_191,fun(fun(U_191,bool),bool)),fun(fun(U_191,bool),fun(U_191,bool)),combc(U_191,fun(U_191,bool),bool),member(U_191)),U_189))),hAPP(U_192,fun(U_191,bool),hAPP(fun(U_191,fun(U_192,bool)),fun(U_192,fun(U_191,bool)),combc(U_191,U_192,bool),hAPP(fun(U_191,U_192),fun(U_191,fun(U_192,bool)),hAPP(fun(U_192,fun(U_192,bool)),fun(fun(U_191,U_192),fun(U_191,fun(U_192,bool))),combb(U_192,fun(U_192,bool),U_191),fequal(U_192)),U_190)),hAPP(U_191,U_192,U_190,sK3(U_192,U_191,U_190,U_189)))))))
    | ~ hBOOL(hAPP(fun(U_192,bool),bool,finite_finite(U_192),hAPP(fun(U_191,bool),fun(U_192,bool),hAPP(fun(U_191,U_192),fun(fun(U_191,bool),fun(U_192,bool)),image(U_191,U_192),U_190),U_189)))
    | hBOOL(hAPP(fun(U_191,bool),bool,finite_finite(U_191),U_189)) ),
    inference(clausify,[status(thm)],[f_79_3]) ).

fof(f_80_1,plain,
    ! [X_b,X_c,A_1,B_1,F,X_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),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_1)))
      | ~ hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_2),A_1))
      | ti(X_b,B_1) != hAPP(X_c,X_b,F,X_2) ),
    inference(fof_nnf,[status(thm)],[fact_50_image__eqI]) ).

fof(f_80_2,plain,
    ! [U_198,U_197,U_196,U_195,U_194,U_193] :
      ( hBOOL(hAPP(fun(U_198,bool),bool,hAPP(U_198,fun(fun(U_198,bool),bool),member(U_198),U_195),hAPP(fun(U_197,bool),fun(U_198,bool),hAPP(fun(U_197,U_198),fun(fun(U_197,bool),fun(U_198,bool)),image(U_197,U_198),U_194),U_196)))
      | ~ hBOOL(hAPP(fun(U_197,bool),bool,hAPP(U_197,fun(fun(U_197,bool),bool),member(U_197),U_193),U_196))
      | ti(U_198,U_195) != hAPP(U_197,U_198,U_194,U_193) ),
    inference(variable_rename,[status(thm)],[f_80_1]) ).

cnf(f_80_3,plain,
    ( hBOOL(hAPP(fun(U_198,bool),bool,hAPP(U_198,fun(fun(U_198,bool),bool),member(U_198),U_195),hAPP(fun(U_197,bool),fun(U_198,bool),hAPP(fun(U_197,U_198),fun(fun(U_197,bool),fun(U_198,bool)),image(U_197,U_198),U_194),U_196)))
    | ~ hBOOL(hAPP(fun(U_197,bool),bool,hAPP(U_197,fun(fun(U_197,bool),bool),member(U_197),U_193),U_196))
    | ti(U_198,U_195) != hAPP(U_197,U_198,U_194,U_193) ),
    inference(clausify,[status(thm)],[f_80_2]) ).

fof(f_81_1,plain,
    ! [X_b,A_1,B] :
      ( ti(fun(X_b,bool),A_1) = ti(fun(X_b,bool),B)
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B),A_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_1),B)) ),
    inference(fof_nnf,[status(thm)],[fact_51_equalityI]) ).

fof(f_81_2,plain,
    ! [U_201,U_200,U_199] :
      ( ti(fun(U_201,bool),U_200) = ti(fun(U_201,bool),U_199)
      | ~ hBOOL(hAPP(fun(U_201,bool),bool,hAPP(fun(U_201,bool),fun(fun(U_201,bool),bool),ord_less_eq(fun(U_201,bool)),U_199),U_200))
      | ~ hBOOL(hAPP(fun(U_201,bool),bool,hAPP(fun(U_201,bool),fun(fun(U_201,bool),bool),ord_less_eq(fun(U_201,bool)),U_200),U_199)) ),
    inference(variable_rename,[status(thm)],[f_81_1]) ).

cnf(f_81_3,plain,
    ( ti(fun(U_201,bool),U_200) = ti(fun(U_201,bool),U_199)
    | ~ hBOOL(hAPP(fun(U_201,bool),bool,hAPP(fun(U_201,bool),fun(fun(U_201,bool),bool),ord_less_eq(fun(U_201,bool)),U_199),U_200))
    | ~ hBOOL(hAPP(fun(U_201,bool),bool,hAPP(fun(U_201,bool),fun(fun(U_201,bool),bool),ord_less_eq(fun(U_201,bool)),U_200),U_199)) ),
    inference(clausify,[status(thm)],[f_81_2]) ).

fof(f_82_1,plain,
    ! [X_b,C_1,A_1,B] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_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_1),B)) ),
    inference(fof_nnf,[status(thm)],[fact_52_subsetD]) ).

fof(f_82_2,plain,
    ! [U_205,U_204,U_203,U_202] :
      ( hBOOL(hAPP(fun(U_205,bool),bool,hAPP(U_205,fun(fun(U_205,bool),bool),member(U_205),U_204),U_202))
      | ~ hBOOL(hAPP(fun(U_205,bool),bool,hAPP(U_205,fun(fun(U_205,bool),bool),member(U_205),U_204),U_203))
      | ~ hBOOL(hAPP(fun(U_205,bool),bool,hAPP(fun(U_205,bool),fun(fun(U_205,bool),bool),ord_less_eq(fun(U_205,bool)),U_203),U_202)) ),
    inference(variable_rename,[status(thm)],[f_82_1]) ).

cnf(f_82_3,plain,
    ( hBOOL(hAPP(fun(U_205,bool),bool,hAPP(U_205,fun(fun(U_205,bool),bool),member(U_205),U_204),U_202))
    | ~ hBOOL(hAPP(fun(U_205,bool),bool,hAPP(U_205,fun(fun(U_205,bool),bool),member(U_205),U_204),U_203))
    | ~ hBOOL(hAPP(fun(U_205,bool),bool,hAPP(fun(U_205,bool),fun(fun(U_205,bool),bool),ord_less_eq(fun(U_205,bool)),U_203),U_202)) ),
    inference(clausify,[status(thm)],[f_82_2]) ).

fof(f_83_1,plain,
    ! [X_b,B_1,A_2,B] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_1),B)))
      | ( ti(X_b,A_2) != ti(X_b,B_1)
        & ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),B)) ) ),
    inference(fof_nnf,[status(thm)],[fact_53_insertCI]) ).

fof(f_83_2,plain,
    ! [U_209,U_208,U_207,U_206] :
      ( hBOOL(hAPP(fun(U_209,bool),bool,hAPP(U_209,fun(fun(U_209,bool),bool),member(U_209),U_207),hAPP(fun(U_209,bool),fun(U_209,bool),hAPP(U_209,fun(fun(U_209,bool),fun(U_209,bool)),insert(U_209),U_208),U_206)))
      | ( ti(U_209,U_207) != ti(U_209,U_208)
        & ~ hBOOL(hAPP(fun(U_209,bool),bool,hAPP(U_209,fun(fun(U_209,bool),bool),member(U_209),U_207),U_206)) ) ),
    inference(variable_rename,[status(thm)],[f_83_1]) ).

cnf(f_83_3,plain,
    ( ~ hBOOL(hAPP(fun(U_209,bool),bool,hAPP(U_209,fun(fun(U_209,bool),bool),member(U_209),U_207),U_206))
    | hBOOL(hAPP(fun(U_209,bool),bool,hAPP(U_209,fun(fun(U_209,bool),bool),member(U_209),U_207),hAPP(fun(U_209,bool),fun(U_209,bool),hAPP(U_209,fun(fun(U_209,bool),fun(U_209,bool)),insert(U_209),U_208),U_206))) ),
    inference(clausify,[status(thm)],[f_83_2]) ).

cnf(f_83_4,plain,
    ( ti(U_209,U_207) != ti(U_209,U_208)
    | hBOOL(hAPP(fun(U_209,bool),bool,hAPP(U_209,fun(fun(U_209,bool),bool),member(U_209),U_207),hAPP(fun(U_209,bool),fun(U_209,bool),hAPP(U_209,fun(fun(U_209,bool),fun(U_209,bool)),insert(U_209),U_208),U_206))) ),
    inference(clausify,[status(thm)],[f_83_2]) ).

fof(f_84_1,plain,
    ! [X_b,A_2,B_1,A_1] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_1))
      | ti(X_b,A_2) = ti(X_b,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_1),A_1))) ),
    inference(fof_nnf,[status(thm)],[fact_54_insertE]) ).

fof(f_84_2,plain,
    ! [U_213,U_212,U_211,U_210] :
      ( hBOOL(hAPP(fun(U_213,bool),bool,hAPP(U_213,fun(fun(U_213,bool),bool),member(U_213),U_212),U_210))
      | ti(U_213,U_212) = ti(U_213,U_211)
      | ~ hBOOL(hAPP(fun(U_213,bool),bool,hAPP(U_213,fun(fun(U_213,bool),bool),member(U_213),U_212),hAPP(fun(U_213,bool),fun(U_213,bool),hAPP(U_213,fun(fun(U_213,bool),fun(U_213,bool)),insert(U_213),U_211),U_210))) ),
    inference(variable_rename,[status(thm)],[f_84_1]) ).

cnf(f_84_3,plain,
    ( hBOOL(hAPP(fun(U_213,bool),bool,hAPP(U_213,fun(fun(U_213,bool),bool),member(U_213),U_212),U_210))
    | ti(U_213,U_212) = ti(U_213,U_211)
    | ~ hBOOL(hAPP(fun(U_213,bool),bool,hAPP(U_213,fun(fun(U_213,bool),bool),member(U_213),U_212),hAPP(fun(U_213,bool),fun(U_213,bool),hAPP(U_213,fun(fun(U_213,bool),fun(U_213,bool)),insert(U_213),U_211),U_210))) ),
    inference(clausify,[status(thm)],[f_84_2]) ).

fof(f_85_1,plain,
    ! [X_b,A_2,B] : hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B))),
    inference(fof_nnf,[status(thm)],[fact_55_insertI1]) ).

fof(f_85_2,plain,
    ! [U_216,U_215,U_214] : hBOOL(hAPP(fun(U_216,bool),bool,hAPP(U_216,fun(fun(U_216,bool),bool),member(U_216),U_215),hAPP(fun(U_216,bool),fun(U_216,bool),hAPP(U_216,fun(fun(U_216,bool),fun(U_216,bool)),insert(U_216),U_215),U_214))),
    inference(variable_rename,[status(thm)],[f_85_1]) ).

cnf(f_85_3,plain,
    hBOOL(hAPP(fun(U_216,bool),bool,hAPP(U_216,fun(fun(U_216,bool),bool),member(U_216),U_215),hAPP(fun(U_216,bool),fun(U_216,bool),hAPP(U_216,fun(fun(U_216,bool),fun(U_216,bool)),insert(U_216),U_215),U_214))),
    inference(clausify,[status(thm)],[f_85_2]) ).

fof(f_86_1,plain,
    ! [X_b,A_2,B] : hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),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),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))),
    inference(fof_nnf,[status(thm)],[fact_56_insert__compr]) ).

fof(f_86_2,plain,
    ! [U_219,U_218,U_217] : hAPP(fun(U_219,bool),fun(U_219,bool),hAPP(U_219,fun(fun(U_219,bool),fun(U_219,bool)),insert(U_219),U_218),U_217) = hAPP(fun(U_219,bool),fun(U_219,bool),collect(U_219),hAPP(fun(U_219,bool),fun(U_219,bool),hAPP(fun(U_219,fun(bool,bool)),fun(fun(U_219,bool),fun(U_219,bool)),combs(U_219,bool,bool),hAPP(fun(U_219,bool),fun(U_219,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_219,bool),fun(U_219,fun(bool,bool))),combb(bool,fun(bool,bool),U_219),fdisj),hAPP(U_219,fun(U_219,bool),hAPP(fun(U_219,fun(U_219,bool)),fun(U_219,fun(U_219,bool)),combc(U_219,U_219,bool),fequal(U_219)),U_218))),hAPP(fun(U_219,bool),fun(U_219,bool),hAPP(fun(U_219,fun(fun(U_219,bool),bool)),fun(fun(U_219,bool),fun(U_219,bool)),combc(U_219,fun(U_219,bool),bool),member(U_219)),U_217))),
    inference(variable_rename,[status(thm)],[f_86_1]) ).

cnf(f_86_3,plain,
    hAPP(fun(U_219,bool),fun(U_219,bool),hAPP(U_219,fun(fun(U_219,bool),fun(U_219,bool)),insert(U_219),U_218),U_217) = hAPP(fun(U_219,bool),fun(U_219,bool),collect(U_219),hAPP(fun(U_219,bool),fun(U_219,bool),hAPP(fun(U_219,fun(bool,bool)),fun(fun(U_219,bool),fun(U_219,bool)),combs(U_219,bool,bool),hAPP(fun(U_219,bool),fun(U_219,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_219,bool),fun(U_219,fun(bool,bool))),combb(bool,fun(bool,bool),U_219),fdisj),hAPP(U_219,fun(U_219,bool),hAPP(fun(U_219,fun(U_219,bool)),fun(U_219,fun(U_219,bool)),combc(U_219,U_219,bool),fequal(U_219)),U_218))),hAPP(fun(U_219,bool),fun(U_219,bool),hAPP(fun(U_219,fun(fun(U_219,bool),bool)),fun(fun(U_219,bool),fun(U_219,bool)),combc(U_219,fun(U_219,bool),bool),member(U_219)),U_217))),
    inference(clausify,[status(thm)],[f_86_2]) ).

fof(f_87_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_57_insert__Collect]) ).

fof(f_87_2,plain,
    ! [U_222,U_221,U_220] : hAPP(fun(U_222,bool),fun(U_222,bool),hAPP(U_222,fun(fun(U_222,bool),fun(U_222,bool)),insert(U_222),U_221),hAPP(fun(U_222,bool),fun(U_222,bool),collect(U_222),U_220)) = hAPP(fun(U_222,bool),fun(U_222,bool),collect(U_222),hAPP(fun(U_222,bool),fun(U_222,bool),hAPP(fun(U_222,fun(bool,bool)),fun(fun(U_222,bool),fun(U_222,bool)),combs(U_222,bool,bool),hAPP(fun(U_222,bool),fun(U_222,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_222,bool),fun(U_222,fun(bool,bool))),combb(bool,fun(bool,bool),U_222),fimplies),hAPP(fun(U_222,bool),fun(U_222,bool),hAPP(fun(bool,bool),fun(fun(U_222,bool),fun(U_222,bool)),combb(bool,bool,U_222),fNot),hAPP(U_222,fun(U_222,bool),hAPP(fun(U_222,fun(U_222,bool)),fun(U_222,fun(U_222,bool)),combc(U_222,U_222,bool),fequal(U_222)),U_221)))),U_220)),
    inference(variable_rename,[status(thm)],[f_87_1]) ).

cnf(f_87_3,plain,
    hAPP(fun(U_222,bool),fun(U_222,bool),hAPP(U_222,fun(fun(U_222,bool),fun(U_222,bool)),insert(U_222),U_221),hAPP(fun(U_222,bool),fun(U_222,bool),collect(U_222),U_220)) = hAPP(fun(U_222,bool),fun(U_222,bool),collect(U_222),hAPP(fun(U_222,bool),fun(U_222,bool),hAPP(fun(U_222,fun(bool,bool)),fun(fun(U_222,bool),fun(U_222,bool)),combs(U_222,bool,bool),hAPP(fun(U_222,bool),fun(U_222,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_222,bool),fun(U_222,fun(bool,bool))),combb(bool,fun(bool,bool),U_222),fimplies),hAPP(fun(U_222,bool),fun(U_222,bool),hAPP(fun(bool,bool),fun(fun(U_222,bool),fun(U_222,bool)),combb(bool,bool,U_222),fNot),hAPP(U_222,fun(U_222,bool),hAPP(fun(U_222,fun(U_222,bool)),fun(U_222,fun(U_222,bool)),combc(U_222,U_222,bool),fequal(U_222)),U_221)))),U_220)),
    inference(clausify,[status(thm)],[f_87_2]) ).

fof(f_88_1,plain,
    ! [X_b,X_2,A_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),X_2),A_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),A_1),
    inference(fof_nnf,[status(thm)],[fact_58_insert__absorb2]) ).

fof(f_88_2,plain,
    ! [U_225,U_224,U_223] : hAPP(fun(U_225,bool),fun(U_225,bool),hAPP(U_225,fun(fun(U_225,bool),fun(U_225,bool)),insert(U_225),U_224),hAPP(fun(U_225,bool),fun(U_225,bool),hAPP(U_225,fun(fun(U_225,bool),fun(U_225,bool)),insert(U_225),U_224),U_223)) = hAPP(fun(U_225,bool),fun(U_225,bool),hAPP(U_225,fun(fun(U_225,bool),fun(U_225,bool)),insert(U_225),U_224),U_223),
    inference(variable_rename,[status(thm)],[f_88_1]) ).

cnf(f_88_3,plain,
    hAPP(fun(U_225,bool),fun(U_225,bool),hAPP(U_225,fun(fun(U_225,bool),fun(U_225,bool)),insert(U_225),U_224),hAPP(fun(U_225,bool),fun(U_225,bool),hAPP(U_225,fun(fun(U_225,bool),fun(U_225,bool)),insert(U_225),U_224),U_223)) = hAPP(fun(U_225,bool),fun(U_225,bool),hAPP(U_225,fun(fun(U_225,bool),fun(U_225,bool)),insert(U_225),U_224),U_223),
    inference(clausify,[status(thm)],[f_88_2]) ).

fof(f_89_1,plain,
    ! [X_b,X_2,Y_2,A_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_2),A_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),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),A_1)),
    inference(fof_nnf,[status(thm)],[fact_59_insert__commute]) ).

fof(f_89_2,plain,
    ! [U_229,U_228,U_227,U_226] : hAPP(fun(U_229,bool),fun(U_229,bool),hAPP(U_229,fun(fun(U_229,bool),fun(U_229,bool)),insert(U_229),U_228),hAPP(fun(U_229,bool),fun(U_229,bool),hAPP(U_229,fun(fun(U_229,bool),fun(U_229,bool)),insert(U_229),U_227),U_226)) = hAPP(fun(U_229,bool),fun(U_229,bool),hAPP(U_229,fun(fun(U_229,bool),fun(U_229,bool)),insert(U_229),U_227),hAPP(fun(U_229,bool),fun(U_229,bool),hAPP(U_229,fun(fun(U_229,bool),fun(U_229,bool)),insert(U_229),U_228),U_226)),
    inference(variable_rename,[status(thm)],[f_89_1]) ).

cnf(f_89_3,plain,
    hAPP(fun(U_229,bool),fun(U_229,bool),hAPP(U_229,fun(fun(U_229,bool),fun(U_229,bool)),insert(U_229),U_228),hAPP(fun(U_229,bool),fun(U_229,bool),hAPP(U_229,fun(fun(U_229,bool),fun(U_229,bool)),insert(U_229),U_227),U_226)) = hAPP(fun(U_229,bool),fun(U_229,bool),hAPP(U_229,fun(fun(U_229,bool),fun(U_229,bool)),insert(U_229),U_227),hAPP(fun(U_229,bool),fun(U_229,bool),hAPP(U_229,fun(fun(U_229,bool),fun(U_229,bool)),insert(U_229),U_228),U_226)),
    inference(clausify,[status(thm)],[f_89_2]) ).

fof(f_90_1,plain,
    ! [X_b,A_2,B_1,A_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_1),A_1)))
        | ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_1))
          & ti(X_b,A_2) != ti(X_b,B_1) ) )
      & ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_1))
        | ti(X_b,A_2) = ti(X_b,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_1),A_1))) ) ),
    inference(fof_nnf,[status(thm)],[fact_60_insert__iff]) ).

fof(f_90_2,plain,
    ! [U_233,U_232,U_231,U_230] :
      ( ( hBOOL(hAPP(fun(U_233,bool),bool,hAPP(U_233,fun(fun(U_233,bool),bool),member(U_233),U_232),hAPP(fun(U_233,bool),fun(U_233,bool),hAPP(U_233,fun(fun(U_233,bool),fun(U_233,bool)),insert(U_233),U_231),U_230)))
        | ( ~ hBOOL(hAPP(fun(U_233,bool),bool,hAPP(U_233,fun(fun(U_233,bool),bool),member(U_233),U_232),U_230))
          & ti(U_233,U_232) != ti(U_233,U_231) ) )
      & ( hBOOL(hAPP(fun(U_233,bool),bool,hAPP(U_233,fun(fun(U_233,bool),bool),member(U_233),U_232),U_230))
        | ti(U_233,U_232) = ti(U_233,U_231)
        | ~ hBOOL(hAPP(fun(U_233,bool),bool,hAPP(U_233,fun(fun(U_233,bool),bool),member(U_233),U_232),hAPP(fun(U_233,bool),fun(U_233,bool),hAPP(U_233,fun(fun(U_233,bool),fun(U_233,bool)),insert(U_233),U_231),U_230))) ) ),
    inference(variable_rename,[status(thm)],[f_90_1]) ).

fof(f_90_3,plain,
    ( ! [U_241,U_239,U_237,U_235] :
        ( hBOOL(hAPP(fun(U_241,bool),bool,hAPP(U_241,fun(fun(U_241,bool),bool),member(U_241),U_239),hAPP(fun(U_241,bool),fun(U_241,bool),hAPP(U_241,fun(fun(U_241,bool),fun(U_241,bool)),insert(U_241),U_237),U_235)))
        | ( ~ hBOOL(hAPP(fun(U_241,bool),bool,hAPP(U_241,fun(fun(U_241,bool),bool),member(U_241),U_239),U_235))
          & ti(U_241,U_239) != ti(U_241,U_237) ) )
    & ! [U_240,U_238,U_236,U_234] :
        ( hBOOL(hAPP(fun(U_240,bool),bool,hAPP(U_240,fun(fun(U_240,bool),bool),member(U_240),U_238),U_234))
        | ti(U_240,U_238) = ti(U_240,U_236)
        | ~ hBOOL(hAPP(fun(U_240,bool),bool,hAPP(U_240,fun(fun(U_240,bool),bool),member(U_240),U_238),hAPP(fun(U_240,bool),fun(U_240,bool),hAPP(U_240,fun(fun(U_240,bool),fun(U_240,bool)),insert(U_240),U_236),U_234))) ) ),
    inference(miniscope,[status(thm)],[f_90_2]) ).

cnf(f_90_4,plain,
    ( hBOOL(hAPP(fun(U_240,bool),bool,hAPP(U_240,fun(fun(U_240,bool),bool),member(U_240),U_238),U_234))
    | ti(U_240,U_238) = ti(U_240,U_236)
    | ~ hBOOL(hAPP(fun(U_240,bool),bool,hAPP(U_240,fun(fun(U_240,bool),bool),member(U_240),U_238),hAPP(fun(U_240,bool),fun(U_240,bool),hAPP(U_240,fun(fun(U_240,bool),fun(U_240,bool)),insert(U_240),U_236),U_234))) ),
    inference(clausify,[status(thm)],[f_90_3]) ).

cnf(f_90_5,plain,
    ( ti(U_241,U_239) != ti(U_241,U_237)
    | hBOOL(hAPP(fun(U_241,bool),bool,hAPP(U_241,fun(fun(U_241,bool),bool),member(U_241),U_239),hAPP(fun(U_241,bool),fun(U_241,bool),hAPP(U_241,fun(fun(U_241,bool),fun(U_241,bool)),insert(U_241),U_237),U_235))) ),
    inference(clausify,[status(thm)],[f_90_3]) ).

cnf(f_90_6,plain,
    ( ~ hBOOL(hAPP(fun(U_241,bool),bool,hAPP(U_241,fun(fun(U_241,bool),bool),member(U_241),U_239),U_235))
    | hBOOL(hAPP(fun(U_241,bool),bool,hAPP(U_241,fun(fun(U_241,bool),bool),member(U_241),U_239),hAPP(fun(U_241,bool),fun(U_241,bool),hAPP(U_241,fun(fun(U_241,bool),fun(U_241,bool)),insert(U_241),U_237),U_235))) ),
    inference(clausify,[status(thm)],[f_90_3]) ).

fof(f_91_1,plain,
    ! [X_b,Y_2,A_1,X_2] :
      ( ( 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_1),X_2))
        | ( ~ hBOOL(hAPP(X_b,bool,A_1,X_2))
          & ti(X_b,Y_2) != ti(X_b,X_2) ) )
      & ( hBOOL(hAPP(X_b,bool,A_1,X_2))
        | ti(X_b,Y_2) = ti(X_b,X_2)
        | ~ 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_1),X_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_61_insert__code]) ).

fof(f_91_2,plain,
    ! [U_245,U_244,U_243,U_242] :
      ( ( hBOOL(hAPP(U_245,bool,hAPP(fun(U_245,bool),fun(U_245,bool),hAPP(U_245,fun(fun(U_245,bool),fun(U_245,bool)),insert(U_245),U_244),U_243),U_242))
        | ( ~ hBOOL(hAPP(U_245,bool,U_243,U_242))
          & ti(U_245,U_244) != ti(U_245,U_242) ) )
      & ( hBOOL(hAPP(U_245,bool,U_243,U_242))
        | ti(U_245,U_244) = ti(U_245,U_242)
        | ~ hBOOL(hAPP(U_245,bool,hAPP(fun(U_245,bool),fun(U_245,bool),hAPP(U_245,fun(fun(U_245,bool),fun(U_245,bool)),insert(U_245),U_244),U_243),U_242)) ) ),
    inference(variable_rename,[status(thm)],[f_91_1]) ).

fof(f_91_3,plain,
    ( ! [U_253,U_251,U_249,U_247] :
        ( hBOOL(hAPP(U_253,bool,hAPP(fun(U_253,bool),fun(U_253,bool),hAPP(U_253,fun(fun(U_253,bool),fun(U_253,bool)),insert(U_253),U_251),U_249),U_247))
        | ( ~ hBOOL(hAPP(U_253,bool,U_249,U_247))
          & ti(U_253,U_251) != ti(U_253,U_247) ) )
    & ! [U_252,U_250,U_248,U_246] :
        ( hBOOL(hAPP(U_252,bool,U_248,U_246))
        | ti(U_252,U_250) = ti(U_252,U_246)
        | ~ hBOOL(hAPP(U_252,bool,hAPP(fun(U_252,bool),fun(U_252,bool),hAPP(U_252,fun(fun(U_252,bool),fun(U_252,bool)),insert(U_252),U_250),U_248),U_246)) ) ),
    inference(miniscope,[status(thm)],[f_91_2]) ).

cnf(f_91_4,plain,
    ( hBOOL(hAPP(U_252,bool,U_248,U_246))
    | ti(U_252,U_250) = ti(U_252,U_246)
    | ~ hBOOL(hAPP(U_252,bool,hAPP(fun(U_252,bool),fun(U_252,bool),hAPP(U_252,fun(fun(U_252,bool),fun(U_252,bool)),insert(U_252),U_250),U_248),U_246)) ),
    inference(clausify,[status(thm)],[f_91_3]) ).

cnf(f_91_5,plain,
    ( ti(U_253,U_251) != ti(U_253,U_247)
    | hBOOL(hAPP(U_253,bool,hAPP(fun(U_253,bool),fun(U_253,bool),hAPP(U_253,fun(fun(U_253,bool),fun(U_253,bool)),insert(U_253),U_251),U_249),U_247)) ),
    inference(clausify,[status(thm)],[f_91_3]) ).

cnf(f_91_6,plain,
    ( ~ hBOOL(hAPP(U_253,bool,U_249,U_247))
    | hBOOL(hAPP(U_253,bool,hAPP(fun(U_253,bool),fun(U_253,bool),hAPP(U_253,fun(fun(U_253,bool),fun(U_253,bool)),insert(U_253),U_251),U_249),U_247)) ),
    inference(clausify,[status(thm)],[f_91_3]) ).

fof(f_92_1,plain,
    ! [X_b,B,X_2,A_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),A_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),B)
          | ti(fun(X_b,bool),A_1) != ti(fun(X_b,bool),B) )
        & ( ti(fun(X_b,bool),A_1) = ti(fun(X_b,bool),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_2),A_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),B) ) )
      | hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B))
      | hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_62_insert__ident]) ).

fof(f_92_2,plain,
    ! [U_257,U_256,U_255,U_254] :
      ( ( ( hAPP(fun(U_257,bool),fun(U_257,bool),hAPP(U_257,fun(fun(U_257,bool),fun(U_257,bool)),insert(U_257),U_255),U_254) = hAPP(fun(U_257,bool),fun(U_257,bool),hAPP(U_257,fun(fun(U_257,bool),fun(U_257,bool)),insert(U_257),U_255),U_256)
          | ti(fun(U_257,bool),U_254) != ti(fun(U_257,bool),U_256) )
        & ( ti(fun(U_257,bool),U_254) = ti(fun(U_257,bool),U_256)
          | hAPP(fun(U_257,bool),fun(U_257,bool),hAPP(U_257,fun(fun(U_257,bool),fun(U_257,bool)),insert(U_257),U_255),U_254) != hAPP(fun(U_257,bool),fun(U_257,bool),hAPP(U_257,fun(fun(U_257,bool),fun(U_257,bool)),insert(U_257),U_255),U_256) ) )
      | hBOOL(hAPP(fun(U_257,bool),bool,hAPP(U_257,fun(fun(U_257,bool),bool),member(U_257),U_255),U_256))
      | hBOOL(hAPP(fun(U_257,bool),bool,hAPP(U_257,fun(fun(U_257,bool),bool),member(U_257),U_255),U_254)) ),
    inference(variable_rename,[status(thm)],[f_92_1]) ).

cnf(f_92_3,plain,
    ( ti(fun(U_257,bool),U_254) = ti(fun(U_257,bool),U_256)
    | hAPP(fun(U_257,bool),fun(U_257,bool),hAPP(U_257,fun(fun(U_257,bool),fun(U_257,bool)),insert(U_257),U_255),U_254) != hAPP(fun(U_257,bool),fun(U_257,bool),hAPP(U_257,fun(fun(U_257,bool),fun(U_257,bool)),insert(U_257),U_255),U_256)
    | hBOOL(hAPP(fun(U_257,bool),bool,hAPP(U_257,fun(fun(U_257,bool),bool),member(U_257),U_255),U_256))
    | hBOOL(hAPP(fun(U_257,bool),bool,hAPP(U_257,fun(fun(U_257,bool),bool),member(U_257),U_255),U_254)) ),
    inference(clausify,[status(thm)],[f_92_2]) ).

cnf(f_92_4,plain,
    ( hAPP(fun(U_257,bool),fun(U_257,bool),hAPP(U_257,fun(fun(U_257,bool),fun(U_257,bool)),insert(U_257),U_255),U_254) = hAPP(fun(U_257,bool),fun(U_257,bool),hAPP(U_257,fun(fun(U_257,bool),fun(U_257,bool)),insert(U_257),U_255),U_256)
    | ti(fun(U_257,bool),U_254) != ti(fun(U_257,bool),U_256)
    | hBOOL(hAPP(fun(U_257,bool),bool,hAPP(U_257,fun(fun(U_257,bool),bool),member(U_257),U_255),U_256))
    | hBOOL(hAPP(fun(U_257,bool),bool,hAPP(U_257,fun(fun(U_257,bool),bool),member(U_257),U_255),U_254)) ),
    inference(clausify,[status(thm)],[f_92_2]) ).

fof(f_93_1,plain,
    ! [X_b,B_1,A_2,B] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_1),B)))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),B)) ),
    inference(fof_nnf,[status(thm)],[fact_63_insertI2]) ).

fof(f_93_2,plain,
    ! [U_261,U_260,U_259,U_258] :
      ( hBOOL(hAPP(fun(U_261,bool),bool,hAPP(U_261,fun(fun(U_261,bool),bool),member(U_261),U_259),hAPP(fun(U_261,bool),fun(U_261,bool),hAPP(U_261,fun(fun(U_261,bool),fun(U_261,bool)),insert(U_261),U_260),U_258)))
      | ~ hBOOL(hAPP(fun(U_261,bool),bool,hAPP(U_261,fun(fun(U_261,bool),bool),member(U_261),U_259),U_258)) ),
    inference(variable_rename,[status(thm)],[f_93_1]) ).

cnf(f_93_3,plain,
    ( hBOOL(hAPP(fun(U_261,bool),bool,hAPP(U_261,fun(fun(U_261,bool),bool),member(U_261),U_259),hAPP(fun(U_261,bool),fun(U_261,bool),hAPP(U_261,fun(fun(U_261,bool),fun(U_261,bool)),insert(U_261),U_260),U_258)))
    | ~ hBOOL(hAPP(fun(U_261,bool),bool,hAPP(U_261,fun(fun(U_261,bool),bool),member(U_261),U_259),U_258)) ),
    inference(clausify,[status(thm)],[f_93_2]) ).

fof(f_94_1,plain,
    ! [X_b,A_2,A_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),A_1) = ti(fun(X_b,bool),A_1)
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_64_insert__absorb]) ).

fof(f_94_2,plain,
    ! [U_264,U_263,U_262] :
      ( hAPP(fun(U_264,bool),fun(U_264,bool),hAPP(U_264,fun(fun(U_264,bool),fun(U_264,bool)),insert(U_264),U_263),U_262) = ti(fun(U_264,bool),U_262)
      | ~ hBOOL(hAPP(fun(U_264,bool),bool,hAPP(U_264,fun(fun(U_264,bool),bool),member(U_264),U_263),U_262)) ),
    inference(variable_rename,[status(thm)],[f_94_1]) ).

cnf(f_94_3,plain,
    ( hAPP(fun(U_264,bool),fun(U_264,bool),hAPP(U_264,fun(fun(U_264,bool),fun(U_264,bool)),insert(U_264),U_263),U_262) = ti(fun(U_264,bool),U_262)
    | ~ hBOOL(hAPP(fun(U_264,bool),bool,hAPP(U_264,fun(fun(U_264,bool),bool),member(U_264),U_263),U_262)) ),
    inference(clausify,[status(thm)],[f_94_2]) ).

fof(f_95_1,plain,
    ! [X_b,A_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_1),A_1)),
    inference(fof_nnf,[status(thm)],[fact_65_subset__refl]) ).

fof(f_95_2,plain,
    ! [U_266,U_265] : hBOOL(hAPP(fun(U_266,bool),bool,hAPP(fun(U_266,bool),fun(fun(U_266,bool),bool),ord_less_eq(fun(U_266,bool)),U_265),U_265)),
    inference(variable_rename,[status(thm)],[f_95_1]) ).

cnf(f_95_3,plain,
    hBOOL(hAPP(fun(U_266,bool),bool,hAPP(fun(U_266,bool),fun(fun(U_266,bool),bool),ord_less_eq(fun(U_266,bool)),U_265),U_265)),
    inference(clausify,[status(thm)],[f_95_2]) ).

fof(f_96_1,plain,
    ! [X_b,A_1,B] :
      ( ( ti(fun(X_b,bool),A_1) = ti(fun(X_b,bool),B)
        | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B),A_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_1),B)) )
      & ( ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B),A_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_1),B)) )
        | ti(fun(X_b,bool),A_1) != ti(fun(X_b,bool),B) ) ),
    inference(fof_nnf,[status(thm)],[fact_66_set__eq__subset]) ).

fof(f_96_2,plain,
    ! [U_269,U_268,U_267] :
      ( ( ti(fun(U_269,bool),U_268) = ti(fun(U_269,bool),U_267)
        | ~ hBOOL(hAPP(fun(U_269,bool),bool,hAPP(fun(U_269,bool),fun(fun(U_269,bool),bool),ord_less_eq(fun(U_269,bool)),U_267),U_268))
        | ~ hBOOL(hAPP(fun(U_269,bool),bool,hAPP(fun(U_269,bool),fun(fun(U_269,bool),bool),ord_less_eq(fun(U_269,bool)),U_268),U_267)) )
      & ( ( hBOOL(hAPP(fun(U_269,bool),bool,hAPP(fun(U_269,bool),fun(fun(U_269,bool),bool),ord_less_eq(fun(U_269,bool)),U_267),U_268))
          & hBOOL(hAPP(fun(U_269,bool),bool,hAPP(fun(U_269,bool),fun(fun(U_269,bool),bool),ord_less_eq(fun(U_269,bool)),U_268),U_267)) )
        | ti(fun(U_269,bool),U_268) != ti(fun(U_269,bool),U_267) ) ),
    inference(variable_rename,[status(thm)],[f_96_1]) ).

fof(f_96_3,plain,
    ( ! [U_275,U_273,U_271] :
        ( ti(fun(U_275,bool),U_273) = ti(fun(U_275,bool),U_271)
        | ~ hBOOL(hAPP(fun(U_275,bool),bool,hAPP(fun(U_275,bool),fun(fun(U_275,bool),bool),ord_less_eq(fun(U_275,bool)),U_271),U_273))
        | ~ hBOOL(hAPP(fun(U_275,bool),bool,hAPP(fun(U_275,bool),fun(fun(U_275,bool),bool),ord_less_eq(fun(U_275,bool)),U_273),U_271)) )
    & ! [U_274,U_272,U_270] :
        ( ( hBOOL(hAPP(fun(U_274,bool),bool,hAPP(fun(U_274,bool),fun(fun(U_274,bool),bool),ord_less_eq(fun(U_274,bool)),U_270),U_272))
          & hBOOL(hAPP(fun(U_274,bool),bool,hAPP(fun(U_274,bool),fun(fun(U_274,bool),bool),ord_less_eq(fun(U_274,bool)),U_272),U_270)) )
        | ti(fun(U_274,bool),U_272) != ti(fun(U_274,bool),U_270) ) ),
    inference(miniscope,[status(thm)],[f_96_2]) ).

cnf(f_96_4,plain,
    ( hBOOL(hAPP(fun(U_274,bool),bool,hAPP(fun(U_274,bool),fun(fun(U_274,bool),bool),ord_less_eq(fun(U_274,bool)),U_272),U_270))
    | ti(fun(U_274,bool),U_272) != ti(fun(U_274,bool),U_270) ),
    inference(clausify,[status(thm)],[f_96_3]) ).

cnf(f_96_5,plain,
    ( hBOOL(hAPP(fun(U_274,bool),bool,hAPP(fun(U_274,bool),fun(fun(U_274,bool),bool),ord_less_eq(fun(U_274,bool)),U_270),U_272))
    | ti(fun(U_274,bool),U_272) != ti(fun(U_274,bool),U_270) ),
    inference(clausify,[status(thm)],[f_96_3]) ).

cnf(f_96_6,plain,
    ( ti(fun(U_275,bool),U_273) = ti(fun(U_275,bool),U_271)
    | ~ hBOOL(hAPP(fun(U_275,bool),bool,hAPP(fun(U_275,bool),fun(fun(U_275,bool),bool),ord_less_eq(fun(U_275,bool)),U_271),U_273))
    | ~ hBOOL(hAPP(fun(U_275,bool),bool,hAPP(fun(U_275,bool),fun(fun(U_275,bool),bool),ord_less_eq(fun(U_275,bool)),U_273),U_271)) ),
    inference(clausify,[status(thm)],[f_96_3]) ).

fof(f_97_1,plain,
    ! [X_b,A_1,B] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_1),B))
      | ti(fun(X_b,bool),A_1) != ti(fun(X_b,bool),B) ),
    inference(fof_nnf,[status(thm)],[fact_67_equalityD1]) ).

fof(f_97_2,plain,
    ! [U_278,U_277,U_276] :
      ( hBOOL(hAPP(fun(U_278,bool),bool,hAPP(fun(U_278,bool),fun(fun(U_278,bool),bool),ord_less_eq(fun(U_278,bool)),U_277),U_276))
      | ti(fun(U_278,bool),U_277) != ti(fun(U_278,bool),U_276) ),
    inference(variable_rename,[status(thm)],[f_97_1]) ).

cnf(f_97_3,plain,
    ( hBOOL(hAPP(fun(U_278,bool),bool,hAPP(fun(U_278,bool),fun(fun(U_278,bool),bool),ord_less_eq(fun(U_278,bool)),U_277),U_276))
    | ti(fun(U_278,bool),U_277) != ti(fun(U_278,bool),U_276) ),
    inference(clausify,[status(thm)],[f_97_2]) ).

fof(f_98_1,plain,
    ! [X_b,A_1,B] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B),A_1))
      | ti(fun(X_b,bool),A_1) != ti(fun(X_b,bool),B) ),
    inference(fof_nnf,[status(thm)],[fact_68_equalityD2]) ).

fof(f_98_2,plain,
    ! [U_281,U_280,U_279] :
      ( hBOOL(hAPP(fun(U_281,bool),bool,hAPP(fun(U_281,bool),fun(fun(U_281,bool),bool),ord_less_eq(fun(U_281,bool)),U_279),U_280))
      | ti(fun(U_281,bool),U_280) != ti(fun(U_281,bool),U_279) ),
    inference(variable_rename,[status(thm)],[f_98_1]) ).

cnf(f_98_3,plain,
    ( hBOOL(hAPP(fun(U_281,bool),bool,hAPP(fun(U_281,bool),fun(fun(U_281,bool),bool),ord_less_eq(fun(U_281,bool)),U_279),U_280))
    | ti(fun(U_281,bool),U_280) != ti(fun(U_281,bool),U_279) ),
    inference(clausify,[status(thm)],[f_98_2]) ).

fof(f_99_1,plain,
    ! [X_b,X_2,A_1,B] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_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_1),B)) ),
    inference(fof_nnf,[status(thm)],[fact_69_in__mono]) ).

fof(f_99_2,plain,
    ! [U_285,U_284,U_283,U_282] :
      ( hBOOL(hAPP(fun(U_285,bool),bool,hAPP(U_285,fun(fun(U_285,bool),bool),member(U_285),U_284),U_282))
      | ~ hBOOL(hAPP(fun(U_285,bool),bool,hAPP(U_285,fun(fun(U_285,bool),bool),member(U_285),U_284),U_283))
      | ~ hBOOL(hAPP(fun(U_285,bool),bool,hAPP(fun(U_285,bool),fun(fun(U_285,bool),bool),ord_less_eq(fun(U_285,bool)),U_283),U_282)) ),
    inference(variable_rename,[status(thm)],[f_99_1]) ).

cnf(f_99_3,plain,
    ( hBOOL(hAPP(fun(U_285,bool),bool,hAPP(U_285,fun(fun(U_285,bool),bool),member(U_285),U_284),U_282))
    | ~ hBOOL(hAPP(fun(U_285,bool),bool,hAPP(U_285,fun(fun(U_285,bool),bool),member(U_285),U_284),U_283))
    | ~ hBOOL(hAPP(fun(U_285,bool),bool,hAPP(fun(U_285,bool),fun(fun(U_285,bool),bool),ord_less_eq(fun(U_285,bool)),U_283),U_282)) ),
    inference(clausify,[status(thm)],[f_99_2]) ).

fof(f_100_1,plain,
    ! [X_b,B,X_2,A_1] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_1),B))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_70_set__rev__mp]) ).

fof(f_100_2,plain,
    ! [U_289,U_288,U_287,U_286] :
      ( hBOOL(hAPP(fun(U_289,bool),bool,hAPP(U_289,fun(fun(U_289,bool),bool),member(U_289),U_287),U_288))
      | ~ hBOOL(hAPP(fun(U_289,bool),bool,hAPP(fun(U_289,bool),fun(fun(U_289,bool),bool),ord_less_eq(fun(U_289,bool)),U_286),U_288))
      | ~ hBOOL(hAPP(fun(U_289,bool),bool,hAPP(U_289,fun(fun(U_289,bool),bool),member(U_289),U_287),U_286)) ),
    inference(variable_rename,[status(thm)],[f_100_1]) ).

cnf(f_100_3,plain,
    ( hBOOL(hAPP(fun(U_289,bool),bool,hAPP(U_289,fun(fun(U_289,bool),bool),member(U_289),U_287),U_288))
    | ~ hBOOL(hAPP(fun(U_289,bool),bool,hAPP(fun(U_289,bool),fun(fun(U_289,bool),bool),ord_less_eq(fun(U_289,bool)),U_286),U_288))
    | ~ hBOOL(hAPP(fun(U_289,bool),bool,hAPP(U_289,fun(fun(U_289,bool),bool),member(U_289),U_287),U_286)) ),
    inference(clausify,[status(thm)],[f_100_2]) ).

fof(f_101_1,plain,
    ! [X_b,X_2,A_1,B] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_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_1),B)) ),
    inference(fof_nnf,[status(thm)],[fact_71_set__mp]) ).

fof(f_101_2,plain,
    ! [U_293,U_292,U_291,U_290] :
      ( hBOOL(hAPP(fun(U_293,bool),bool,hAPP(U_293,fun(fun(U_293,bool),bool),member(U_293),U_292),U_290))
      | ~ hBOOL(hAPP(fun(U_293,bool),bool,hAPP(U_293,fun(fun(U_293,bool),bool),member(U_293),U_292),U_291))
      | ~ hBOOL(hAPP(fun(U_293,bool),bool,hAPP(fun(U_293,bool),fun(fun(U_293,bool),bool),ord_less_eq(fun(U_293,bool)),U_291),U_290)) ),
    inference(variable_rename,[status(thm)],[f_101_1]) ).

cnf(f_101_3,plain,
    ( hBOOL(hAPP(fun(U_293,bool),bool,hAPP(U_293,fun(fun(U_293,bool),bool),member(U_293),U_292),U_290))
    | ~ hBOOL(hAPP(fun(U_293,bool),bool,hAPP(U_293,fun(fun(U_293,bool),bool),member(U_293),U_292),U_291))
    | ~ hBOOL(hAPP(fun(U_293,bool),bool,hAPP(fun(U_293,bool),fun(fun(U_293,bool),bool),ord_less_eq(fun(U_293,bool)),U_291),U_290)) ),
    inference(clausify,[status(thm)],[f_101_2]) ).

fof(f_102_1,plain,
    ! [X_b,C,A_1,B] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_1),C))
      | ~ hBOOL(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),C))
      | ~ hBOOL(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_1),B)) ),
    inference(fof_nnf,[status(thm)],[fact_72_subset__trans]) ).

fof(f_102_2,plain,
    ! [U_297,U_296,U_295,U_294] :
      ( hBOOL(hAPP(fun(U_297,bool),bool,hAPP(fun(U_297,bool),fun(fun(U_297,bool),bool),ord_less_eq(fun(U_297,bool)),U_295),U_296))
      | ~ hBOOL(hAPP(fun(U_297,bool),bool,hAPP(fun(U_297,bool),fun(fun(U_297,bool),bool),ord_less_eq(fun(U_297,bool)),U_294),U_296))
      | ~ hBOOL(hAPP(fun(U_297,bool),bool,hAPP(fun(U_297,bool),fun(fun(U_297,bool),bool),ord_less_eq(fun(U_297,bool)),U_295),U_294)) ),
    inference(variable_rename,[status(thm)],[f_102_1]) ).

cnf(f_102_3,plain,
    ( hBOOL(hAPP(fun(U_297,bool),bool,hAPP(fun(U_297,bool),fun(fun(U_297,bool),bool),ord_less_eq(fun(U_297,bool)),U_295),U_296))
    | ~ hBOOL(hAPP(fun(U_297,bool),bool,hAPP(fun(U_297,bool),fun(fun(U_297,bool),bool),ord_less_eq(fun(U_297,bool)),U_294),U_296))
    | ~ hBOOL(hAPP(fun(U_297,bool),bool,hAPP(fun(U_297,bool),fun(fun(U_297,bool),bool),ord_less_eq(fun(U_297,bool)),U_295),U_294)) ),
    inference(clausify,[status(thm)],[f_102_2]) ).

fof(f_103_1,plain,
    ! [X_b,A_1,B] :
      ( ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B),A_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_1),B)) )
      | ti(fun(X_b,bool),A_1) != ti(fun(X_b,bool),B) ),
    inference(fof_nnf,[status(thm)],[fact_73_equalityE]) ).

fof(f_103_2,plain,
    ! [U_300,U_299,U_298] :
      ( ( hBOOL(hAPP(fun(U_300,bool),bool,hAPP(fun(U_300,bool),fun(fun(U_300,bool),bool),ord_less_eq(fun(U_300,bool)),U_298),U_299))
        & hBOOL(hAPP(fun(U_300,bool),bool,hAPP(fun(U_300,bool),fun(fun(U_300,bool),bool),ord_less_eq(fun(U_300,bool)),U_299),U_298)) )
      | ti(fun(U_300,bool),U_299) != ti(fun(U_300,bool),U_298) ),
    inference(variable_rename,[status(thm)],[f_103_1]) ).

cnf(f_103_3,plain,
    ( hBOOL(hAPP(fun(U_300,bool),bool,hAPP(fun(U_300,bool),fun(fun(U_300,bool),bool),ord_less_eq(fun(U_300,bool)),U_299),U_298))
    | ti(fun(U_300,bool),U_299) != ti(fun(U_300,bool),U_298) ),
    inference(clausify,[status(thm)],[f_103_2]) ).

cnf(f_103_4,plain,
    ( hBOOL(hAPP(fun(U_300,bool),bool,hAPP(fun(U_300,bool),fun(fun(U_300,bool),bool),ord_less_eq(fun(U_300,bool)),U_298),U_299))
    | ti(fun(U_300,bool),U_299) != ti(fun(U_300,bool),U_298) ),
    inference(clausify,[status(thm)],[f_103_2]) ).

fof(f_104_1,plain,
    ! [X_b,X_c,F,G] :
      ( ti(fun(X_b,X_c),F) = ti(fun(X_b,X_c),G)
      | ? [X_1] : hAPP(X_b,X_c,F,X_1) != hAPP(X_b,X_c,G,X_1) ),
    inference(fof_nnf,[status(thm)],[fact_74_ext]) ).

fof(f_104_2,plain,
    ! [U_305,U_304,U_303,U_302] :
      ( ti(fun(U_305,U_304),U_303) = ti(fun(U_305,U_304),U_302)
      | ? [U_301] : hAPP(U_305,U_304,U_303,U_301) != hAPP(U_305,U_304,U_302,U_301) ),
    inference(variable_rename,[status(thm)],[f_104_1]) ).

fof(f_104_3,plain,
    ! [U_305,U_304,U_303,U_302] :
      ( ti(fun(U_305,U_304),U_303) = ti(fun(U_305,U_304),U_302)
      | hAPP(U_305,U_304,U_303,sK4(U_305,U_304,U_303,U_302)) != hAPP(U_305,U_304,U_302,sK4(U_305,U_304,U_303,U_302)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_301,sK4(U_305,U_304,U_303,U_302))],[f_104_2]) ).

cnf(f_104_4,plain,
    ( ti(fun(U_305,U_304),U_303) = ti(fun(U_305,U_304),U_302)
    | hAPP(U_305,U_304,U_303,sK4(U_305,U_304,U_303,U_302)) != hAPP(U_305,U_304,U_302,sK4(U_305,U_304,U_303,U_302)) ),
    inference(clausify,[status(thm)],[f_104_3]) ).

fof(f_105_1,plain,
    ! [X_b,X_2,A_1] :
      ( ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1))
        | ~ hBOOL(hAPP(X_b,bool,A_1,X_2)) )
      & ( hBOOL(hAPP(X_b,bool,A_1,X_2))
        | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_75_mem__def]) ).

fof(f_105_2,plain,
    ! [U_308,U_307,U_306] :
      ( ( hBOOL(hAPP(fun(U_308,bool),bool,hAPP(U_308,fun(fun(U_308,bool),bool),member(U_308),U_307),U_306))
        | ~ hBOOL(hAPP(U_308,bool,U_306,U_307)) )
      & ( hBOOL(hAPP(U_308,bool,U_306,U_307))
        | ~ hBOOL(hAPP(fun(U_308,bool),bool,hAPP(U_308,fun(fun(U_308,bool),bool),member(U_308),U_307),U_306)) ) ),
    inference(variable_rename,[status(thm)],[f_105_1]) ).

fof(f_105_3,plain,
    ( ! [U_314,U_312,U_310] :
        ( hBOOL(hAPP(fun(U_314,bool),bool,hAPP(U_314,fun(fun(U_314,bool),bool),member(U_314),U_312),U_310))
        | ~ hBOOL(hAPP(U_314,bool,U_310,U_312)) )
    & ! [U_313,U_311,U_309] :
        ( hBOOL(hAPP(U_313,bool,U_309,U_311))
        | ~ hBOOL(hAPP(fun(U_313,bool),bool,hAPP(U_313,fun(fun(U_313,bool),bool),member(U_313),U_311),U_309)) ) ),
    inference(miniscope,[status(thm)],[f_105_2]) ).

cnf(f_105_4,plain,
    ( hBOOL(hAPP(U_313,bool,U_309,U_311))
    | ~ hBOOL(hAPP(fun(U_313,bool),bool,hAPP(U_313,fun(fun(U_313,bool),bool),member(U_313),U_311),U_309)) ),
    inference(clausify,[status(thm)],[f_105_3]) ).

cnf(f_105_5,plain,
    ( hBOOL(hAPP(fun(U_314,bool),bool,hAPP(U_314,fun(fun(U_314,bool),bool),member(U_314),U_312),U_310))
    | ~ hBOOL(hAPP(U_314,bool,U_310,U_312)) ),
    inference(clausify,[status(thm)],[f_105_3]) ).

fof(f_106_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_106_2,plain,
    ! [U_316,U_315] : hAPP(fun(U_316,bool),fun(U_316,bool),collect(U_316),U_315) = ti(fun(U_316,bool),U_315),
    inference(variable_rename,[status(thm)],[f_106_1]) ).

cnf(f_106_3,plain,
    hAPP(fun(U_316,bool),fun(U_316,bool),collect(U_316),U_315) = ti(fun(U_316,bool),U_315),
    inference(clausify,[status(thm)],[f_106_2]) ).

fof(f_107_1,plain,
    ! [X_b,X_c,Z,F,A_1] :
      ( ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Z),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_1)))
        | ! [X_1] :
            ( ti(X_b,Z) != 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_1)) ) )
      & ( ? [X_1] :
            ( ti(X_b,Z) = 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_1)) )
        | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Z),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_1))) ) ),
    inference(fof_nnf,[status(thm)],[fact_77_image__iff]) ).

fof(f_107_2,plain,
    ! [U_323,U_322,U_321,U_320,U_319] :
      ( ( hBOOL(hAPP(fun(U_323,bool),bool,hAPP(U_323,fun(fun(U_323,bool),bool),member(U_323),U_321),hAPP(fun(U_322,bool),fun(U_323,bool),hAPP(fun(U_322,U_323),fun(fun(U_322,bool),fun(U_323,bool)),image(U_322,U_323),U_320),U_319)))
        | ! [U_318] :
            ( ti(U_323,U_321) != hAPP(U_322,U_323,U_320,U_318)
            | ~ hBOOL(hAPP(fun(U_322,bool),bool,hAPP(U_322,fun(fun(U_322,bool),bool),member(U_322),U_318),U_319)) ) )
      & ( ? [U_317] :
            ( ti(U_323,U_321) = hAPP(U_322,U_323,U_320,U_317)
            & hBOOL(hAPP(fun(U_322,bool),bool,hAPP(U_322,fun(fun(U_322,bool),bool),member(U_322),U_317),U_319)) )
        | ~ hBOOL(hAPP(fun(U_323,bool),bool,hAPP(U_323,fun(fun(U_323,bool),bool),member(U_323),U_321),hAPP(fun(U_322,bool),fun(U_323,bool),hAPP(fun(U_322,U_323),fun(fun(U_322,bool),fun(U_323,bool)),image(U_322,U_323),U_320),U_319))) ) ),
    inference(variable_rename,[status(thm)],[f_107_1]) ).

fof(f_107_3,plain,
    ( ! [U_333,U_331,U_329,U_327,U_325] :
        ( hBOOL(hAPP(fun(U_333,bool),bool,hAPP(U_333,fun(fun(U_333,bool),bool),member(U_333),U_329),hAPP(fun(U_331,bool),fun(U_333,bool),hAPP(fun(U_331,U_333),fun(fun(U_331,bool),fun(U_333,bool)),image(U_331,U_333),U_327),U_325)))
        | ! [U_318] :
            ( ti(U_333,U_329) != hAPP(U_331,U_333,U_327,U_318)
            | ~ hBOOL(hAPP(fun(U_331,bool),bool,hAPP(U_331,fun(fun(U_331,bool),bool),member(U_331),U_318),U_325)) ) )
    & ! [U_332,U_330,U_328,U_326,U_324] :
        ( ? [U_317] :
            ( ti(U_332,U_328) = hAPP(U_330,U_332,U_326,U_317)
            & hBOOL(hAPP(fun(U_330,bool),bool,hAPP(U_330,fun(fun(U_330,bool),bool),member(U_330),U_317),U_324)) )
        | ~ hBOOL(hAPP(fun(U_332,bool),bool,hAPP(U_332,fun(fun(U_332,bool),bool),member(U_332),U_328),hAPP(fun(U_330,bool),fun(U_332,bool),hAPP(fun(U_330,U_332),fun(fun(U_330,bool),fun(U_332,bool)),image(U_330,U_332),U_326),U_324))) ) ),
    inference(miniscope,[status(thm)],[f_107_2]) ).

fof(f_107_4,plain,
    ( ! [U_333,U_331,U_329,U_327,U_325] :
        ( hBOOL(hAPP(fun(U_333,bool),bool,hAPP(U_333,fun(fun(U_333,bool),bool),member(U_333),U_329),hAPP(fun(U_331,bool),fun(U_333,bool),hAPP(fun(U_331,U_333),fun(fun(U_331,bool),fun(U_333,bool)),image(U_331,U_333),U_327),U_325)))
        | ! [U_318] :
            ( ti(U_333,U_329) != hAPP(U_331,U_333,U_327,U_318)
            | ~ hBOOL(hAPP(fun(U_331,bool),bool,hAPP(U_331,fun(fun(U_331,bool),bool),member(U_331),U_318),U_325)) ) )
    & ! [U_332,U_330,U_328,U_326,U_324] :
        ( ( ti(U_332,U_328) = hAPP(U_330,U_332,U_326,sK5(U_332,U_330,U_328,U_326,U_324))
          & hBOOL(hAPP(fun(U_330,bool),bool,hAPP(U_330,fun(fun(U_330,bool),bool),member(U_330),sK5(U_332,U_330,U_328,U_326,U_324)),U_324)) )
        | ~ hBOOL(hAPP(fun(U_332,bool),bool,hAPP(U_332,fun(fun(U_332,bool),bool),member(U_332),U_328),hAPP(fun(U_330,bool),fun(U_332,bool),hAPP(fun(U_330,U_332),fun(fun(U_330,bool),fun(U_332,bool)),image(U_330,U_332),U_326),U_324))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_317,sK5(U_332,U_330,U_328,U_326,U_324))],[f_107_3]) ).

cnf(f_107_5,plain,
    ( hBOOL(hAPP(fun(U_330,bool),bool,hAPP(U_330,fun(fun(U_330,bool),bool),member(U_330),sK5(U_332,U_330,U_328,U_326,U_324)),U_324))
    | ~ hBOOL(hAPP(fun(U_332,bool),bool,hAPP(U_332,fun(fun(U_332,bool),bool),member(U_332),U_328),hAPP(fun(U_330,bool),fun(U_332,bool),hAPP(fun(U_330,U_332),fun(fun(U_330,bool),fun(U_332,bool)),image(U_330,U_332),U_326),U_324))) ),
    inference(clausify,[status(thm)],[f_107_4]) ).

cnf(f_107_6,plain,
    ( ti(U_332,U_328) = hAPP(U_330,U_332,U_326,sK5(U_332,U_330,U_328,U_326,U_324))
    | ~ hBOOL(hAPP(fun(U_332,bool),bool,hAPP(U_332,fun(fun(U_332,bool),bool),member(U_332),U_328),hAPP(fun(U_330,bool),fun(U_332,bool),hAPP(fun(U_330,U_332),fun(fun(U_330,bool),fun(U_332,bool)),image(U_330,U_332),U_326),U_324))) ),
    inference(clausify,[status(thm)],[f_107_4]) ).

cnf(f_107_7,plain,
    ( hBOOL(hAPP(fun(U_333,bool),bool,hAPP(U_333,fun(fun(U_333,bool),bool),member(U_333),U_329),hAPP(fun(U_331,bool),fun(U_333,bool),hAPP(fun(U_331,U_333),fun(fun(U_331,bool),fun(U_333,bool)),image(U_331,U_333),U_327),U_325)))
    | ti(U_333,U_329) != hAPP(U_331,U_333,U_327,U_318)
    | ~ hBOOL(hAPP(fun(U_331,bool),bool,hAPP(U_331,fun(fun(U_331,bool),bool),member(U_331),U_318),U_325)) ),
    inference(clausify,[status(thm)],[f_107_4]) ).

fof(f_108_1,plain,
    ! [X_c,X_b,F,X_2,A_1] :
      ( 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)),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_1)))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_78_imageI]) ).

fof(f_108_2,plain,
    ! [U_338,U_337,U_336,U_335,U_334] :
      ( hBOOL(hAPP(fun(U_338,bool),bool,hAPP(U_338,fun(fun(U_338,bool),bool),member(U_338),hAPP(U_337,U_338,U_336,U_335)),hAPP(fun(U_337,bool),fun(U_338,bool),hAPP(fun(U_337,U_338),fun(fun(U_337,bool),fun(U_338,bool)),image(U_337,U_338),U_336),U_334)))
      | ~ hBOOL(hAPP(fun(U_337,bool),bool,hAPP(U_337,fun(fun(U_337,bool),bool),member(U_337),U_335),U_334)) ),
    inference(variable_rename,[status(thm)],[f_108_1]) ).

cnf(f_108_3,plain,
    ( hBOOL(hAPP(fun(U_338,bool),bool,hAPP(U_338,fun(fun(U_338,bool),bool),member(U_338),hAPP(U_337,U_338,U_336,U_335)),hAPP(fun(U_337,bool),fun(U_338,bool),hAPP(fun(U_337,U_338),fun(fun(U_337,bool),fun(U_338,bool)),image(U_337,U_338),U_336),U_334)))
    | ~ hBOOL(hAPP(fun(U_337,bool),bool,hAPP(U_337,fun(fun(U_337,bool),bool),member(U_337),U_335),U_334)) ),
    inference(clausify,[status(thm)],[f_108_2]) ).

fof(f_109_1,plain,
    ! [X_c,X_b,B_1,F,X_2,A_1] :
      ( hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),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_1)))
      | ti(X_c,B_1) != 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_1)) ),
    inference(fof_nnf,[status(thm)],[fact_79_rev__image__eqI]) ).

fof(f_109_2,plain,
    ! [U_344,U_343,U_342,U_341,U_340,U_339] :
      ( hBOOL(hAPP(fun(U_344,bool),bool,hAPP(U_344,fun(fun(U_344,bool),bool),member(U_344),U_342),hAPP(fun(U_343,bool),fun(U_344,bool),hAPP(fun(U_343,U_344),fun(fun(U_343,bool),fun(U_344,bool)),image(U_343,U_344),U_341),U_339)))
      | ti(U_344,U_342) != hAPP(U_343,U_344,U_341,U_340)
      | ~ hBOOL(hAPP(fun(U_343,bool),bool,hAPP(U_343,fun(fun(U_343,bool),bool),member(U_343),U_340),U_339)) ),
    inference(variable_rename,[status(thm)],[f_109_1]) ).

cnf(f_109_3,plain,
    ( hBOOL(hAPP(fun(U_344,bool),bool,hAPP(U_344,fun(fun(U_344,bool),bool),member(U_344),U_342),hAPP(fun(U_343,bool),fun(U_344,bool),hAPP(fun(U_343,U_344),fun(fun(U_343,bool),fun(U_344,bool)),image(U_343,U_344),U_341),U_339)))
    | ti(U_344,U_342) != hAPP(U_343,U_344,U_341,U_340)
    | ~ hBOOL(hAPP(fun(U_343,bool),bool,hAPP(U_343,fun(fun(U_343,bool),bool),member(U_343),U_340),U_339)) ),
    inference(clausify,[status(thm)],[f_109_2]) ).

fof(f_110_1,plain,
    ! [X_b,X_1,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_1),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_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)),Xa))),
    inference(fof_nnf,[status(thm)],[fact_80_insert__compr__raw]) ).

fof(f_110_2,plain,
    ! [U_347,U_346,U_345] : hAPP(fun(U_347,bool),fun(U_347,bool),hAPP(U_347,fun(fun(U_347,bool),fun(U_347,bool)),insert(U_347),U_346),U_345) = hAPP(fun(U_347,bool),fun(U_347,bool),collect(U_347),hAPP(fun(U_347,bool),fun(U_347,bool),hAPP(fun(U_347,fun(bool,bool)),fun(fun(U_347,bool),fun(U_347,bool)),combs(U_347,bool,bool),hAPP(fun(U_347,bool),fun(U_347,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_347,bool),fun(U_347,fun(bool,bool))),combb(bool,fun(bool,bool),U_347),fdisj),hAPP(U_347,fun(U_347,bool),hAPP(fun(U_347,fun(U_347,bool)),fun(U_347,fun(U_347,bool)),combc(U_347,U_347,bool),fequal(U_347)),U_346))),hAPP(fun(U_347,bool),fun(U_347,bool),hAPP(fun(U_347,fun(fun(U_347,bool),bool)),fun(fun(U_347,bool),fun(U_347,bool)),combc(U_347,fun(U_347,bool),bool),member(U_347)),U_345))),
    inference(variable_rename,[status(thm)],[f_110_1]) ).

cnf(f_110_3,plain,
    hAPP(fun(U_347,bool),fun(U_347,bool),hAPP(U_347,fun(fun(U_347,bool),fun(U_347,bool)),insert(U_347),U_346),U_345) = hAPP(fun(U_347,bool),fun(U_347,bool),collect(U_347),hAPP(fun(U_347,bool),fun(U_347,bool),hAPP(fun(U_347,fun(bool,bool)),fun(fun(U_347,bool),fun(U_347,bool)),combs(U_347,bool,bool),hAPP(fun(U_347,bool),fun(U_347,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_347,bool),fun(U_347,fun(bool,bool))),combb(bool,fun(bool,bool),U_347),fdisj),hAPP(U_347,fun(U_347,bool),hAPP(fun(U_347,fun(U_347,bool)),fun(U_347,fun(U_347,bool)),combc(U_347,U_347,bool),fequal(U_347)),U_346))),hAPP(fun(U_347,bool),fun(U_347,bool),hAPP(fun(U_347,fun(fun(U_347,bool),bool)),fun(fun(U_347,bool),fun(U_347,bool)),combc(U_347,fun(U_347,bool),bool),member(U_347)),U_345))),
    inference(clausify,[status(thm)],[f_110_2]) ).

fof(f_111_1,plain,
    ! [X_c,X_b,X_d,F,G,A_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_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_1)) = 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_1),
    inference(fof_nnf,[status(thm)],[fact_81_image__image]) ).

fof(f_111_2,plain,
    ! [U_353,U_352,U_351,U_350,U_349,U_348] : hAPP(fun(U_353,bool),fun(U_352,bool),hAPP(fun(U_353,U_352),fun(fun(U_353,bool),fun(U_352,bool)),image(U_353,U_352),U_350),hAPP(fun(U_351,bool),fun(U_353,bool),hAPP(fun(U_351,U_353),fun(fun(U_351,bool),fun(U_353,bool)),image(U_351,U_353),U_349),U_348)) = hAPP(fun(U_351,bool),fun(U_352,bool),hAPP(fun(U_351,U_352),fun(fun(U_351,bool),fun(U_352,bool)),image(U_351,U_352),hAPP(fun(U_351,U_353),fun(U_351,U_352),hAPP(fun(U_353,U_352),fun(fun(U_351,U_353),fun(U_351,U_352)),combb(U_353,U_352,U_351),U_350),U_349)),U_348),
    inference(variable_rename,[status(thm)],[f_111_1]) ).

cnf(f_111_3,plain,
    hAPP(fun(U_353,bool),fun(U_352,bool),hAPP(fun(U_353,U_352),fun(fun(U_353,bool),fun(U_352,bool)),image(U_353,U_352),U_350),hAPP(fun(U_351,bool),fun(U_353,bool),hAPP(fun(U_351,U_353),fun(fun(U_351,bool),fun(U_353,bool)),image(U_351,U_353),U_349),U_348)) = hAPP(fun(U_351,bool),fun(U_352,bool),hAPP(fun(U_351,U_352),fun(fun(U_351,bool),fun(U_352,bool)),image(U_351,U_352),hAPP(fun(U_351,U_353),fun(U_351,U_352),hAPP(fun(U_353,U_352),fun(fun(U_351,U_353),fun(U_351,U_352)),combb(U_353,U_352,U_351),U_350),U_349)),U_348),
    inference(clausify,[status(thm)],[f_111_2]) ).

fof(f_112_1,plain,
    ! [X_b,Y_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),combi(X_b)),Y_1) = ti(fun(X_b,bool),Y_1),
    inference(fof_nnf,[status(thm)],[fact_82_image__ident]) ).

fof(f_112_2,plain,
    ! [U_355,U_354] : hAPP(fun(U_355,bool),fun(U_355,bool),hAPP(fun(U_355,U_355),fun(fun(U_355,bool),fun(U_355,bool)),image(U_355,U_355),combi(U_355)),U_354) = ti(fun(U_355,bool),U_354),
    inference(variable_rename,[status(thm)],[f_112_1]) ).

cnf(f_112_3,plain,
    hAPP(fun(U_355,bool),fun(U_355,bool),hAPP(fun(U_355,U_355),fun(fun(U_355,bool),fun(U_355,bool)),image(U_355,U_355),combi(U_355)),U_354) = ti(fun(U_355,bool),U_354),
    inference(clausify,[status(thm)],[f_112_2]) ).

fof(f_113_1,plain,
    ! [X_b,B,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),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))),
    inference(fof_nnf,[status(thm)],[fact_83_subset__insertI]) ).

fof(f_113_2,plain,
    ! [U_358,U_357,U_356] : hBOOL(hAPP(fun(U_358,bool),bool,hAPP(fun(U_358,bool),fun(fun(U_358,bool),bool),ord_less_eq(fun(U_358,bool)),U_357),hAPP(fun(U_358,bool),fun(U_358,bool),hAPP(U_358,fun(fun(U_358,bool),fun(U_358,bool)),insert(U_358),U_356),U_357))),
    inference(variable_rename,[status(thm)],[f_113_1]) ).

cnf(f_113_3,plain,
    hBOOL(hAPP(fun(U_358,bool),bool,hAPP(fun(U_358,bool),fun(fun(U_358,bool),bool),ord_less_eq(fun(U_358,bool)),U_357),hAPP(fun(U_358,bool),fun(U_358,bool),hAPP(U_358,fun(fun(U_358,bool),fun(U_358,bool)),insert(U_358),U_356),U_357))),
    inference(clausify,[status(thm)],[f_113_2]) ).

fof(f_114_1,plain,
    ! [X_b,X_2,A_1,B] :
      ( ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),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),A_1)),B))
        | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_1),B))
        | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B)) )
      & ( ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_1),B))
          & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B)) )
        | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),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),A_1)),B)) ) ),
    inference(fof_nnf,[status(thm)],[fact_84_insert__subset]) ).

fof(f_114_2,plain,
    ! [U_362,U_361,U_360,U_359] :
      ( ( hBOOL(hAPP(fun(U_362,bool),bool,hAPP(fun(U_362,bool),fun(fun(U_362,bool),bool),ord_less_eq(fun(U_362,bool)),hAPP(fun(U_362,bool),fun(U_362,bool),hAPP(U_362,fun(fun(U_362,bool),fun(U_362,bool)),insert(U_362),U_361),U_360)),U_359))
        | ~ hBOOL(hAPP(fun(U_362,bool),bool,hAPP(fun(U_362,bool),fun(fun(U_362,bool),bool),ord_less_eq(fun(U_362,bool)),U_360),U_359))
        | ~ hBOOL(hAPP(fun(U_362,bool),bool,hAPP(U_362,fun(fun(U_362,bool),bool),member(U_362),U_361),U_359)) )
      & ( ( hBOOL(hAPP(fun(U_362,bool),bool,hAPP(fun(U_362,bool),fun(fun(U_362,bool),bool),ord_less_eq(fun(U_362,bool)),U_360),U_359))
          & hBOOL(hAPP(fun(U_362,bool),bool,hAPP(U_362,fun(fun(U_362,bool),bool),member(U_362),U_361),U_359)) )
        | ~ hBOOL(hAPP(fun(U_362,bool),bool,hAPP(fun(U_362,bool),fun(fun(U_362,bool),bool),ord_less_eq(fun(U_362,bool)),hAPP(fun(U_362,bool),fun(U_362,bool),hAPP(U_362,fun(fun(U_362,bool),fun(U_362,bool)),insert(U_362),U_361),U_360)),U_359)) ) ),
    inference(variable_rename,[status(thm)],[f_114_1]) ).

fof(f_114_3,plain,
    ( ! [U_370,U_368,U_366,U_364] :
        ( hBOOL(hAPP(fun(U_370,bool),bool,hAPP(fun(U_370,bool),fun(fun(U_370,bool),bool),ord_less_eq(fun(U_370,bool)),hAPP(fun(U_370,bool),fun(U_370,bool),hAPP(U_370,fun(fun(U_370,bool),fun(U_370,bool)),insert(U_370),U_368),U_366)),U_364))
        | ~ hBOOL(hAPP(fun(U_370,bool),bool,hAPP(fun(U_370,bool),fun(fun(U_370,bool),bool),ord_less_eq(fun(U_370,bool)),U_366),U_364))
        | ~ hBOOL(hAPP(fun(U_370,bool),bool,hAPP(U_370,fun(fun(U_370,bool),bool),member(U_370),U_368),U_364)) )
    & ! [U_369,U_367,U_365,U_363] :
        ( ( hBOOL(hAPP(fun(U_369,bool),bool,hAPP(fun(U_369,bool),fun(fun(U_369,bool),bool),ord_less_eq(fun(U_369,bool)),U_365),U_363))
          & hBOOL(hAPP(fun(U_369,bool),bool,hAPP(U_369,fun(fun(U_369,bool),bool),member(U_369),U_367),U_363)) )
        | ~ hBOOL(hAPP(fun(U_369,bool),bool,hAPP(fun(U_369,bool),fun(fun(U_369,bool),bool),ord_less_eq(fun(U_369,bool)),hAPP(fun(U_369,bool),fun(U_369,bool),hAPP(U_369,fun(fun(U_369,bool),fun(U_369,bool)),insert(U_369),U_367),U_365)),U_363)) ) ),
    inference(miniscope,[status(thm)],[f_114_2]) ).

cnf(f_114_4,plain,
    ( hBOOL(hAPP(fun(U_369,bool),bool,hAPP(U_369,fun(fun(U_369,bool),bool),member(U_369),U_367),U_363))
    | ~ hBOOL(hAPP(fun(U_369,bool),bool,hAPP(fun(U_369,bool),fun(fun(U_369,bool),bool),ord_less_eq(fun(U_369,bool)),hAPP(fun(U_369,bool),fun(U_369,bool),hAPP(U_369,fun(fun(U_369,bool),fun(U_369,bool)),insert(U_369),U_367),U_365)),U_363)) ),
    inference(clausify,[status(thm)],[f_114_3]) ).

cnf(f_114_5,plain,
    ( hBOOL(hAPP(fun(U_369,bool),bool,hAPP(fun(U_369,bool),fun(fun(U_369,bool),bool),ord_less_eq(fun(U_369,bool)),U_365),U_363))
    | ~ hBOOL(hAPP(fun(U_369,bool),bool,hAPP(fun(U_369,bool),fun(fun(U_369,bool),bool),ord_less_eq(fun(U_369,bool)),hAPP(fun(U_369,bool),fun(U_369,bool),hAPP(U_369,fun(fun(U_369,bool),fun(U_369,bool)),insert(U_369),U_367),U_365)),U_363)) ),
    inference(clausify,[status(thm)],[f_114_3]) ).

cnf(f_114_6,plain,
    ( hBOOL(hAPP(fun(U_370,bool),bool,hAPP(fun(U_370,bool),fun(fun(U_370,bool),bool),ord_less_eq(fun(U_370,bool)),hAPP(fun(U_370,bool),fun(U_370,bool),hAPP(U_370,fun(fun(U_370,bool),fun(U_370,bool)),insert(U_370),U_368),U_366)),U_364))
    | ~ hBOOL(hAPP(fun(U_370,bool),bool,hAPP(fun(U_370,bool),fun(fun(U_370,bool),bool),ord_less_eq(fun(U_370,bool)),U_366),U_364))
    | ~ hBOOL(hAPP(fun(U_370,bool),bool,hAPP(U_370,fun(fun(U_370,bool),bool),member(U_370),U_368),U_364)) ),
    inference(clausify,[status(thm)],[f_114_3]) ).

fof(f_115_1,plain,
    ! [X_b,B,X_2,A_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_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),B)))
          | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_1),B)) )
        & ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_1),B))
          | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_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),B))) ) )
      | hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_85_subset__insert]) ).

fof(f_115_2,plain,
    ! [U_374,U_373,U_372,U_371] :
      ( ( ( hBOOL(hAPP(fun(U_374,bool),bool,hAPP(fun(U_374,bool),fun(fun(U_374,bool),bool),ord_less_eq(fun(U_374,bool)),U_371),hAPP(fun(U_374,bool),fun(U_374,bool),hAPP(U_374,fun(fun(U_374,bool),fun(U_374,bool)),insert(U_374),U_372),U_373)))
          | ~ hBOOL(hAPP(fun(U_374,bool),bool,hAPP(fun(U_374,bool),fun(fun(U_374,bool),bool),ord_less_eq(fun(U_374,bool)),U_371),U_373)) )
        & ( hBOOL(hAPP(fun(U_374,bool),bool,hAPP(fun(U_374,bool),fun(fun(U_374,bool),bool),ord_less_eq(fun(U_374,bool)),U_371),U_373))
          | ~ hBOOL(hAPP(fun(U_374,bool),bool,hAPP(fun(U_374,bool),fun(fun(U_374,bool),bool),ord_less_eq(fun(U_374,bool)),U_371),hAPP(fun(U_374,bool),fun(U_374,bool),hAPP(U_374,fun(fun(U_374,bool),fun(U_374,bool)),insert(U_374),U_372),U_373))) ) )
      | hBOOL(hAPP(fun(U_374,bool),bool,hAPP(U_374,fun(fun(U_374,bool),bool),member(U_374),U_372),U_371)) ),
    inference(variable_rename,[status(thm)],[f_115_1]) ).

cnf(f_115_3,plain,
    ( hBOOL(hAPP(fun(U_374,bool),bool,hAPP(fun(U_374,bool),fun(fun(U_374,bool),bool),ord_less_eq(fun(U_374,bool)),U_371),U_373))
    | ~ hBOOL(hAPP(fun(U_374,bool),bool,hAPP(fun(U_374,bool),fun(fun(U_374,bool),bool),ord_less_eq(fun(U_374,bool)),U_371),hAPP(fun(U_374,bool),fun(U_374,bool),hAPP(U_374,fun(fun(U_374,bool),fun(U_374,bool)),insert(U_374),U_372),U_373)))
    | hBOOL(hAPP(fun(U_374,bool),bool,hAPP(U_374,fun(fun(U_374,bool),bool),member(U_374),U_372),U_371)) ),
    inference(clausify,[status(thm)],[f_115_2]) ).

cnf(f_115_4,plain,
    ( hBOOL(hAPP(fun(U_374,bool),bool,hAPP(fun(U_374,bool),fun(fun(U_374,bool),bool),ord_less_eq(fun(U_374,bool)),U_371),hAPP(fun(U_374,bool),fun(U_374,bool),hAPP(U_374,fun(fun(U_374,bool),fun(U_374,bool)),insert(U_374),U_372),U_373)))
    | ~ hBOOL(hAPP(fun(U_374,bool),bool,hAPP(fun(U_374,bool),fun(fun(U_374,bool),bool),ord_less_eq(fun(U_374,bool)),U_371),U_373))
    | hBOOL(hAPP(fun(U_374,bool),bool,hAPP(U_374,fun(fun(U_374,bool),bool),member(U_374),U_372),U_371)) ),
    inference(clausify,[status(thm)],[f_115_2]) ).

fof(f_116_1,plain,
    ! [X_b,B_1,A_1,B] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_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),B_1),B)))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_1),B)) ),
    inference(fof_nnf,[status(thm)],[fact_86_subset__insertI2]) ).

fof(f_116_2,plain,
    ! [U_378,U_377,U_376,U_375] :
      ( hBOOL(hAPP(fun(U_378,bool),bool,hAPP(fun(U_378,bool),fun(fun(U_378,bool),bool),ord_less_eq(fun(U_378,bool)),U_376),hAPP(fun(U_378,bool),fun(U_378,bool),hAPP(U_378,fun(fun(U_378,bool),fun(U_378,bool)),insert(U_378),U_377),U_375)))
      | ~ hBOOL(hAPP(fun(U_378,bool),bool,hAPP(fun(U_378,bool),fun(fun(U_378,bool),bool),ord_less_eq(fun(U_378,bool)),U_376),U_375)) ),
    inference(variable_rename,[status(thm)],[f_116_1]) ).

cnf(f_116_3,plain,
    ( hBOOL(hAPP(fun(U_378,bool),bool,hAPP(fun(U_378,bool),fun(fun(U_378,bool),bool),ord_less_eq(fun(U_378,bool)),U_376),hAPP(fun(U_378,bool),fun(U_378,bool),hAPP(U_378,fun(fun(U_378,bool),fun(U_378,bool)),insert(U_378),U_377),U_375)))
    | ~ hBOOL(hAPP(fun(U_378,bool),bool,hAPP(fun(U_378,bool),fun(fun(U_378,bool),bool),ord_less_eq(fun(U_378,bool)),U_376),U_375)) ),
    inference(clausify,[status(thm)],[f_116_2]) ).

fof(f_117_1,plain,
    ! [X_b,A_2,C,D] :
      ( hBOOL(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)),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)))
      | ~ hBOOL(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),D)) ),
    inference(fof_nnf,[status(thm)],[fact_87_insert__mono]) ).

fof(f_117_2,plain,
    ! [U_382,U_381,U_380,U_379] :
      ( hBOOL(hAPP(fun(U_382,bool),bool,hAPP(fun(U_382,bool),fun(fun(U_382,bool),bool),ord_less_eq(fun(U_382,bool)),hAPP(fun(U_382,bool),fun(U_382,bool),hAPP(U_382,fun(fun(U_382,bool),fun(U_382,bool)),insert(U_382),U_381),U_380)),hAPP(fun(U_382,bool),fun(U_382,bool),hAPP(U_382,fun(fun(U_382,bool),fun(U_382,bool)),insert(U_382),U_381),U_379)))
      | ~ hBOOL(hAPP(fun(U_382,bool),bool,hAPP(fun(U_382,bool),fun(fun(U_382,bool),bool),ord_less_eq(fun(U_382,bool)),U_380),U_379)) ),
    inference(variable_rename,[status(thm)],[f_117_1]) ).

cnf(f_117_3,plain,
    ( hBOOL(hAPP(fun(U_382,bool),bool,hAPP(fun(U_382,bool),fun(fun(U_382,bool),bool),ord_less_eq(fun(U_382,bool)),hAPP(fun(U_382,bool),fun(U_382,bool),hAPP(U_382,fun(fun(U_382,bool),fun(U_382,bool)),insert(U_382),U_381),U_380)),hAPP(fun(U_382,bool),fun(U_382,bool),hAPP(U_382,fun(fun(U_382,bool),fun(U_382,bool)),insert(U_382),U_381),U_379)))
    | ~ hBOOL(hAPP(fun(U_382,bool),bool,hAPP(fun(U_382,bool),fun(fun(U_382,bool),bool),ord_less_eq(fun(U_382,bool)),U_380),U_379)) ),
    inference(clausify,[status(thm)],[f_117_2]) ).

fof(f_118_1,plain,
    ! [X_c,X_b,F,A_2,B] : hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),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)) = 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)),
    inference(fof_nnf,[status(thm)],[fact_88_image__insert]) ).

fof(f_118_2,plain,
    ! [U_387,U_386,U_385,U_384,U_383] : hAPP(fun(U_387,bool),fun(U_386,bool),hAPP(fun(U_387,U_386),fun(fun(U_387,bool),fun(U_386,bool)),image(U_387,U_386),U_385),hAPP(fun(U_387,bool),fun(U_387,bool),hAPP(U_387,fun(fun(U_387,bool),fun(U_387,bool)),insert(U_387),U_384),U_383)) = hAPP(fun(U_386,bool),fun(U_386,bool),hAPP(U_386,fun(fun(U_386,bool),fun(U_386,bool)),insert(U_386),hAPP(U_387,U_386,U_385,U_384)),hAPP(fun(U_387,bool),fun(U_386,bool),hAPP(fun(U_387,U_386),fun(fun(U_387,bool),fun(U_386,bool)),image(U_387,U_386),U_385),U_383)),
    inference(variable_rename,[status(thm)],[f_118_1]) ).

cnf(f_118_3,plain,
    hAPP(fun(U_387,bool),fun(U_386,bool),hAPP(fun(U_387,U_386),fun(fun(U_387,bool),fun(U_386,bool)),image(U_387,U_386),U_385),hAPP(fun(U_387,bool),fun(U_387,bool),hAPP(U_387,fun(fun(U_387,bool),fun(U_387,bool)),insert(U_387),U_384),U_383)) = hAPP(fun(U_386,bool),fun(U_386,bool),hAPP(U_386,fun(fun(U_386,bool),fun(U_386,bool)),insert(U_386),hAPP(U_387,U_386,U_385,U_384)),hAPP(fun(U_387,bool),fun(U_386,bool),hAPP(fun(U_387,U_386),fun(fun(U_387,bool),fun(U_386,bool)),image(U_387,U_386),U_385),U_383)),
    inference(clausify,[status(thm)],[f_118_2]) ).

fof(f_119_1,plain,
    ! [X_c,X_b,F,X_2,A_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),hAPP(X_b,X_c,F,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),A_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_1)
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_89_insert__image]) ).

fof(f_119_2,plain,
    ! [U_392,U_391,U_390,U_389,U_388] :
      ( hAPP(fun(U_392,bool),fun(U_392,bool),hAPP(U_392,fun(fun(U_392,bool),fun(U_392,bool)),insert(U_392),hAPP(U_391,U_392,U_390,U_389)),hAPP(fun(U_391,bool),fun(U_392,bool),hAPP(fun(U_391,U_392),fun(fun(U_391,bool),fun(U_392,bool)),image(U_391,U_392),U_390),U_388)) = hAPP(fun(U_391,bool),fun(U_392,bool),hAPP(fun(U_391,U_392),fun(fun(U_391,bool),fun(U_392,bool)),image(U_391,U_392),U_390),U_388)
      | ~ hBOOL(hAPP(fun(U_391,bool),bool,hAPP(U_391,fun(fun(U_391,bool),bool),member(U_391),U_389),U_388)) ),
    inference(variable_rename,[status(thm)],[f_119_1]) ).

cnf(f_119_3,plain,
    ( hAPP(fun(U_392,bool),fun(U_392,bool),hAPP(U_392,fun(fun(U_392,bool),fun(U_392,bool)),insert(U_392),hAPP(U_391,U_392,U_390,U_389)),hAPP(fun(U_391,bool),fun(U_392,bool),hAPP(fun(U_391,U_392),fun(fun(U_391,bool),fun(U_392,bool)),image(U_391,U_392),U_390),U_388)) = hAPP(fun(U_391,bool),fun(U_392,bool),hAPP(fun(U_391,U_392),fun(fun(U_391,bool),fun(U_392,bool)),image(U_391,U_392),U_390),U_388)
    | ~ hBOOL(hAPP(fun(U_391,bool),bool,hAPP(U_391,fun(fun(U_391,bool),bool),member(U_391),U_389),U_388)) ),
    inference(clausify,[status(thm)],[f_119_2]) ).

fof(f_120_1,plain,
    ! [X_b,X_c,B,F,A_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),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_1)))
        | ! [AA] :
            ( ti(fun(X_b,bool),B) != hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),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_1)) ) )
      & ( ? [AA] :
            ( ti(fun(X_b,bool),B) = hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),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_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),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_1))) ) ),
    inference(fof_nnf,[status(thm)],[fact_90_subset__image__iff]) ).

fof(f_120_2,plain,
    ! [U_399,U_398,U_397,U_396,U_395] :
      ( ( hBOOL(hAPP(fun(U_399,bool),bool,hAPP(fun(U_399,bool),fun(fun(U_399,bool),bool),ord_less_eq(fun(U_399,bool)),U_397),hAPP(fun(U_398,bool),fun(U_399,bool),hAPP(fun(U_398,U_399),fun(fun(U_398,bool),fun(U_399,bool)),image(U_398,U_399),U_396),U_395)))
        | ! [U_394] :
            ( ti(fun(U_399,bool),U_397) != hAPP(fun(U_398,bool),fun(U_399,bool),hAPP(fun(U_398,U_399),fun(fun(U_398,bool),fun(U_399,bool)),image(U_398,U_399),U_396),U_394)
            | ~ hBOOL(hAPP(fun(U_398,bool),bool,hAPP(fun(U_398,bool),fun(fun(U_398,bool),bool),ord_less_eq(fun(U_398,bool)),U_394),U_395)) ) )
      & ( ? [U_393] :
            ( ti(fun(U_399,bool),U_397) = hAPP(fun(U_398,bool),fun(U_399,bool),hAPP(fun(U_398,U_399),fun(fun(U_398,bool),fun(U_399,bool)),image(U_398,U_399),U_396),U_393)
            & hBOOL(hAPP(fun(U_398,bool),bool,hAPP(fun(U_398,bool),fun(fun(U_398,bool),bool),ord_less_eq(fun(U_398,bool)),U_393),U_395)) )
        | ~ hBOOL(hAPP(fun(U_399,bool),bool,hAPP(fun(U_399,bool),fun(fun(U_399,bool),bool),ord_less_eq(fun(U_399,bool)),U_397),hAPP(fun(U_398,bool),fun(U_399,bool),hAPP(fun(U_398,U_399),fun(fun(U_398,bool),fun(U_399,bool)),image(U_398,U_399),U_396),U_395))) ) ),
    inference(variable_rename,[status(thm)],[f_120_1]) ).

fof(f_120_3,plain,
    ( ! [U_409,U_407,U_405,U_403,U_401] :
        ( hBOOL(hAPP(fun(U_409,bool),bool,hAPP(fun(U_409,bool),fun(fun(U_409,bool),bool),ord_less_eq(fun(U_409,bool)),U_405),hAPP(fun(U_407,bool),fun(U_409,bool),hAPP(fun(U_407,U_409),fun(fun(U_407,bool),fun(U_409,bool)),image(U_407,U_409),U_403),U_401)))
        | ! [U_394] :
            ( ti(fun(U_409,bool),U_405) != hAPP(fun(U_407,bool),fun(U_409,bool),hAPP(fun(U_407,U_409),fun(fun(U_407,bool),fun(U_409,bool)),image(U_407,U_409),U_403),U_394)
            | ~ hBOOL(hAPP(fun(U_407,bool),bool,hAPP(fun(U_407,bool),fun(fun(U_407,bool),bool),ord_less_eq(fun(U_407,bool)),U_394),U_401)) ) )
    & ! [U_408,U_406,U_404,U_402,U_400] :
        ( ? [U_393] :
            ( ti(fun(U_408,bool),U_404) = hAPP(fun(U_406,bool),fun(U_408,bool),hAPP(fun(U_406,U_408),fun(fun(U_406,bool),fun(U_408,bool)),image(U_406,U_408),U_402),U_393)
            & hBOOL(hAPP(fun(U_406,bool),bool,hAPP(fun(U_406,bool),fun(fun(U_406,bool),bool),ord_less_eq(fun(U_406,bool)),U_393),U_400)) )
        | ~ 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_404),hAPP(fun(U_406,bool),fun(U_408,bool),hAPP(fun(U_406,U_408),fun(fun(U_406,bool),fun(U_408,bool)),image(U_406,U_408),U_402),U_400))) ) ),
    inference(miniscope,[status(thm)],[f_120_2]) ).

fof(f_120_4,plain,
    ( ! [U_409,U_407,U_405,U_403,U_401] :
        ( hBOOL(hAPP(fun(U_409,bool),bool,hAPP(fun(U_409,bool),fun(fun(U_409,bool),bool),ord_less_eq(fun(U_409,bool)),U_405),hAPP(fun(U_407,bool),fun(U_409,bool),hAPP(fun(U_407,U_409),fun(fun(U_407,bool),fun(U_409,bool)),image(U_407,U_409),U_403),U_401)))
        | ! [U_394] :
            ( ti(fun(U_409,bool),U_405) != hAPP(fun(U_407,bool),fun(U_409,bool),hAPP(fun(U_407,U_409),fun(fun(U_407,bool),fun(U_409,bool)),image(U_407,U_409),U_403),U_394)
            | ~ hBOOL(hAPP(fun(U_407,bool),bool,hAPP(fun(U_407,bool),fun(fun(U_407,bool),bool),ord_less_eq(fun(U_407,bool)),U_394),U_401)) ) )
    & ! [U_408,U_406,U_404,U_402,U_400] :
        ( ( ti(fun(U_408,bool),U_404) = hAPP(fun(U_406,bool),fun(U_408,bool),hAPP(fun(U_406,U_408),fun(fun(U_406,bool),fun(U_408,bool)),image(U_406,U_408),U_402),sK6(U_408,U_406,U_404,U_402,U_400))
          & hBOOL(hAPP(fun(U_406,bool),bool,hAPP(fun(U_406,bool),fun(fun(U_406,bool),bool),ord_less_eq(fun(U_406,bool)),sK6(U_408,U_406,U_404,U_402,U_400)),U_400)) )
        | ~ 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_404),hAPP(fun(U_406,bool),fun(U_408,bool),hAPP(fun(U_406,U_408),fun(fun(U_406,bool),fun(U_408,bool)),image(U_406,U_408),U_402),U_400))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_393,sK6(U_408,U_406,U_404,U_402,U_400))],[f_120_3]) ).

cnf(f_120_5,plain,
    ( hBOOL(hAPP(fun(U_406,bool),bool,hAPP(fun(U_406,bool),fun(fun(U_406,bool),bool),ord_less_eq(fun(U_406,bool)),sK6(U_408,U_406,U_404,U_402,U_400)),U_400))
    | ~ 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_404),hAPP(fun(U_406,bool),fun(U_408,bool),hAPP(fun(U_406,U_408),fun(fun(U_406,bool),fun(U_408,bool)),image(U_406,U_408),U_402),U_400))) ),
    inference(clausify,[status(thm)],[f_120_4]) ).

cnf(f_120_6,plain,
    ( ti(fun(U_408,bool),U_404) = hAPP(fun(U_406,bool),fun(U_408,bool),hAPP(fun(U_406,U_408),fun(fun(U_406,bool),fun(U_408,bool)),image(U_406,U_408),U_402),sK6(U_408,U_406,U_404,U_402,U_400))
    | ~ 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_404),hAPP(fun(U_406,bool),fun(U_408,bool),hAPP(fun(U_406,U_408),fun(fun(U_406,bool),fun(U_408,bool)),image(U_406,U_408),U_402),U_400))) ),
    inference(clausify,[status(thm)],[f_120_4]) ).

cnf(f_120_7,plain,
    ( hBOOL(hAPP(fun(U_409,bool),bool,hAPP(fun(U_409,bool),fun(fun(U_409,bool),bool),ord_less_eq(fun(U_409,bool)),U_405),hAPP(fun(U_407,bool),fun(U_409,bool),hAPP(fun(U_407,U_409),fun(fun(U_407,bool),fun(U_409,bool)),image(U_407,U_409),U_403),U_401)))
    | ti(fun(U_409,bool),U_405) != hAPP(fun(U_407,bool),fun(U_409,bool),hAPP(fun(U_407,U_409),fun(fun(U_407,bool),fun(U_409,bool)),image(U_407,U_409),U_403),U_394)
    | ~ hBOOL(hAPP(fun(U_407,bool),bool,hAPP(fun(U_407,bool),fun(fun(U_407,bool),bool),ord_less_eq(fun(U_407,bool)),U_394),U_401)) ),
    inference(clausify,[status(thm)],[f_120_4]) ).

fof(f_121_1,plain,
    ! [X_c,X_b,F,A_1,B] :
      ( 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_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),B)))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_1),B)) ),
    inference(fof_nnf,[status(thm)],[fact_91_image__mono]) ).

fof(f_121_2,plain,
    ! [U_414,U_413,U_412,U_411,U_410] :
      ( hBOOL(hAPP(fun(U_414,bool),bool,hAPP(fun(U_414,bool),fun(fun(U_414,bool),bool),ord_less_eq(fun(U_414,bool)),hAPP(fun(U_413,bool),fun(U_414,bool),hAPP(fun(U_413,U_414),fun(fun(U_413,bool),fun(U_414,bool)),image(U_413,U_414),U_412),U_411)),hAPP(fun(U_413,bool),fun(U_414,bool),hAPP(fun(U_413,U_414),fun(fun(U_413,bool),fun(U_414,bool)),image(U_413,U_414),U_412),U_410)))
      | ~ hBOOL(hAPP(fun(U_413,bool),bool,hAPP(fun(U_413,bool),fun(fun(U_413,bool),bool),ord_less_eq(fun(U_413,bool)),U_411),U_410)) ),
    inference(variable_rename,[status(thm)],[f_121_1]) ).

cnf(f_121_3,plain,
    ( hBOOL(hAPP(fun(U_414,bool),bool,hAPP(fun(U_414,bool),fun(fun(U_414,bool),bool),ord_less_eq(fun(U_414,bool)),hAPP(fun(U_413,bool),fun(U_414,bool),hAPP(fun(U_413,U_414),fun(fun(U_413,bool),fun(U_414,bool)),image(U_413,U_414),U_412),U_411)),hAPP(fun(U_413,bool),fun(U_414,bool),hAPP(fun(U_413,U_414),fun(fun(U_413,bool),fun(U_414,bool)),image(U_413,U_414),U_412),U_410)))
    | ~ hBOOL(hAPP(fun(U_413,bool),bool,hAPP(fun(U_413,bool),fun(fun(U_413,bool),bool),ord_less_eq(fun(U_413,bool)),U_411),U_410)) ),
    inference(clausify,[status(thm)],[f_121_2]) ).

fof(f_122_1,plain,
    ! [X_b,X_c,B_1,F,A_1] :
      ( ? [X_1] :
          ( hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_1),A_1))
          & ti(X_b,B_1) = hAPP(X_c,X_b,F,X_1) )
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),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_1))) ),
    inference(fof_nnf,[status(thm)],[fact_92_imageE]) ).

fof(f_122_2,plain,
    ! [U_420,U_419,U_418,U_417,U_416] :
      ( ? [U_415] :
          ( hBOOL(hAPP(fun(U_419,bool),bool,hAPP(U_419,fun(fun(U_419,bool),bool),member(U_419),U_415),U_416))
          & ti(U_420,U_418) = hAPP(U_419,U_420,U_417,U_415) )
      | ~ hBOOL(hAPP(fun(U_420,bool),bool,hAPP(U_420,fun(fun(U_420,bool),bool),member(U_420),U_418),hAPP(fun(U_419,bool),fun(U_420,bool),hAPP(fun(U_419,U_420),fun(fun(U_419,bool),fun(U_420,bool)),image(U_419,U_420),U_417),U_416))) ),
    inference(variable_rename,[status(thm)],[f_122_1]) ).

fof(f_122_3,plain,
    ! [U_420,U_419,U_418,U_417,U_416] :
      ( ( hBOOL(hAPP(fun(U_419,bool),bool,hAPP(U_419,fun(fun(U_419,bool),bool),member(U_419),sK7(U_420,U_419,U_418,U_417,U_416)),U_416))
        & ti(U_420,U_418) = hAPP(U_419,U_420,U_417,sK7(U_420,U_419,U_418,U_417,U_416)) )
      | ~ hBOOL(hAPP(fun(U_420,bool),bool,hAPP(U_420,fun(fun(U_420,bool),bool),member(U_420),U_418),hAPP(fun(U_419,bool),fun(U_420,bool),hAPP(fun(U_419,U_420),fun(fun(U_419,bool),fun(U_420,bool)),image(U_419,U_420),U_417),U_416))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_415,sK7(U_420,U_419,U_418,U_417,U_416))],[f_122_2]) ).

cnf(f_122_4,plain,
    ( ti(U_420,U_418) = hAPP(U_419,U_420,U_417,sK7(U_420,U_419,U_418,U_417,U_416))
    | ~ hBOOL(hAPP(fun(U_420,bool),bool,hAPP(U_420,fun(fun(U_420,bool),bool),member(U_420),U_418),hAPP(fun(U_419,bool),fun(U_420,bool),hAPP(fun(U_419,U_420),fun(fun(U_419,bool),fun(U_420,bool)),image(U_419,U_420),U_417),U_416))) ),
    inference(clausify,[status(thm)],[f_122_3]) ).

cnf(f_122_5,plain,
    ( hBOOL(hAPP(fun(U_419,bool),bool,hAPP(U_419,fun(fun(U_419,bool),bool),member(U_419),sK7(U_420,U_419,U_418,U_417,U_416)),U_416))
    | ~ hBOOL(hAPP(fun(U_420,bool),bool,hAPP(U_420,fun(fun(U_420,bool),bool),member(U_420),U_418),hAPP(fun(U_419,bool),fun(U_420,bool),hAPP(fun(U_419,U_420),fun(fun(U_419,bool),fun(U_420,bool)),image(U_419,U_420),U_417),U_416))) ),
    inference(clausify,[status(thm)],[f_122_3]) ).

fof(f_123_1,plain,
    ! [X_b,B,A_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_1),B))
      | ? [X_1] :
          ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B))
          & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_93_subsetI]) ).

fof(f_123_2,plain,
    ! [U_424,U_423,U_422] :
      ( hBOOL(hAPP(fun(U_424,bool),bool,hAPP(fun(U_424,bool),fun(fun(U_424,bool),bool),ord_less_eq(fun(U_424,bool)),U_422),U_423))
      | ? [U_421] :
          ( ~ hBOOL(hAPP(fun(U_424,bool),bool,hAPP(U_424,fun(fun(U_424,bool),bool),member(U_424),U_421),U_423))
          & hBOOL(hAPP(fun(U_424,bool),bool,hAPP(U_424,fun(fun(U_424,bool),bool),member(U_424),U_421),U_422)) ) ),
    inference(variable_rename,[status(thm)],[f_123_1]) ).

fof(f_123_3,plain,
    ! [U_424,U_423,U_422] :
      ( hBOOL(hAPP(fun(U_424,bool),bool,hAPP(fun(U_424,bool),fun(fun(U_424,bool),bool),ord_less_eq(fun(U_424,bool)),U_422),U_423))
      | ( ~ hBOOL(hAPP(fun(U_424,bool),bool,hAPP(U_424,fun(fun(U_424,bool),bool),member(U_424),sK8(U_424,U_423,U_422)),U_423))
        & hBOOL(hAPP(fun(U_424,bool),bool,hAPP(U_424,fun(fun(U_424,bool),bool),member(U_424),sK8(U_424,U_423,U_422)),U_422)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_421,sK8(U_424,U_423,U_422))],[f_123_2]) ).

cnf(f_123_4,plain,
    ( hBOOL(hAPP(fun(U_424,bool),bool,hAPP(U_424,fun(fun(U_424,bool),bool),member(U_424),sK8(U_424,U_423,U_422)),U_422))
    | hBOOL(hAPP(fun(U_424,bool),bool,hAPP(fun(U_424,bool),fun(fun(U_424,bool),bool),ord_less_eq(fun(U_424,bool)),U_422),U_423)) ),
    inference(clausify,[status(thm)],[f_123_3]) ).

cnf(f_123_5,plain,
    ( ~ hBOOL(hAPP(fun(U_424,bool),bool,hAPP(U_424,fun(fun(U_424,bool),bool),member(U_424),sK8(U_424,U_423,U_422)),U_423))
    | hBOOL(hAPP(fun(U_424,bool),bool,hAPP(fun(U_424,bool),fun(fun(U_424,bool),bool),ord_less_eq(fun(U_424,bool)),U_422),U_423)) ),
    inference(clausify,[status(thm)],[f_123_3]) ).

fof(f_124_1,plain,
    ! [I,Pa,K] :
      ( hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),K),I)))
      | ? [N_2] :
          ( ~ hBOOL(hAPP(nat,bool,Pa,N_2))
          & hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,N_2))) )
      | ~ hBOOL(hAPP(nat,bool,Pa,K)) ),
    inference(fof_nnf,[status(thm)],[fact_94_zero__induct__lemma]) ).

fof(f_124_2,plain,
    ! [U_428,U_427,U_426] :
      ( hBOOL(hAPP(nat,bool,U_427,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_426),U_428)))
      | ? [U_425] :
          ( ~ hBOOL(hAPP(nat,bool,U_427,U_425))
          & hBOOL(hAPP(nat,bool,U_427,hAPP(nat,nat,suc,U_425))) )
      | ~ hBOOL(hAPP(nat,bool,U_427,U_426)) ),
    inference(variable_rename,[status(thm)],[f_124_1]) ).

fof(f_124_3,plain,
    ! [U_428,U_427,U_426] :
      ( hBOOL(hAPP(nat,bool,U_427,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_426),U_428)))
      | ( ~ hBOOL(hAPP(nat,bool,U_427,sK9(U_428,U_427,U_426)))
        & hBOOL(hAPP(nat,bool,U_427,hAPP(nat,nat,suc,sK9(U_428,U_427,U_426)))) )
      | ~ hBOOL(hAPP(nat,bool,U_427,U_426)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_425,sK9(U_428,U_427,U_426))],[f_124_2]) ).

cnf(f_124_4,plain,
    ( hBOOL(hAPP(nat,bool,U_427,hAPP(nat,nat,suc,sK9(U_428,U_427,U_426))))
    | hBOOL(hAPP(nat,bool,U_427,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_426),U_428)))
    | ~ hBOOL(hAPP(nat,bool,U_427,U_426)) ),
    inference(clausify,[status(thm)],[f_124_3]) ).

cnf(f_124_5,plain,
    ( ~ hBOOL(hAPP(nat,bool,U_427,sK9(U_428,U_427,U_426)))
    | hBOOL(hAPP(nat,bool,U_427,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_426),U_428)))
    | ~ hBOOL(hAPP(nat,bool,U_427,U_426)) ),
    inference(clausify,[status(thm)],[f_124_3]) ).

fof(f_125_1,plain,
    ! [N_1,M_1] :
      ( ? [M] : M_1 = hAPP(nat,nat,suc,M)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N_1)),M_1)) ),
    inference(fof_nnf,[status(thm)],[fact_95_Suc__le__D]) ).

fof(f_125_2,plain,
    ! [U_431,U_430] :
      ( ? [U_429] : U_430 = hAPP(nat,nat,suc,U_429)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_431)),U_430)) ),
    inference(variable_rename,[status(thm)],[f_125_1]) ).

fof(f_125_3,plain,
    ! [U_431,U_430] :
      ( U_430 = hAPP(nat,nat,suc,sK10(U_431,U_430))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_431)),U_430)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_429,sK10(U_431,U_430))],[f_125_2]) ).

cnf(f_125_4,plain,
    ( U_430 = hAPP(nat,nat,suc,sK10(U_431,U_430))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_431)),U_430)) ),
    inference(clausify,[status(thm)],[f_125_3]) ).

fof(f_126_1,plain,
    ! [X_c,X_b,F,B,A_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_1)),B))
      | ? [X_1] :
          ( ~ 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)),B))
          & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_96_image__subsetI]) ).

fof(f_126_2,plain,
    ! [U_437,U_436,U_435,U_434,U_433] :
      ( hBOOL(hAPP(fun(U_437,bool),bool,hAPP(fun(U_437,bool),fun(fun(U_437,bool),bool),ord_less_eq(fun(U_437,bool)),hAPP(fun(U_436,bool),fun(U_437,bool),hAPP(fun(U_436,U_437),fun(fun(U_436,bool),fun(U_437,bool)),image(U_436,U_437),U_435),U_433)),U_434))
      | ? [U_432] :
          ( ~ hBOOL(hAPP(fun(U_437,bool),bool,hAPP(U_437,fun(fun(U_437,bool),bool),member(U_437),hAPP(U_436,U_437,U_435,U_432)),U_434))
          & hBOOL(hAPP(fun(U_436,bool),bool,hAPP(U_436,fun(fun(U_436,bool),bool),member(U_436),U_432),U_433)) ) ),
    inference(variable_rename,[status(thm)],[f_126_1]) ).

fof(f_126_3,plain,
    ! [U_437,U_436,U_435,U_434,U_433] :
      ( hBOOL(hAPP(fun(U_437,bool),bool,hAPP(fun(U_437,bool),fun(fun(U_437,bool),bool),ord_less_eq(fun(U_437,bool)),hAPP(fun(U_436,bool),fun(U_437,bool),hAPP(fun(U_436,U_437),fun(fun(U_436,bool),fun(U_437,bool)),image(U_436,U_437),U_435),U_433)),U_434))
      | ( ~ hBOOL(hAPP(fun(U_437,bool),bool,hAPP(U_437,fun(fun(U_437,bool),bool),member(U_437),hAPP(U_436,U_437,U_435,sK11(U_437,U_436,U_435,U_434,U_433))),U_434))
        & hBOOL(hAPP(fun(U_436,bool),bool,hAPP(U_436,fun(fun(U_436,bool),bool),member(U_436),sK11(U_437,U_436,U_435,U_434,U_433)),U_433)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_432,sK11(U_437,U_436,U_435,U_434,U_433))],[f_126_2]) ).

cnf(f_126_4,plain,
    ( hBOOL(hAPP(fun(U_436,bool),bool,hAPP(U_436,fun(fun(U_436,bool),bool),member(U_436),sK11(U_437,U_436,U_435,U_434,U_433)),U_433))
    | hBOOL(hAPP(fun(U_437,bool),bool,hAPP(fun(U_437,bool),fun(fun(U_437,bool),bool),ord_less_eq(fun(U_437,bool)),hAPP(fun(U_436,bool),fun(U_437,bool),hAPP(fun(U_436,U_437),fun(fun(U_436,bool),fun(U_437,bool)),image(U_436,U_437),U_435),U_433)),U_434)) ),
    inference(clausify,[status(thm)],[f_126_3]) ).

cnf(f_126_5,plain,
    ( ~ hBOOL(hAPP(fun(U_437,bool),bool,hAPP(U_437,fun(fun(U_437,bool),bool),member(U_437),hAPP(U_436,U_437,U_435,sK11(U_437,U_436,U_435,U_434,U_433))),U_434))
    | hBOOL(hAPP(fun(U_437,bool),bool,hAPP(fun(U_437,bool),fun(fun(U_437,bool),bool),ord_less_eq(fun(U_437,bool)),hAPP(fun(U_436,bool),fun(U_437,bool),hAPP(fun(U_436,U_437),fun(fun(U_436,bool),fun(U_437,bool)),image(U_436,U_437),U_435),U_433)),U_434)) ),
    inference(clausify,[status(thm)],[f_126_3]) ).

fof(f_127_1,plain,
    ! [X_a] :
      ( ! [X] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),X))
      | ~ preorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_97_order__refl]) ).

fof(f_127_2,plain,
    ! [U_439] :
      ( ! [U_438] : hBOOL(hAPP(U_439,bool,hAPP(U_439,fun(U_439,bool),ord_less_eq(U_439),U_438),U_438))
      | ~ preorder(U_439) ),
    inference(variable_rename,[status(thm)],[f_127_1]) ).

cnf(f_127_3,plain,
    ( hBOOL(hAPP(U_439,bool,hAPP(U_439,fun(U_439,bool),ord_less_eq(U_439),U_438),U_438))
    | ~ preorder(U_439) ),
    inference(clausify,[status(thm)],[f_127_2]) ).

fof(f_128_1,plain,
    ! [N] :
      ( ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),N))
        | ! [M] :
          ? [X_1] :
            ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X_1),M))
            & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_1),N)) ) )
      & ( ? [M] :
          ! [X_1] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X_1),M))
            | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_1),N)) )
        | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),N)) ) ),
    inference(fof_nnf,[status(thm)],[fact_98_finite__nat__set__iff__bounded__le]) ).

fof(f_128_2,plain,
    ! [U_444] :
      ( ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_444))
        | ! [U_443] :
          ? [U_442] :
            ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_442),U_443))
            & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_442),U_444)) ) )
      & ( ? [U_441] :
          ! [U_440] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_440),U_441))
            | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_440),U_444)) )
        | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_444)) ) ),
    inference(variable_rename,[status(thm)],[f_128_1]) ).

fof(f_128_3,plain,
    ( ! [U_446] :
        ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_446))
        | ! [U_443] :
          ? [U_442] :
            ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_442),U_443))
            & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_442),U_446)) ) )
    & ! [U_445] :
        ( ? [U_441] :
          ! [U_440] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_440),U_441))
            | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_440),U_445)) )
        | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_445)) ) ),
    inference(miniscope,[status(thm)],[f_128_2]) ).

fof(f_128_4,plain,
    ( ! [U_446] :
        ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_446))
        | ! [U_443] :
          ? [U_442] :
            ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_442),U_443))
            & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_442),U_446)) ) )
    & ! [U_445] :
        ( ! [U_440] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_440),sK12(U_445)))
            | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_440),U_445)) )
        | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_445)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_441,sK12(U_445))],[f_128_3]) ).

fof(f_128_5,plain,
    ( ! [U_446] :
        ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_446))
        | ! [U_443] :
            ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sK13(U_446,U_443)),U_443))
            & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK13(U_446,U_443)),U_446)) ) )
    & ! [U_445] :
        ( ! [U_440] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_440),sK12(U_445)))
            | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_440),U_445)) )
        | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_445)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_442,sK13(U_446,U_443))],[f_128_4]) ).

cnf(f_128_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_440),sK12(U_445)))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_440),U_445))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_445)) ),
    inference(clausify,[status(thm)],[f_128_5]) ).

cnf(f_128_7,plain,
    ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK13(U_446,U_443)),U_446))
    | hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_446)) ),
    inference(clausify,[status(thm)],[f_128_5]) ).

cnf(f_128_8,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sK13(U_446,U_443)),U_443))
    | hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_446)) ),
    inference(clausify,[status(thm)],[f_128_5]) ).

fof(f_129_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_129_2,plain,
    ! [U_448,U_447] :
      ( preorder(fun(U_448,U_447))
      | ~ preorder(U_447) ),
    inference(variable_rename,[status(thm)],[f_129_1]) ).

cnf(f_129_3,plain,
    ( preorder(fun(U_448,U_447))
    | ~ preorder(U_447) ),
    inference(clausify,[status(thm)],[f_129_2]) ).

fof(f_130_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_130_2,plain,
    ! [U_450,U_449] :
      ( finite_finite_1(fun(U_450,U_449))
      | ~ finite_finite_1(U_450)
      | ~ finite_finite_1(U_449) ),
    inference(variable_rename,[status(thm)],[f_130_1]) ).

cnf(f_130_3,plain,
    ( finite_finite_1(fun(U_450,U_449))
    | ~ finite_finite_1(U_450)
    | ~ finite_finite_1(U_449) ),
    inference(clausify,[status(thm)],[f_130_2]) ).

fof(f_131_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_131_2,plain,
    ! [U_452,U_451] :
      ( order(fun(U_452,U_451))
      | ~ order(U_451) ),
    inference(variable_rename,[status(thm)],[f_131_1]) ).

cnf(f_131_3,plain,
    ( order(fun(U_452,U_451))
    | ~ order(U_451) ),
    inference(clausify,[status(thm)],[f_131_2]) ).

fof(f_132_1,plain,
    preorder(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Orderings_Opreorder]) ).

cnf(f_132_2,plain,
    preorder(nat),
    inference(clausify,[status(thm)],[f_132_1]) ).

fof(f_133_1,plain,
    order(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Orderings_Oorder]) ).

cnf(f_133_2,plain,
    order(nat),
    inference(clausify,[status(thm)],[f_133_1]) ).

fof(f_134_1,plain,
    preorder(bool),
    inference(fof_nnf,[status(thm)],[arity_HOL_Obool___Orderings_Opreorder]) ).

cnf(f_134_2,plain,
    preorder(bool),
    inference(clausify,[status(thm)],[f_134_1]) ).

fof(f_135_1,plain,
    finite_finite_1(bool),
    inference(fof_nnf,[status(thm)],[arity_HOL_Obool___Finite__Set_Ofinite]) ).

cnf(f_135_2,plain,
    finite_finite_1(bool),
    inference(clausify,[status(thm)],[f_135_1]) ).

fof(f_136_1,plain,
    order(bool),
    inference(fof_nnf,[status(thm)],[arity_HOL_Obool___Orderings_Oorder]) ).

cnf(f_136_2,plain,
    order(bool),
    inference(clausify,[status(thm)],[f_136_1]) ).

fof(f_137_1,plain,
    ! [T,A] : ti(T,ti(T,A)) = ti(T,A),
    inference(fof_nnf,[status(thm)],[help_ti_idem]) ).

fof(f_137_2,plain,
    ! [U_454,U_453] : ti(U_454,ti(U_454,U_453)) = ti(U_454,U_453),
    inference(variable_rename,[status(thm)],[f_137_1]) ).

cnf(f_137_3,plain,
    ti(U_454,ti(U_454,U_453)) = ti(U_454,U_453),
    inference(clausify,[status(thm)],[f_137_2]) ).

fof(f_138_1,plain,
    ! [P] :
      ( ~ hBOOL(P)
      | ~ hBOOL(hAPP(bool,bool,fNot,P)) ),
    inference(fof_nnf,[status(thm)],[help_fNot_1_1_U]) ).

fof(f_138_2,plain,
    ! [U_455] :
      ( ~ hBOOL(U_455)
      | ~ hBOOL(hAPP(bool,bool,fNot,U_455)) ),
    inference(variable_rename,[status(thm)],[f_138_1]) ).

cnf(f_138_3,plain,
    ( ~ hBOOL(U_455)
    | ~ hBOOL(hAPP(bool,bool,fNot,U_455)) ),
    inference(clausify,[status(thm)],[f_138_2]) ).

fof(f_139_1,plain,
    ! [P] :
      ( hBOOL(hAPP(bool,bool,fNot,P))
      | hBOOL(P) ),
    inference(fof_nnf,[status(thm)],[help_fNot_2_1_U]) ).

fof(f_139_2,plain,
    ! [U_456] :
      ( hBOOL(hAPP(bool,bool,fNot,U_456))
      | hBOOL(U_456) ),
    inference(variable_rename,[status(thm)],[f_139_1]) ).

cnf(f_139_3,plain,
    ( hBOOL(hAPP(bool,bool,fNot,U_456))
    | hBOOL(U_456) ),
    inference(clausify,[status(thm)],[f_139_2]) ).

fof(f_140_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_140_2,plain,
    ! [U_462,U_461,U_460,U_459,U_458,U_457] : hAPP(U_462,U_461,hAPP(fun(U_462,U_460),fun(U_462,U_461),hAPP(fun(U_460,U_461),fun(fun(U_462,U_460),fun(U_462,U_461)),combb(U_460,U_461,U_462),U_459),U_458),U_457) = hAPP(U_460,U_461,U_459,hAPP(U_462,U_460,U_458,U_457)),
    inference(variable_rename,[status(thm)],[f_140_1]) ).

cnf(f_140_3,plain,
    hAPP(U_462,U_461,hAPP(fun(U_462,U_460),fun(U_462,U_461),hAPP(fun(U_460,U_461),fun(fun(U_462,U_460),fun(U_462,U_461)),combb(U_460,U_461,U_462),U_459),U_458),U_457) = hAPP(U_460,U_461,U_459,hAPP(U_462,U_460,U_458,U_457)),
    inference(clausify,[status(thm)],[f_140_2]) ).

fof(f_141_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_141_2,plain,
    ! [U_468,U_467,U_466,U_465,U_464,U_463] : hAPP(U_468,U_467,hAPP(U_466,fun(U_468,U_467),hAPP(fun(U_468,fun(U_466,U_467)),fun(U_466,fun(U_468,U_467)),combc(U_468,U_466,U_467),U_465),U_464),U_463) = hAPP(U_466,U_467,hAPP(U_468,fun(U_466,U_467),U_465,U_463),U_464),
    inference(variable_rename,[status(thm)],[f_141_1]) ).

cnf(f_141_3,plain,
    hAPP(U_468,U_467,hAPP(U_466,fun(U_468,U_467),hAPP(fun(U_468,fun(U_466,U_467)),fun(U_466,fun(U_468,U_467)),combc(U_468,U_466,U_467),U_465),U_464),U_463) = hAPP(U_466,U_467,hAPP(U_468,fun(U_466,U_467),U_465,U_463),U_464),
    inference(clausify,[status(thm)],[f_141_2]) ).

fof(f_142_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_142_2,plain,
    ! [U_470,U_469] : hAPP(U_470,U_470,combi(U_470),U_469) = ti(U_470,U_469),
    inference(variable_rename,[status(thm)],[f_142_1]) ).

cnf(f_142_3,plain,
    hAPP(U_470,U_470,combi(U_470),U_469) = ti(U_470,U_469),
    inference(clausify,[status(thm)],[f_142_2]) ).

fof(f_143_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_143_2,plain,
    ! [U_476,U_475,U_474,U_473,U_472,U_471] : hAPP(U_476,U_475,hAPP(fun(U_476,U_474),fun(U_476,U_475),hAPP(fun(U_476,fun(U_474,U_475)),fun(fun(U_476,U_474),fun(U_476,U_475)),combs(U_476,U_474,U_475),U_473),U_472),U_471) = hAPP(U_474,U_475,hAPP(U_476,fun(U_474,U_475),U_473,U_471),hAPP(U_476,U_474,U_472,U_471)),
    inference(variable_rename,[status(thm)],[f_143_1]) ).

cnf(f_143_3,plain,
    hAPP(U_476,U_475,hAPP(fun(U_476,U_474),fun(U_476,U_475),hAPP(fun(U_476,fun(U_474,U_475)),fun(fun(U_476,U_474),fun(U_476,U_475)),combs(U_476,U_474,U_475),U_473),U_472),U_471) = hAPP(U_474,U_475,hAPP(U_476,fun(U_474,U_475),U_473,U_471),hAPP(U_476,U_474,U_472,U_471)),
    inference(clausify,[status(thm)],[f_143_2]) ).

fof(f_144_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_144_2,plain,
    ! [U_478,U_477] :
      ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,U_477),U_478))
      | ~ hBOOL(U_478)
      | ~ hBOOL(U_477) ),
    inference(variable_rename,[status(thm)],[f_144_1]) ).

fof(f_144_3,plain,
    ! [U_478] :
      ( ! [U_477] :
          ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,U_477),U_478))
          | ~ hBOOL(U_477) )
      | ~ hBOOL(U_478) ),
    inference(miniscope,[status(thm)],[f_144_2]) ).

cnf(f_144_4,plain,
    ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,U_477),U_478))
    | ~ hBOOL(U_477)
    | ~ hBOOL(U_478) ),
    inference(clausify,[status(thm)],[f_144_3]) ).

fof(f_145_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_145_2,plain,
    ! [U_480,U_479] :
      ( hBOOL(U_480)
      | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,U_480),U_479)) ),
    inference(variable_rename,[status(thm)],[f_145_1]) ).

fof(f_145_3,plain,
    ! [U_480] :
      ( ! [U_479] : ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,U_480),U_479))
      | hBOOL(U_480) ),
    inference(miniscope,[status(thm)],[f_145_2]) ).

cnf(f_145_4,plain,
    ( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,U_480),U_479))
    | hBOOL(U_480) ),
    inference(clausify,[status(thm)],[f_145_3]) ).

fof(f_146_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_146_2,plain,
    ! [U_482,U_481] :
      ( hBOOL(U_481)
      | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,U_482),U_481)) ),
    inference(variable_rename,[status(thm)],[f_146_1]) ).

cnf(f_146_3,plain,
    ( hBOOL(U_481)
    | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,U_482),U_481)) ),
    inference(clausify,[status(thm)],[f_146_2]) ).

fof(f_147_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_147_2,plain,
    ! [U_484,U_483] :
      ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,U_483),U_484))
      | ~ hBOOL(U_483) ),
    inference(variable_rename,[status(thm)],[f_147_1]) ).

cnf(f_147_3,plain,
    ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,U_483),U_484))
    | ~ hBOOL(U_483) ),
    inference(clausify,[status(thm)],[f_147_2]) ).

fof(f_148_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_148_2,plain,
    ! [U_486,U_485] :
      ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,U_486),U_485))
      | ~ hBOOL(U_485) ),
    inference(variable_rename,[status(thm)],[f_148_1]) ).

cnf(f_148_3,plain,
    ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,U_486),U_485))
    | ~ hBOOL(U_485) ),
    inference(clausify,[status(thm)],[f_148_2]) ).

fof(f_149_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_149_2,plain,
    ! [U_488,U_487] :
      ( hBOOL(U_487)
      | hBOOL(U_488)
      | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,U_488),U_487)) ),
    inference(variable_rename,[status(thm)],[f_149_1]) ).

fof(f_149_3,plain,
    ! [U_488] :
      ( ! [U_487] :
          ( hBOOL(U_487)
          | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,U_488),U_487)) )
      | hBOOL(U_488) ),
    inference(miniscope,[status(thm)],[f_149_2]) ).

cnf(f_149_4,plain,
    ( hBOOL(U_487)
    | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,U_488),U_487))
    | hBOOL(U_488) ),
    inference(clausify,[status(thm)],[f_149_3]) ).

fof(f_150_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_150_2,plain,
    ! [U_491,U_490,U_489] :
      ( ti(U_491,U_490) = ti(U_491,U_489)
      | ~ hBOOL(hAPP(U_491,bool,hAPP(U_491,fun(U_491,bool),fequal(U_491),U_490),U_489)) ),
    inference(variable_rename,[status(thm)],[f_150_1]) ).

cnf(f_150_3,plain,
    ( ti(U_491,U_490) = ti(U_491,U_489)
    | ~ hBOOL(hAPP(U_491,bool,hAPP(U_491,fun(U_491,bool),fequal(U_491),U_490),U_489)) ),
    inference(clausify,[status(thm)],[f_150_2]) ).

fof(f_151_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_151_2,plain,
    ! [U_494,U_493,U_492] :
      ( hBOOL(hAPP(U_494,bool,hAPP(U_494,fun(U_494,bool),fequal(U_494),U_493),U_492))
      | ti(U_494,U_493) != ti(U_494,U_492) ),
    inference(variable_rename,[status(thm)],[f_151_1]) ).

cnf(f_151_3,plain,
    ( hBOOL(hAPP(U_494,bool,hAPP(U_494,fun(U_494,bool),fequal(U_494),U_493),U_492))
    | ti(U_494,U_493) != ti(U_494,U_492) ),
    inference(clausify,[status(thm)],[f_151_2]) ).

fof(f_152_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_152_2,plain,
    ! [U_496,U_495] :
      ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,U_495),U_496))
      | hBOOL(U_495) ),
    inference(variable_rename,[status(thm)],[f_152_1]) ).

cnf(f_152_3,plain,
    ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,U_495),U_496))
    | hBOOL(U_495) ),
    inference(clausify,[status(thm)],[f_152_2]) ).

fof(f_153_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_153_2,plain,
    ! [U_498,U_497] :
      ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,U_498),U_497))
      | ~ hBOOL(U_497) ),
    inference(variable_rename,[status(thm)],[f_153_1]) ).

cnf(f_153_3,plain,
    ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,U_498),U_497))
    | ~ hBOOL(U_497) ),
    inference(clausify,[status(thm)],[f_153_2]) ).

fof(f_154_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_154_2,plain,
    ! [U_500,U_499] :
      ( hBOOL(U_499)
      | ~ hBOOL(U_500)
      | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,U_500),U_499)) ),
    inference(variable_rename,[status(thm)],[f_154_1]) ).

fof(f_154_3,plain,
    ! [U_500] :
      ( ! [U_499] :
          ( hBOOL(U_499)
          | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,U_500),U_499)) )
      | ~ hBOOL(U_500) ),
    inference(miniscope,[status(thm)],[f_154_2]) ).

cnf(f_154_4,plain,
    ( hBOOL(U_499)
    | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,U_500),U_499))
    | ~ hBOOL(U_500) ),
    inference(clausify,[status(thm)],[f_154_3]) ).

fof(f_155_1,plain,
    hBOOL(hAPP(fun(pname,bool),bool,finite_finite(pname),u)),
    inference(fof_nnf,[status(thm)],[conj_0]) ).

cnf(f_155_2,plain,
    hBOOL(hAPP(fun(pname,bool),bool,finite_finite(pname),u)),
    inference(clausify,[status(thm)],[f_155_1]) ).

fof(f_156_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]) ).

cnf(f_156_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(clausify,[status(thm)],[f_156_1]) ).

fof(f_157_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]) ).

cnf(f_157_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(clausify,[status(thm)],[f_157_1]) ).

fof(f_158_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]) ).

cnf(f_158_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(clausify,[status(thm)],[f_158_1]) ).

fof(f_159_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]) ).

cnf(f_159_2,plain,
    hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u)),
    inference(clausify,[status(thm)],[f_159_1]) ).

fof(f_160_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]) ).

cnf(f_160_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(clausify,[status(thm)],[f_160_1]) ).

fof(f_161_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_161_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_161_1]) ).

cnf(f_161_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_161_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,
    ( 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_10,axiom,
    ( finite_card(Eq_x_0) = finite_card(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_11,axiom,
    ( finite_finite(Eq_x_0) = finite_finite(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_12,axiom,
    ( minus_minus(Eq_x_0) = minus_minus(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_13,axiom,
    ( undefined(Eq_x_0) = undefined(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_14,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_15,axiom,
    ( collect(Eq_x_0) = collect(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_16,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_17,axiom,
    ( insert(Eq_x_0) = insert(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_18,axiom,
    ( fequal(Eq_x_0) = fequal(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_19,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_20,axiom,
    ( member(Eq_x_0) = member(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_21,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_22,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_23,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_24,axiom,
    ( sK4(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK4(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_25,axiom,
    ( sK5(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK5(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_26,axiom,
    ( sK6(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK6(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_27,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_28,axiom,
    ( sK8(Eq_x_0,Eq_x_1,Eq_x_2) = sK8(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_29,axiom,
    ( sK9(Eq_x_0,Eq_x_1,Eq_x_2) = sK9(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_30,axiom,
    ( sK10(Eq_x_0,Eq_x_1) = sK10(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_31,axiom,
    ( sK11(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK11(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_32,axiom,
    ( sK12(Eq_x_0) = sK12(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_33,axiom,
    ( sK13(Eq_x_0,Eq_x_1) = sK13(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_34,axiom,
    ( preorder(Eq_y_0)
    | ~ preorder(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_35,axiom,
    ( hBOOL(Eq_y_0)
    | ~ hBOOL(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_36,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_37,axiom,
    ( order(Eq_y_0)
    | ~ order(Eq_x_0)
    | 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+5 : 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
% 0.08/0.39  % Computer : n020.cluster.edu
% 0.08/0.39  % Model    : x86_64 x86_64
% 0.08/0.39  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.39  % Memory   : 8046.5625MB
% 0.08/0.39  % OS       : Linux 6.8.0-71-generic
% 0.08/0.39  % CPULimit : 300
% 0.08/0.39  % WCLimit  : 300
% 0.08/0.39  % DateTime : Sun Sep 20 05:42:33 UTC 2026
% 0.08/0.39  % CPUTime  : 
% 4.02/4.36  % SZS status Theorem for theBenchmark
% 4.02/4.36  % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------